Multiuser MIMO OFDM Based TDD TDMA for Next Generation Wireless Communication Systems

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Wireless Pers Commun (2010) 52:289324DOI 10.1007/s11277-008-9649-0

Multiuser MIMO OFDM Based TDD/TDMA for Next

Generation Wireless Communication Systems

Lu Zhaogan Rao Yuan Zhang Taiyi Wang Liejun

Published online: 2 December 2008 Springer Science+Business Media, LLC. 2008

Abstract Multiple-input multiple-output (MIMO) wireless technology in combination

with orthogonal frequency division multiplexing (MIMO OFDM) is an attractive air-inter-

face solution for next-generation wireless local area networks (WLANs), wireless metro-

politan area networks (WMANs), and fourth-generation mobile cellular wireless systems.

In this paper, one multiuser MIMO OFDM systems with TDD/TDMA was proposed for

next-generation wireless mobile communications, i.e., TDD/TDMA 4G, which can avoid

or alleviate the specific limitations of existing techniques designed for multiuser MIMOOFDM systems in broadband wireless mobile channel scenarios, i.e., bad performance and

extreme complexity of multiuser detectors for rank-deficient multiuser MIMO OFDM sys-

tems with CDMA as access modes, extreme challenges of spatial MIMO channel estimators

in rank-deficient MIMO OFDM systems, and exponential growth complexity of optimal

sub-carrier allocations for OFDMA-based MIMO OFDM systems. Furthermore, inspired

from the Steiner channel estimation method in multi-user CDMA uplink wireless channels,

we proposed a new design scheme of training sequence in time domain to conduct channel

estimation. Training sequences of different transmit antennas can be simply obtained by trun-

cating the circular extension of one basic training sequence, and the pilot matrix assembled

by these training sequences is one circular matrix with good reversibility. A novel eigenmode

transmission was also given in this paper, and data symbols encoded by spacetime codes

can be steered to these eigenmodes similar to MIMO wireless communication systems with

single-carrier transmission. At the same time an improved water-filling scheme was also

described for determining the optimal transmit powers for orthogonal eigenmodes. The clas-

sical water-filling strategy is firstly adopted to determine the optimal power allocation and

correspondent bit numbers for every eigenmode, followed by a residual power reallocation

L. Zhaogan (B) Z. Taiyi W. LiejunSchool of Electronic & Information Engineering, Xian Jiaotong University,

Xian, Peoples Republic of China

e-mail: [email protected]

R. Yuan

Software Engineering School, Xian Jiaotong University,

Xian, Peoples Republic of China

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290 L. Zhaogan et al.

to further determine the additional bit numbers carried by every eigenmode. Compared with

classical water-filling schemes, it canalso obtainlarger throughputs viaresidualpower alloca-

tion. At last, three typical implementation schemes of multiuser MIMO OFDM with TDMA,

CDMA and OFDMA, i.e., TDD/TDMA 4G, VSF-OFCDM and FuTURE B3G TDD, were

testedby numerical simulations.Results indicated that theproposed multiuserMIMO OFDMsystem schemes with TDD/TDMA, i.e., TDD/TDMA 4G, can achieve comparable system

performance and throughputs with low complexity and radio resource overhead to that of

DoCoMo MIMO VSF-OFCDM and FuTURE B3G TDD.

Keywords Multiple-input multiple-output Orthogonal frequency division multiplexing Multiuser diversity Link adaptation Channel estimation

1 Introduction

In recent years, orthogonal frequency-division multiplexing (OFDM) [1] has emerged as

a promising air-interface technique. In the context of wired environments, OFDM tech-

niques are also known as Discrete MultiTone (DMT) [2] transmissions and are employed

in the American National Standards Institutes (ANSI) Asymmetric Digital Subscriber Line

(ADSL) [3], High-bit-rate Digital Subscriber Line (HDSL) [4], and Very-high-speed Dig-

ital Subscriber Line (VDSL) [5] standards as well as in the European Telecommunication

Standard Institutes (ETSI) [6] VDSL applications. In wireless scenarios, OFDM has been

advocated by many European standards, such as Digital Audio Broadcasting (DAB) [7],

Digital Video Broadcasting for Terrestrial Television (DVB-T) [8], Digital Video Broad-casting for Handheld Terminals (DVB-H) [9], Wireless Local Area Networks (WLANs)

[10], and Broadband Radio Access Networks (BRANs) [11]. Furthermore, OFDM has been

ratified as a standard or has been considered as a candidate standard by a number of stan-

dardization groups of the Institute of Electrical and Electronics Engineers (IEEE), such

as IEEE 802.11a [12], IEEE 802.11g [13], IEEE 802.11n [14], IEEE 802.16 [15], and

so on.

The main merit of OFDM is the fact that the radio channel is divided into many narrow-

band, low-rate, frequency-nonselective sub-channelsor sub-carriers,so thatmultiple symbols

can be transmitted in parallel, while maintaining a high spectral efficiency. Each sub-carrier

may also deliver information for a different user, resulting in a simple multiple access schemeknown as orthogonal frequency division multiple access (OFDMA) [16]. This enables dif-

ferent media such as video, graphics, speech, text, or other data to be transmitted within

the same radio link, depending on the specific types of services and their quality-of-service

(QoS) requirements. Furthermore, in OFDM systems different modulation schemes can be

employed for different sub-carriers or even for different users. Besides its implementation-

al flexibility, the low complexity required in transmission and reception with the attainable

high performance, render OFDM a highly attractive candidate for high data-rate communi-

cations over time-varying frequency-selective radio channels. Incorporating channel coding

techniques into OFDM systems, which results in Coded OFDM (COFDM) [17], allows us

to maintain robustness against frequency-selective fading channels, where busty errors are

encountered at specific sub-carriers in the frequency domain (FD). Additionally, when using

a cyclic prefix [18], OFDM exhibits a high resilience against the ISI introduced by multi-

path propagation. Moreover, based on conventional code divisions, an orthogonal frequency

and code division multiplexing system (OFCDM) [19] could be used to combat the severe

multi-path interference. Two dimensional spreading with both time and frequency domain

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Multiuser MIMO OFDM Based TDD/TDMA 291

spreading is employed in the OFDCM system. The total spreading factor (N) is the prod-

uct of time domain spreading factor (Nt) and frequency domain spreading factor (NF), i.e.,

N = Nt NF. In order to work in different cell environments, orthogonal variable spreadingfactor (VSF) is adopted for two-dimensional spreading, and the resultant OFCDM system is

called VSF-OFCDM [20,21].However, high data-rate wireless communications have attracted significant interest and

constitute a substantial research challenge in the context of the emerging WLANs and

other indoor multimedia networks. Specifically, the employment of multiple antennas at

both the transmitter and the receiver, which is widely referred to as the MIMO technique

[22], constitutes a cost-effective approach to high-throughput wireless communications. As

a key building block of next-generation wireless communication systems, MIMOs are capa-

ble of supporting significantly higher data rates than the universal mobile telecommuni-

cations system (UMTS) and the high-speed downlink packet access (HSDPA)-based 3G

networks [23]. Briefly, compared to single-input single-output (SISO) systems, the capac-

ity of a wireless link increases linearly with the minimum of the number of transmitter or

the receiver antennas [22]. The data rate can be increased by spatial multiplexing with-

out consuming more frequency resources and without increasing the total transmit power.

Furthermore, dramatic reduction of the effects of fading due to the increased diversity

could also be done, though this is particularly beneficial when the different channels fade

independently.

In order to provide more larger data transmission in wireless doubly selective fading chan-

nel scenarios, the combination of MIMO and OFDM is an attractive air-interface solution for

next-generation WLANs, wireless metropolitan area networks (WMANs), and fourth-gen-

eration mobile cellular wireless systems. MIMO OFDM, which is claimed to be inventedby Airgo Networks [24], has formed the foundation of all candidate standards proposed

for IEEE 802.11n [14]. In recent years, this topic has attracted substantial research efforts,

addressing numerous aspects, such as system capacity [25], space/time/frequency coding

[26], peak-to-average power ratio (PAPR) control [27], channel estimation [28], receiver

design [29], etc. Recently, Paulraj etal. [30] and Stber etal. [31] provided compelling over-

views of MIMO OFDM communications. Furthermore, Nortel Networks has developed a

MIMO OFDM prototype [31] during late 2004, which demonstrates thesuperiority of MIMO

OFDM over todays networks in terms of the achievable data rate. So, up to now, several

fourth-generation mobile cellular wireless systems based MIMO and OFDM were given

by recent literatures [3241], such as VSF-OFCDM by Japan DoCoMo [3234] (DoCoMoMIMO VSF-OFCDM), TDD-MIMO-OFDM by China FuTURE project [3538] (FuTURE

B3G TDD), TDD-CDM-OFDM as the evolved version of TD-SCDMA by Datang Mobile

[3841], and so on.

Undoubtedly, MIMO OFDM has demonstrated a high potential for employment in future

high rate wireless communication systems [30]. However, the associated detection and chan-

nel estimation techniques found in the multiuser MIMO OFDM literature have various

limitations. In this paper, we firstly discussed specific limitations of existing techniques

designed for multiuser MIMO OFDM systems, and then multiuser MIMO OFDM systems

based TDD/TDMA for fourth-generation mobile wireless communications (TDD/TDMA4G) was given and compared to those systems with OFCDM and OFDMA as multiuser

access modes in terms of multiuser diversity, channel estimation overhead and complex-

ity. Then, we showed different numerical simulation results of proposed multiuser MIMO

OFDM systems based TDD/TDMA and other FuTURE B3G TDD and VSF-OFCDM

systems, respectively.

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2 Limitations of Existing Multiuser MIMO OFDM Systems

2.1 Multiuser Detection

Among the various multi-user detectors (MUDs), the classic linear least squares (LS) [1,42]and MMSE [1,29,42] MUDs exhibit a low complexity at the cost of a limited performance.

By contrast, the high-complexity optimum maximum-likelihood (ML) MUD [1,42] is capa-

ble of achieving the best performance owing to invoking an exhaustive search, which imposes

a computational complexity typically increasing exponentially with the number of simulta-

neous users supported by the MIMO OFDM system and, thus rendering its implementation

prohibitive in high-user-load scenarios.

In the literature, a range of suboptimal nonlinear MUDs have also been proposed, such

as for example the MUDs based on successive interference cancellation (SIC) [1,42] or par-

allel interference cancellation (PIC) [1,42] techniques. Explicitly, instead of detecting and

demodulating the users signals in a sequential manner, as the LS and MMSE MUDs do, the

PIC and SIC MUDs invoke an iterative processing technique that combines detection and

demodulation. More specifically, the output signal generated during the previous detection

iteration is demodulated and fed back to the input of the MUD for the next iterative detection

step. Similar techniques invoking decision-feedback have been applied also in the context of

classic channel equalization.

However, since the philosophy of both the PIC and SIC MUDs is based on the principle

of removing the effects of the interfering users during each detection stage, they are prone to

error propagation occurring during the consecutive detection stages due to the erroneously

detectedsignals of theprevious stages[1]. In order to mitigate theeffectsof error propagation,an attractive design alternative is to simultaneously detect all the users signals, rather than

invoking iterative interference cancellation schemes. Recently, another family of multiuser

detection schemes referred to as sphere decoders (SDs) [43,44] as well as their derivatives

such as the optimized hierarchy reduced search algorithm (OHRSA)-aided MUD [45], have

also been proposed for multiuser systems, which are capable of achieving ML performance

at a lower complexity. Other MUD techniques, for example those based on the minimum bit

error rate (MBER) MUD algorithms [46] have also been advocated.

As far as we are concerned, however, most of the above-mentioned techniques were pro-

posed for the systems, where the number of users N is less than or equal to the number

of receivers Q, referred to here as the under-loaded or fully loaded scenarios, respectively.Nonetheless, in practical applications it is possible that N exceeds Q, which is often referred

to as a rank-deficient scenario, where we have no control over the number of users roam-

ing in the base stations coverage area. In rank deficient systems the (Q N)-dimensionalMIMO channel matrix representing the (Q N) number of channel links becomes singularand, hence, noninvertible, thus rendering the degree of freedom of the detector insufficiently

high for detecting the signals of all the transmitters in its vicinity. This will catastrophically

degrade the performance of numerous known detection approaches, such as for example

the Vertical Bell Labs Layered SpaceTime architecture (V-BLAST) detector of [43], the

LS/MMSE algorithms of [1,42] and the QR Decomposition combined with the M-algorithm

(QRD-M) algorithm of[47].

2.2 Channel Estimation

In MIMO OFDM systems accurate channel estimation is required at the receiver for the sake

of invoking both coherent demodulation and interference cancellation. Compared to single-

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input single-output (SISO) systems, channel estimation in the MIMO scenario becomes more

challenging, since a significantly increasednumber of independent transmitter receiver chan-

nel links have to be estimated simultaneously for each sub-carrier. Moreover, the interfering

signals of the other transmitter antennas have to be suppressed.

In the literature, a number of blind channel estimation techniques have been proposed forMIMO OFDM systems [48], where an attempt is made to avoid the reduction of the effective

throughout by dispensing with the transmission of known FD channel sounding pilots. How-

ever, most of these approaches suffer from either slow convergence rates or performance

degradation, owing to the inherent limitations of blind search mechanisms. By contrast,

the techniques benefiting from explicit training with the aid of known reference/pilot signals

are typically capable of achieving a better performance at the cost of a reduced effective

system throughput. For example, Li etal. [49] proposed an approach of exploiting both trans-

mitter diversity and the delay profile characteristics of typical mobile channels, which was

further simplified and enhanced in [28,29,50], respectively. Other schemes employed MMSE

[50], constrained least-squares (CLS) [51], iterative LS [39], QRD-M [52] as well as second-

order statistics (SOS)-based subspace estimation [53] or techniques based on the received

signals time-of-arrival (TOA) [54], etc. Some researchers have focused their attention on

designingoptimum training patterns or structures [28]. Furthermore,various jointapproaches

combining channel estimation with data symbol detection at the receiver were also proposed

for CDMA [54], SISO OFDM [55] and MIMO OFDM [52] systems.

However, in the context of BLAST or SDMA type multiuser MIMO OFDM systems, all

channel estimation techniques found in the literature were developed under the assumption

of either the under-loaded [53] or the fully loaded [51,54] scenario mentioned above. Unsur-

prisingly, in rank-deficient MIMO OFDM systems the task of channel estimation becomesextremely challenging, since the associated significant degradation of the rank-deficient

MUDs performance will inevitably result in a further degraded performance of the asso-

ciated channel estimators, especially in decision-directed type receivers, which are quite

sensitive to error propagation [1].

2.3 Sub-carrier Allocations

In traditional OFDMA system, e.g., 802.16 [56], different users are assigned different fre-

quency basis vectors so that each users signals can be detected at different frequency bands

without interfering with one other. As a result, OFDMA enjoys the merit of easy decoding

at the user side. Such simplicity is particularly appealing during downlink operations where

the processing power at user terminals is often limited. For fixed or portable applications

where the radio channels are slowly varying, an intrinsic advantage of OFDMA over other

multiple access methods is its capability to exploit the so-called multiuser diversity embed-

ded in diverse frequency-selective channels [5759]. The promise of simply receivers and

high system performance has landed OFDMA as one of the prime multiple access schemes

for future generation broadband wireless networks, e.g., 802.16a-e.

In principle, OFDMA and MIMO can be synergistically integrated to offer the benefits

of both system simplicity and high performance. Such is indeed an active topic within theIEEE 802.16/20 standardization bodies. Despite these promises, a few fundamental questions

remain as whether or not OFDMA/MIMO is the right choice for multiuser communications.

For example, the optimality of OFDMA/MIMO in the multiuser multi-carrier system is yet to

be established. To achieve the capacity bound however, one must solve a multiuser sub-car-

rier allocation and the optimal power allocation jointly. The computational cost for finding

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the optimal solution is exponential with respect to the number sub-carriers and polynomial

with respect to the number of users. However, for the suboptimal sub-carrier allocation cri-

teria [60] for OFDMA MIMO systems, namely, the Product-criterion and the Sum-criterion,

the computation complexity of these suboptimal approaches are still grow linearly with the

number of users and the number of sub-carriers.

3 Overview of Multiuser MIMO OFDM with TDD/TDMA

Thetarget frequency band forTDD/TDMA4G is 25GHz dueto favorable propagation char-

acteristics and low radio frequency (RF) equipment cost. The broadband channel is typically

non-LOS channel and includes impairments such as time-selective fading and frequency-

selective fading. According to technical requirements of the broadband cellular channel and

constraints of practical of hardware and RF, the physical (PHY) design of TDD/TDMA 4G

systems is given in following.

3.1 System Parameters

The time interval of channel estimation and the sub-carrier separation for multiple-carrier

transmission are determined by coherence time and bandwidth of wireless channels, respec-

tively. So, coherence time and bandwidth of target channels for TDD/TDMA 4G systems, is

firstly determined in followings. As the proposed TDD/TDMA 4G systems can fit for target

cellular channel scenarios, we consider the typical multi-path fading propagation conditions

[61] as target scenarios, and use the ITU Vehicular Channel Models (channel B) [61] as targetcellular channels.

According to the tapped-delay-line parameters of the ITU Vehicular Channel (channel B),

which has maximum root mean square delay r ms = 4, 000ns, its coherence bandwidth (Bc)can be achieved by [62].

Bc = 15r ms

= 50 kHz (1)

For mobile stations (MS) with 500km/h, the channel coherence time (Tc) is calculated by its

corresponding Doppler frequency ( fd = 924.3Hz) [62], i.e.,

Tc =

9

16f2d= 1.07 ms (2)

As pointed out in literature [63], it is suitable to take one third of coherence bandwidth (Bc)

as sub-carrier frequency spacing, for the reasons of complexity of FFT for small frequency

spacing and poor performance for large frequency spacing. Firstly, guard time (TG ) is taken

as four times the root mean square delay of cellular channels, i.e., TG

=16us. Subsequently,

the length of OFDM symbols (Ts ) is taken as five times that of guard time, i.e., Ts = 80us.So, subcarrier spacing (f) is given as

f = 1Ts TG = 15.625 kHz (3)

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Ts1 Ts2 Ts3 Ts4 Ts5

675us

Guard Slot96chips

Ts6Ts01.28Mchips

DwPTS96chips

UpPTS160chips

Switching

Point

Uplink Slot

Sub-frame (5ms)

Data(352chips) Data(352chips)Mimable

144chips

GP

16chips

Downlink Slot

Fig. 1 Frame structure of TD-SCDMA with 7 data time slots, 2 synchronization slots and 1 switch slots for

up links and down links

Then, the 20MHz bandwidth can be divided into 1,280 sub-channels rather than the number

of 2 integer power. In order to efficiently implement FFT, carrier number (K) is assumed to

2,048, and the subcarrier spacing is finally given as

f = BK

= 9.765625 kHz (4)

where B denotes channel bandwidth (B = 20MHz).In practical OFDM systems, many sub-carriers are used as guard bands and DC carrier

to keep interference from other systems. If carrier spacing is taken as 9.765625kHz, many

sub-carriers could not be utilized completely. So, in order to increase spectrum efficiency,

carrier spacing should be larger that given in (4). Here, the carrier spacing for 802.16a wire-

less local networks [64], is taken as the carrier spacing of TDD/TDMA 4G systems, i.e.,

f = 11.16kHz, which is much smaller than the coherence bandwidth as showed in (3).The first 127 and last 128 sub-carriers are usedas lower frequency and higher frequency guard

bands respectively, and DC carrier is reserved. The residual 1,792 sub-carriers are used to

transport data symbols, completely, without pilot symbols inserted into fixed sub-carriers.

3.2 Frame Structure

In order to meet the requirement [65] of fast beam forming in high moving speed as 120km/h

when the smart antenna technology is deployed, the length of radio sub-frame is taken as

5ms similar to that of TD-SCDMA radio sub-frame as shown by Fig.1, other than 10ms inWCDMA/TDD systems.

As shown in Fig.2, a radio frame with duration of 5ms is subdivided into seven main

time slots (TS) of 675s duration each and four special time slots: down link synchroniza-

tion (DwPTS), switch slot from down links to up links (TTG slot), up link synchronization

(UpPTS), and switch slot from up links to down links (RTG slot). Time slot TS0 is always

used for downlinks, whereas the other time slots can be used for either up links or downlinks,

depending on flexible switching point configuration. The location information about TTG

Slot, UpPTS and switch points would be sent to mobile stations by information transported in

TS0. As the synchronization slot for down links, DwPTS can calibrate the synchronizationbetween BS and MS, estimate and compensate carrier frequency offset due to frequency

drift of carrier generators at transmitter and receivers. So does the UpPTS for up links. Due

to the requirement of synchronization accuracy of timing and carriers, their durations are

determined to 75us so that BS and MS can achieve the same synchronization performance.

For systems with TDD, switch slots between up links and down links should be greater than

the maximum round time of radio between transmitter and receivers, that is double of the

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Ts1 ........ TsN

675us TTG Slot (75us)

Ts1

DwPTS (75us) UpPTS (75us) RTG Slot (50us)

Uplink SlotDownlink Slot

Sub-frame (5ms)

TsM

Fig. 2 Frame structure of TDD/TDMA 4G systems with 7 data time slots, 2 synchronization slots and 2

switch slots for up links and down links

TS 0 TS 1 TS 2 TS 3 TS 4 TS 5 ... TS 7

Sync TS Short TS Long TS

Radio frame 5 ms

1 2 3 1 P 1 2 3 4 5 P

P

1 2 3 4 . P. .13

Sync Sync

Guard time 1106 s

Data

Switch pointPilot

P

Guard time 215 s

Fig. 3 Frame structure of FuTURE B3G TDD systems with 1 synchronization slot, 2 short data time slots,

5 long data time slots, and 1 switch point for uplinks and downlinks

Forward link

Reverse link

(a)

(b)

Fig. 4 Frame structure of two slots with duration 0.5ms for DoCoMo 4G VSF-OFCDM forward links and

MC-CDMA reverse links, where time and frequency domain spreading are used to improve system diversity

gains

maximum radio delay profiles [64]. According to the profiles of the ITU Vehicular Channel(channel B), after refering to frame structure in 802.16a TDD [64] and inital frame stru-

acture in TD-SCDMA [66], the durations for TTG and RTG is 75 and 50us, respectively,

under the limation of the 5ms radio sub-frame length. Furthermore, we also give the radio

frame structures of FuTRUE B3G TDD and DoCoMo 4G schemes, as shown by Figs. 3, 4,

respectively.

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Fig. 5 Burst structure of

TDD/TDMA 4G systems, where

Midamble is training sequence

for channel estimation in time

domain and the estimated

channel information is used to

decoding data symbols before

and after Midamble

S1 S2 Midamble S3 S4

125us 175us

Slot (675us)

256 256 128

1536

Fig. 6 Structureof synchronization slot for TDD/TDMA 4G systems, where timing synchronizationand fine-

coarse carrier frequency synchronization can be done by identical training sequences distributed in different

intervals

3.3 Burst Structure

The burst structure of the data time slots consists of four data blocks and one training signal

for channel estimation in time domain, as showed in Fig. 5. Actually, one data block is one

MIMO OFDM symbol, whose duration is 125us, while midamble is the training symbols for

channel estimations in time domain and the estimated channel information is used to decode

data symbols before and after midamble codes. The sample rate of IFFT/FFT for data blocks

is 20.48MHz.

3.4 Synchronization Slots

In proposed TDD/TDMA 4G systems, links between BS and MS are actually equivalent to

point to point links, so synchronization slots for up links and down links have the same slot

structures and consist of 1,536 samples. According to the strategies [67,68] for timing syn-

chronization and carrier frequency offset estimation, a novel synchronization slot is designed

to conduct timing synchronization and the fine and coarse carrier frequency offset estimation

through identical training sequences distributed in different intervals, as displayed in Fig. 6.Firstly, two identical training sequences S1 transmitted in seriesby transmitters areused to

obtain coarse timing synchronization by calculating the delay correlation function of training

sequences. Subsequently, fine timingsynchronization is done through two training sequences

S3. Furthermore, the conjoint two S3 have small time delay with large frequency offset esti-

mation range, and can be also used to conduct coarse frequency offset estimation. Then,

different delay S2 and S3 have large delay with small frequency offset estimation range and

are used to perform fine frequency offset estimation by averaging their estimated frequency

offsets.

4 Transceiver Architecture

Considering a TDD/TDMA4Gsystems with two and eight antennas atMS and BS, its system

architecture is designed as showed in Fig. 7, where the simplified block diagrams of MS and

BS are given in Fig. 7a, b, respectively. Furthermore, adaptive modulation and codes (AMC),

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Fig. 7 System Architecture of TDD/TDMA 4G System with 4 8 antennas at MS and BS, respectively, andadaptive modulation and codes (AMC), adaptive power control (APC) and adaptive space time codes (ASTC)

are used to conduct link adaptation with eigenmodes

adaptive power control (APC) and adaptive space time codes (ASTC) are used to conductlink adaptation with eigenmodes detailed in Sect. 7.1. Compared with DoCoMo 4G [3234]

and FuTURE B3G TDD [3538], the proposed TDD/TDMA 4G systems have smaller car-

rier bandwidth and simple implementation, and can fit for larger cell area with fast fading

channel scenarios. Whats more, the configuration with 2 8 antennas at MS and BS couldalso make TDD/TDMA 4G system serve as an evolution version of TDS-CDMA 3G system

[3941], proposed by Datang Mobile. Their system configuration could be found in Table 1.

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Table 1 System configuration of TDD/TDMA 4G, DoCoMo 4G and FuTURE B3G TDD

TDD/TDMA 4G DoCoMo 4G FuTURE B3G TDD

VFS-OFDM MC/DS-CDMA (Uplink)

(Downlink)

FFT/IFFT sample

rate

20.48 Msps 135 Msps 24.15 Msps

Carrier frequency 2GHz 4.635 GHz 4.9GHz 3.5 GHz

Chip rate 16.384 Mcps

FFT size 2,048 1,024 1,024

Carrier spacing 11.16 kHz 131.836 kHz 20 MHz 19.5 kHz

Number of low

frequency guard

sub-carrier

127 127 69

Number of highfrequency guard

sub-carrier

128 128 70

Number of pilot

sub-carrier

0 0 52

Number of data

sub-carrier

1,792 768 2 832

Cyclic prefix

duration (s)

25 1.674 10.6

Symbol duration

(s)

125 9.259 53

Length of radio

frame (ms)

5 0.481 (48 Data+ 4

Pilot symbols)

0.5 5

Bandwidth 20MHz 100 MHz 40 MHz 20 MHz

Antenna

configuration

2 8 2 4 2 4 2 8

Number of

sub-carrier

2,048 1,024 2 1,024

Wireless access TDMA CDMA CDMA TDMA/OFDMA

Duplex TDD FDD TDD

5 System Model

Let us consider the MIMO OFDM system with Mt transmit and Mr receive antennas, and

an OFDM modulation is conducted on K sub-carriers, as illustrated in Fig. 8. Firstly, one

universal spacetime code can be defined as a rate T/K Mt K design scheme over onecomplex subfield A of complex field, whose codeword matrix X is one Mt K matrix withentries obtained from the K-linear combinations of T data symbols and their conjugates.

If one codeword matrix X is represented as a column vector by stacking its columns, the col-

umn vector can be delineated as the linear transform ofT data symbols and their conjugates,

i.e.,

vec (X) = s (5)

where vec () denotes the column vector by stacking the columns of a matrix into one columnvector, s is a column vector whose elements consist ofT data symbols and their conjugates,

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Space-Time Coder

S/P

S/P

S/P

Insert Pilots

Insert Pilots

Insert Pilots

IFFT

IFFT

IFFT

CP

CP

CP

P/S

P/S

P/S

1x

2x

tM

x

s

Transmitter

S/P

S/P

S/P

R CP

S/P R CP

R CP

IFFT

IFFT

IFFT

Space-Time Decoder

CFO & ChannelEstimation

s1y

2y

rMy

Receiver

(a)

(b)

Fig. 8 Discrete-time equivalent base-band model of MIMO OFDM block transmission systems

and the transform matrix is denoted as the generation matrixof the spacetime code design

scheme.

A space time code is used to encode a data symbol vector s along spacetime directions

with T data symbols and their conjugates, while a least squared spacetime decoder is used to

restore the transmitted data symbols by decoding the received spacetime signals. In order to

delineate the system model compactly, we omit the time indicator of MIMO OFDM symbols

and neglect symbol timing errors and frequency offsets. Assume a MIMO OFDM only can

carry one spacetime codeword, so the receive signals in a MIMO OFDM symbol period

can be given as

y (n, k) =Mt1m=0

H[n,m] (k)x(m, k) + w (n, k) , n = 1, . . . , Mr, k = 1, . . . , T (6)

where y (n, k) is the received data at the k-th carrier of the n-th receive antenna, H[n,m] (k)represents the fading coefficient at the k-th carrier of the spatial channel between the n-th

receive antenna and the m-th transmit antenna, x(m, k) denotes the element at m-th row and

k-th column of a spacetime codeword matrix X, andw (n, k) is the channel noise at the k-th

carrier for the n-th receive antenna.

Substituting the sum term in (6) by its matrix form, we rewrite (6) as

y (n, k) = H [:, n] (k) x (:, k) + w (n, k) (7)

where x (

:, k) is the k-th column of spacetime codewordX, H [

:, n] (k) is the n-th column of

the MIMO channel fading coefficient matrix H (k) at k-th carriers, which can be delineated as

H (k) =

H[1, 1] (k) H[1, 2] (k) H[1, Mt] (k)H[2, 1] (k) H[2, 2] (k) H[2, Mt] (k)

......

...

H[Mr, 1] (k) H[Mr, 2] (k) H[Mr, Mt] (k)

(8)

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Let y (n, :) denote the received signal vector at the n-th receive antenna in one MIMO OFDMsymbol period, we can rewrite (7) into matrix form as followings.

y (:, n)T = H [:, n] (1)

H [

:, n] (2)

. . .

H [:, n] (T)

H(:,n)

x (:, 1)x (

:, 2)...

x (:, T)

x

+ [w (:, n)] T (9)

where w (n, :) is the channel white noise corresponding to y (n, :), and x = vec (X). Thus,in one MIMO OFDM symbol period, assembling the received signals from all the receive

antennas into matrix form, we can get

vec yT = Hs + vec wT (10)

where y = [y(1, :)T, y(2, :)T,,y(Mr,:)T], w = [w(1, :)T, w(2, :)T,, w(Mr, :)T], H =H (:, 1)T , H (:, 2)T , . . . H (:, Mr)T

T.

According to (10), the least squared estimation ofs can be achieved as following

s =

H1

vec

yT

+ w (11)

where w =

H

1

vec

wT

. Then, sinces consistsofT data symbols andtheir conjugates,

the transmitted data can be derived from s, completely. Moreover, for the scenario where oneMIMO OFDM symbol can carry multiple spacetime code words, the similar results can

also be derived in the same way.

However, Assuming that perfect channel state information is available at the receiver, the

maximum likelihood decoding rule for space time code words is given by

X = arg minX

Mrn=1

Kk=1

y (n, k) M1m=0

H[n,m] (k)x(m, k)

2

(12)

where the minimization is performed over all possible spacetime code words and x(m, k)

denotes the element of X at m-th row and k-th column.

6 Stainer Channel Estimation

In fact, spatial channels for every receive antenna in MIMO links can be considered as

multiple-input single-out (MISO) channels, i.e., equivalents of links in multi-user CDMA

uplinks. So, in order to achieve good channel estimation in rank-deficient MIMO OFDM sys-

tems, we generalize the Steiner channel estimation in uplink CDMA wireless links [69,70]

to estimate MIMO OFDM spatial channels.

6.1 Training Sequences

As showed in Sect. 3, the midamble symbols are used to conduct channel estimation and track

channel fluctuation information, and both data symbols before and after midamble can be

checked out according the estimated channel states by midamble. Compared with FuTURE

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( )1m

L K W+

W

WW

mL

Fig. 9 Construction of midamble by truncating the circular extended version of a basic sequence, where Lmand W denote the length of training sequence and spatial channel impulse respondence, respectively

B3G TDD systems [3538], channel estimation overhead is reduced greatly with simple

implementation. The midamble code with duration about 175us consists of 3,585 samples,

and is obtained by truncating the circular extended version as showed in Fig. 9.

Denote L m as length of training sequence, W as length of spatial channel impulse respon-

dence, and L = W Mt as length of a basic sequence, which can be delineated asm = (m1,m2, . . . ,mL) (13)

Its circular extension version is given by

m = m1, m2, . . . , mLm+(Mt1)W (14)where the first L elements are consistent with corresponding elements of the basic sequence

and other elements are determined by

mi = miL , i = (L + 1) , . . . , [Lm + (Mt 1) W] (15)Then, training sequences for different transmit antennas are obtained by truncating the cir-

cular extended version. Furthermore, the pilot for the u-th transmit antenna is presented as

m(u) =

m(u)1 ,m

(u)2 , . . . ,m

(u)Lm

(16)

where

m

(u)

i = mi+(Mt1)W, i = 1, . . . , Lm, u = 1, . . . , Mt (17)If the design parameters showed above can be denoted as a quaternion (L m , L , Mt, W), there

exists the following relationship among these parameters, i.e.,

W =

L m

Mt + 1, L = W Mt (18)

where operator . denotes the largest integer not more than a given real number in theoperator.

However, the trainingsequences givenby (16) aregenerally described asbinary sequences,

and should be converted into complex number. Firstly, they are re-presented as bi-polarsequences and then further converted into complex numbers. Denote m(u) as one bi-polarsequence, m

(u)c as its correspondent complex form, which can be determined by

m(u)c (i) = (j)i m(u)(i), i = 1, . . . , L (19)where j is unit of imaginary number.

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It is the elaborately designed training symbols as showed above, that result in the circular

pilot matrix. So, the pilot sequence pilot design scheme can avoid matrix inversion calcula-

tion with good robustness to rank-deficient MIMO OFDM systems, and the complexity of

MIMO channel estimation can be further reduced.

6.2 Estimation Algorithm

For the considering MIMO OFDM systems, one receive antenna must estimate all the spatial

channels between the receive antenna and all the transmit antennas, simultaneously. Then, the

channel information estimated by all receive antennas will be assembled together to coher-

ently decode data symbols carried by one MIMO OFDM symbol. Therefore, the following

algorithm will be described for one receive antenna, the same counterparts can be easily

applied to all the receive antennas.

Provided that all spatial channels for MIMO radio links have the same delay profiles, thechannel impulse response (CIR) between the u-th transmit antenna and the receive antenna,

is described as

h(u) =

h(u)1 , h

(u)2 , . . . , h

(u)W

T, u = 1, 2, . . . , Mt (20)

Furthermore, training sequence transmitted by the u-th transmit antenna is given by

m(u) =

m(u)1 ,m

(u)2 , . . . ,m

(u)L+W1

T(21)

which is obtained by truncating the first L+

W

1 elements from designed training sequence

as showed above. After spatial channel filtering, its received version is given by

e(u) = G(u)h(u) + w(u), u = 1, 2, . . . , Mt (22)where e(u) and w(u) denote received training symbols andcorrespondent noise vector, respec-

tively, and G(u)is the pilot symbol matrix assembled by training sequence from the u-th

transmit antenna, which can be delineated as

G(u) =

m(u)1

m(u)2 m

(u)1

... ... . . .

m(u)W m

(u)W1 m(u)1

... m(u)W m

(u)2

......

...

m(u)W+L1 m

(u)W+L2 m(u)L

m(u)W+L1

...

. ..

..

.m(u)W+L1

(23)

According to linear convolution theory [71], the received training symbols are the polluted

version of training symbols transmitted by the u-th transmit antenna. Hence, their first W1elements and last W1 elements will be discarded away as theyare interferedby the transmitsignals before and after pilot sequence, respectively. So, the usable received data is given by

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e(u) =

e(u)W , e

(u)W , . . . , e

(u)W+L1

T(24)

At the same time, let w(u) =w(u)W , w

(u)W+1, . . . , w

(u)W+L1

T

, we could obtain following

relationship based on formula (22)e(u) = G(u)h(u) + w(u) (25)

where G(u) isonesub-matrix consistingof all therowsbetween the W-throwand(W+L1)-th row of pilot matrix G(u), i.e.,

G(u) =

m(u)W m

(u)W1 m(u)1

... m(u)W m

(u)2

......

...

m(u)W+L1 m(u)W+L2 m(u)L

(26)

In fact, the received data at one receive antennas is the superimposed data from all transmit

antennas, which can be described as

e =Mtu=1

e(u) (27)

which could be further expressed in matrix form according to (25), i.e.,

e=

Gh+

w (28)

Simultaneously, other terms in (28) expression are given by

G =

G(Mt), G(Mt1), . . . , G(1)

; w =Mtu=1

w(u); h =

h(Mt)T,h(Mt1)T, . . . ,h(1)TT(29)

Assume the noise vector in (28) is a wide-sense stationary (WSS) complex Gaussian vector

with zero means and covariance matrix given by RL = 2I, where 2 is noise variance andI is L-order unit matrix. Then, according to (28), the spatial channels between all transmit

antennas and the receive antenna, could be estimated by

h =

GHG1

GHe (30)

IfG is invertible, the above expression is further rewritten as

h = h + G1w (31)Moreover, according to (26) and (29), G is actually a L-order circular matrix, which could

be diagonalized by an unitary DFT matrix [71], i.e.,

G = FFH (32)where F is a L-order DFT matrix, is a L-order diagonal matrix whose elements are given

by the DFT of the basic training sequence. Subsequently, substitute (32) into (30), then we

will get

h = F1FHe (33)

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T1.1

T2.2

TMt,Mt

null null

nullnull

null null

Tx1

Tx2

TxMt

Mt OFDM symbol duration

Staggered preamble

T1.1

T2.2

TMt,Mt

Tx1

Tx2

TxMt

Mt OFDM symbol duration

Overlapped preamble

T1.2 T1.Mt

T2.1 T2.Mt

TMt,1 TMt.2

(a) (b)

Fig. 10 Two typical pilot patterns for channel estimation in MIMO OFDM systems, where pilot sequences

transmitted by every transmit antenna are designed to be orthogonal to each other and carried by Mt OFDM

symbols as used in common MIMO OFDM channel estimation approaches

where operator F() and FH() could be explained as performing DFT and inverse discreteFourier transformation (IDFT) to one vector, respectively. So, we can be rewritten (33) intoan alternative form as

h = dftdft(e) ./idft(m) (34)where operator dft() and idft() denote to perform DFT and IDFT on a vector, respectively,while ()./() denotes array right division operator in element-wise. Note that m is the reverseversion of basic sequence m, the result spatial channel are also estimated in the reverse order.

Here, we use the appropriator intervals as bandwidth overhead of channel estimation,which are quantified into sample periods in corresponding MIMO OFDM system configu-

rations, and the number of multiplication as metric of complexity for channel estimation.

The bandwidth overhead and complexity for different channel estimation approaches are

analyzed and compared with each other in the followings.

For the frequency approaches [72,73], pilot sequences transmitted by every transmit

antenna are designed to be orthogonal to each other and carried by Mt OFDM symbols

at least, and the corresponding pilot patterns can be showed in Fig. 10. Following these

schemes, Mt times K-IFFT for OFDM modulation, Mt times K-FFT for OFDM demodula-

tion and Mt

K times division are needed to estimate all the spatial channels between all the

transmit antennas and the receive antenna. However, MtL samples must be observed at onereceive antenna to estimate the Mt spatial channel impulse responses in the time approaches

[74,75]. The training sequences transmitted at different antennas only occupy Mt L sam-ples. Firstly, one Mt L matrix inversion is involved to estimate all the CIRs of Mt spatialchannels, and then these spatial CIRs must be further converted into frequency domain via

Mt times K-FFT transforms to obtain corresponding fading coefficients at different carriers.

As a result, Mt times K-FFT and a Mt L dimension matrix inversion calculation are usedto obtain these MIMO OFDM channel coefficients. Without matrix inversion, it will take a

Mt L point IFFT, two Mt L point FFT and Mt times K-FFT for the Steiner scheme toobtain all MIMO OFDM sub-channel coefficients with the same bandwidth overhead as thetime approaches.

Their bandwidth overheadandcomplexityaredelineated in Table2, where the generalized

Steiner approach is indicated to have smaller bandwidth overhead andcomplexity when com-

pared with frequency and time approaches, respectively. Thus, the scheme can make good

tradeoff between classical frequency approaches and classical time approaches with respect

to complexity and bandwidth overhead.

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Table 2 Bandwidth overhead and complexity for Steiner scheme, classical frequency and time approaches,

respectively

Scheme candidate Bandwidth overhead Complexity

(sample period) (multiplication operations)

Frequency scheme 5MtK/4 2MtK(log2K + 1)Time scheme MtL MtKlog2K+ (MtL)2.37Steiner scheme MtL 3MtLlog2L + MtKlog2K

7 Link Adaptation

Whenchannelparametersare knownat thetransmitter, thecapacityof MIMO OFDMsystems

can be further increasedby adaptivelyassigning transmitted power to orthogonal eigenmodesaccording to the water-filling rule [76]. At transmitters, the transmitted signals of differ-

ent carriers are usually eigen beam formed independently to orthogonal modes of spatial

channels at every sub-channel in MIMO OFDM systems [7779], which can be formed via

spatial filtering according to the singular value decomposition (SVD) of channel matrix at

transmitters. However, these eigenmodes can not be used to steer the data symbols encoded

by spacetime codes, as one spacetime codeword is transferred simultaneously by multiple

carriers, while the eigenmodes are obtained at every carriers. So, when coupled with adap-

tive power and bit allocation, these eigenmodes have many disadvantages relative to their

counterparts of MIMO systems in single-carrier transmission.

(a) These eigenmodes ignore the effects of spacetime diversity gains on the equivalent

signal noise ratios of data symbols encoded by one spacetime coder.

(b) For the MIMO OFDM system configured with low rate spacetime codes, it will be

difficult to conduct adaptive power allocation as a large number of eigenmodes exist,

compared with data symbols carried by one MIMO OFDM symbol.

(c) It is also difficult to determine the modulation order of data symbols encoded in one

spacetime codeword, as one spacetime codeword is carried by many eigenmodes at

multiple carriers.

Therefore, these eigenmodes can be viewed as the simple generalization of their counterpartsof MIMO systems in single-carrier transmission for conveniently analyzing system capacity,

but not reflect the fact of one spacetime codeword being carried by multiple sub-channels.

Here, we present a new approach to construct orthogonal eigenmodes in MIMO OFDM

systems. For theMIMO OFDM systems with least-squared decoders,orthogonal eigenmodes

can be obtained by the SVD of equivalent channel matrix in system models, where one gen-

eral spacetime code is considered in general way. The result eigenmodes are correspondent

to data symbols encoded in spacetime code words carried by one MIMO OFDM symbol.

Thus, the novel eigenmodes can be used directly to steer adaptive power allocation to data

symbols and their bit allocations, as usually do in the MIMO systems with single-carrier

transmission.

7.1 Eigenmodes with Spacetime Codes

By the singular value decomposition of equivalent channel matrixes, the eigenmodes in (10)

can be disclosed in the same way as their counterparts in single-carrier MIMO systems [80].

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Let H = H, it can be decomposed into orthogonal eigenmodes by singular value decom-position as showed

H = UDVH (35)

where Uand Vdenote the unitary matrices representing the left and right eigenvectors ofH,

respectively, and D is a diagonal matrix, whose elements are the ordered singular values of

H, i.e., the corresponding fading coefficients of those orthogonal eigenmodes.

Then, substituting H by its SVD, we can get

UHvec

yT

= DVHs + UHvec

wT

(36)

Now, let y = UHvecyT

,s = VHs, w = UHvec

wT

, and (36) can be rewritten as

y = Ds + w (37)Furthermore, it is also equivalent to

yi =i s

i +wi (i = 1, 2, . . . , r)

yi = wi (i = r + 1, r + 2, . . . ,min(Mt, Mr))(38)

where r andi are the rank ofH and its i-th singular value, respectively.

As the equivalent channel matrix H includes the generation matrix of spacetime codes,

the eigenmodes obtained by (37) can also reflect the corresponding spacetime diversity

gains of spacetime codes. Furthermore, these eigenmodes have unique corresponding rela-tions with the data symbols, transported by one MIMO OFDM symbol. Thus, according to

these eigenmodes and power allocation schemes, it is very easy to determine the modulation

orders of these data symbols and their transmit power. So, when compared with the classical

eigenmodes for different carriers as showed in reference [7779], adaptive spatial processing

could be performed conveniently with these novel eigenmodes.

Furthermore, as the relations between the equivalent channel matrix and the generation

matrix of one spacetime code, system capacity is significantly effected on by the code

rate of spacetime codes. For one spacetime code scheme with one unitary generation

matrix, the spacetime diversity does not change the corresponding system capacities with-

out spacetime codes. That is, the number of data symbols in the novel eigenmodes should

be identical to that in classical eigenmodes. So, there exists M = 2 T/K for spacetimecodes that could keep system capacity unchanged, and only Alamouti spacetime code exists

for a transmitter with two antennas, when T/K is not more than one. For other spacetime

codes, system capacity will increase in inverse proportion to spacetime code rates, i.e., the

larger the transmission rate, the more the system capacity. In Sect.5, this will be disclosed

by numerical simulation results.

Generally speaking, the classical eigenmodes at different carriers for MIMO OFDM sys-

tems can be viewed as one simple extension of the eigenmodes in MIMO systems in single-

carrier transmission, which fit for the analysis of system capacity other than link adaptationtechniques. However, besides system capacity analysis, the novel Eigenmode transmission

can couple spacetime codes and link adaptation techniques, perfectly. Furthermore, the

number of novel eigenmodes is only limited to the number of the transmitted data symbols

carried by one MIMO OFDM symbol, while M M eigenmodes have to be disclosed toconduct power allocation to data symbols transported in these eigenmodes.

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7.2 Improved Water-Filling Power Allocation

Based on adaptive modulation margin adaptive (MA) principals [80], link adaptation tech-

niques can be implemented from two aspects, i.e., adaptive power allocation under total

transmit power constraint for maximal transported bits, and adaptive bits allocation undertotal transmit bits for minimal transmit power, respectively. Under the constraints of given

total power and targetbit error ratio (BER),we only consider how toconduct power allocation

to orthogonal eigenmodes to maximize transmit bits.

In order to maximize the transported total bits, an improved water-filling power allocation

scheme is given on the base of classical water-filling schemes. According to the scheme,

the adaptive power and bit allocation are conducted in two steps. Firstly, an initial power

allocation is given by classical water-filling scheme, i.e., the first step is executed to initially

allocate the power for different orthogonal eigenmodes according to the classical water-fill-

ing scheme. Then, after determining the transported bits at channel eigenmodes, the residual

power is reallocated among these eigenmodes to transport additional bits.

For given target BER (Pe), the transmit power for an additive white Gaussian noise

(AWGN) channel to transmit c bits information with M-QAM modulation, is given by [81]

P (c) = 2

3

Q1

Pe

4

2 2c 1 (39)

where Q (x) = 12

x et2/2dt is denoted as complementary error function. Then, for given

transmit power, the number of bits transported by the AWGN channel, can be derived accord-

ing to (39), as showed in the following formula

c = floor

log2

1 + 3P

2

Q1

Pe

4

2(40)

where floor denotes the operator to round towards minus infinity.

Now, we present the details of the improved water-filling scheme, which is conducted in

tow steps as showed in followings.

7.2.1 Initial Power Allocation Based Water-filling Scheme

For the eigenmodes given by (38), the power allocation scheme can be described as an opti-

mal problem to maximize the system capacity under the constraint of given total transmit

power, i.e.,

Cmax = maxPi (i=1,...,r)

ri=1

log2

1 + Pii

2

st.

ri=1

Pi = K P (41)

where C denotes system capacity, while P is the given total transmit power. According to

water-filling power allocation algorithm, the optimal power allocation can be given by

Pi = max

0, 2

i

(i = 1, 2, . . . , r) (42)

where = 1r

K P +ri=1 2i , and 2 is noise variance of orthogonal eigenmodes,

assumed to have the same variance.

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The power allocated to orthogonal eigenmodes as showed in (42), is called water-filling

powerto distinguish different power allocation results in the following. With the water-filling

powerallocated the i -th eigenmode, its maximal bits carried can be given by (11), that is

ci = floorlog2 1 + 3Pi2

Q1 Pe42 , (i = 1, 2, . . . , r) (43)

However, according to (39), the necessary power to transmit ci bits is determined by

Pi = 2

3

Q1

Pe

4

2 2ci 1, (i = 1, 2, . . . , r) (44)

which is called the expectation power to transmit ci bits. Clearly, the water-filling power

for the i-th eigenmode is larger than its expectation power, and their difference is named as

residual power, which will be further reallocated among these eigenmodes.

7.2.2 Reallocation of Residual Power

Subsequently, on the basis of the power allocation results in the first period, we calculate the

additional power to transmit an additional bit at the i-th eigenmode. i.e.,

Pi = [P (ci + 1) P (ci )]/2i , (i = 1, 2, . . . , r) (45)which is called additional power. Then, an accumulative sum sequence is obtained by a

sorted version ofadditional power in ascending order at all the eigenmodes. The elements

in the accumulative sum sequence, not more than the total residual power, can be found

out, and the eigenmodes corresponding with these elements can transport an additional bit.

So, the additional powers of these eigenmodes are allocated to these eigenmodes from the

total residual power, whose residual power after reallocation, i.e., total overplus power, is

averagely allocated to all the eigenmodes. At last, the bit number of these eigenmodes should

be increased by one, respectively.

8 Performance Analysis

Let us consider the maximum likelihood decoding as shown in (12). Assuming that ideal CSI

is available at the receiver, for a given realization of the fading channel H, the pairwise error

probability of transmitting X and deciding in favor of another codeword X at the decoder

conditioned on H is given by

P

X, X |H

expd2H

X, X

Es4N0

(46)

where Es is the average symbol energy, N0 is the noise power spectral density. Let

hj =

hj,1T

,hj,1

T, . . . ,

hj,1

T1L Mt

, Wk = kIL Mt, ek =

x1k x

1k

x2k x2k...

xMtk xMtk

Mt1

and d2H(X, X) is given by

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d2H

X, X

=

Mrj=1

hj DH (X,X) hHj (47)

Here, d2

HX, X is an L Mt L Mt matrix given byDH

X, X

=

Kk=1

Wkek (Wkek)H (48)

It is clear that matrix DH

X, X

is a variable depending on the codeword difference and

the channel delay profile. Let us denote the rank ofDH

X, X

by rh . Since DH

X, X

is

nonnegative definite Hermitian, the eigen-values of the matrix can be ordered as

1 2 rh 0Therefore, we can obtain the pairwise error probability over a frequency-selective fading

channel by averaging (46) with respect to the channel coefficients. It is upper bounded by

P

X, X

1 rh

j=1

1 + j 1

4N0

Mr rh

j=1j

MR Es

4N0

rhMr(49)

Note that this performance upper-bound is similar to the upper-bound on slow Rayleigh fad-

ing channels. The systems on frequency-selective fading channels can achieve a diversity

gain ofrhMr and a coding gain ofrh

j=1 j1/rhd2u , where d2u is the squared Euclidean

distance of the reference uncoded system.

According to time division multiple access, there is only one user that can communicate

to base stations at one time. However, in order to meet the access requirements of multiple

users in one period, three different scheduler schemes, could be used, i.e., max total capacity

scheduler (MCs), Round Robin scheduler (RRs) and proportional fairness scheduler (PFs).

We assume that the fading is quasi-static and the channel is unknown at the transmitter but

perfectly known at the receiver. Since the channel is described by a non-ergodic random

process, we define the instantaneous channel capacity as the mutual information conditioned

on the channel responses. The instantaneous channel capacity is a random variable.For each realization of the random channel frequency response, the instantaneous channel

capacity for i-th user is given by

Ci = 1K

Kk=1

log2

det

IMr + SNR Hki

Hki

H, i = 1, 2, . . . , N (50)

where IMr is the identity matrix of size Mr, Hk is an Mr Mt channel matrix and SNR is

the signal-to-noise ratio per receive antenna.

8.1 Max Total Capacity Scheduler

The first scheduler is greedy one which is based on the max sum capacity of the user channel.

Based on the water filling, the available power of the Node B is allocated to the two eigen-

modes, and then the sum capacity is calculated. The user with the maximum sum capacity

is scheduled to transmit in the next TTI. This max Capacity scheduler provides maximum

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system capacity at the expense of fairness, because all the resource may be allocated to a

single user which has always the best channel conditions. The capacity of multiuser diversity

is given by

C

=max

i=1,...,N{Ci

}(51)

8.2 Round Robin Scheduler

The Round Robin (RR) scheduler provides a fair sharing of resources (frames) at the expense

of system throughput. The user is scheduled to transmit in turn, in which the channel capacity

of user is not considered. The system total capacity is given by

C=

1

N

N

i=1

Ci

(52)

8.3 Proportional Fairness Scheduler

The proportional fairness scheduler is a tradeoff between the throughput and the fairness. An

ideal scheduling interval is assumed and scheduling is performed on a frame by frame basis.

The user with the largest metric value as follow is scheduled to transmit

wi

=ci

ci, i

=1, 2, . . . , N (53)

ci is the user transmission capability, calculated as Eq. 50. If the current user transmits data,

the average throughput of user i is updated as

ci = ci (1 ) + ci , i = 1, 2, . . . , N (54)Otherwise

ci = ci , i = 1, 2, . . . , N (55)Here, the forgetting factor , is a positive constant but less than 1. Thus, the system total

capacity is given by

C =N

i=1wi Ci (56)

9 Numerical Evaluation

In this section, some representative numerical results were presented to evaluate system per-

formances in terms of system capacities with multiuser diversity, throughput and complexity,and system bit error ratios (BER) when link adaptation was assumed for the proposed multi-

user MIMO OFDM system schemes with TDD/TDMA as access modes. In order to conduct

comparisons among different 4G system schemes, three typical implementation schemes of

multiuserMIMO OFDM with TDMA,CDMA and OFDMA, i.e., TDD/TDMA 4G,DoCoMo

MIMO VSF-OFCDM and FuTURE B3G TDD, were tested in the same simulation configu-

rations, which was given by Table 3. Furthermore, this kind of test results could reflect their

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Table 3 System configuration

parameterSystem parameters Values

Bandwidth 20MHz

Carrier frequency 5 GHz

Number of subcarriers 1,024Subcarrier spacing 19.5kHz

OFDM symbol duration 64us (51.2 + 12.8: effectivesymbol+guard interval)

Antennas configuration 4 2 (Base stations: 4, Mobilestations: 2)

Vehicle velocity 120 km/h

MIMO channel model 3GPP Vehicle A channel,

uncorrelated MIMO

Doppler frequency 556 Hz

Channel estimation algorithm Time domain pilots+FFT-based

performances respectively, as their performance metrics were normalized to their system

bandwidth in following experiments.

9.1 System Capacity with Multiuser Diversity

Assumethat thestatesofspatial MIMO channels wereonly knownat transmitters, normalized

system capacity respected to system bandwidth, was used to evaluate system performance

under the cases of multiuser scenarios. When the max total capacity scheduler as shown

above were used for multiple user schedules, the three typical multiuser MIMO OFDM

system schemes, i.e., TDD/TDMA 4G, DoCoMo MIMO VSF-OFCDM and FuTURE B3G

TDD, were evaluated in terms of system total capacity with 32 users.

The numerical simulation results were achieved by the common system configurations as

shown in Table 3, while their physical frame structure are kept different. For multiple user

scenarios, multiuser diversity gain can be achieved by exploiting the independent frequency

and spatial selective fading one another. For the proposed TDD/TDMA 4G schemes, TDMAwas implemented by assign the whole timeslot to only one user during one schedule period.

However, more multiuser diversity gains can be obtained by other access modes, such as

OFDMA, CDMA or OFCDM. As indicated by Fig. 11, much larger system capacity was

obtained by DoCoMo MIMO VSF-OFCDM system, when compared with other two multi-

user MIMO OFDM system schemes. However, at the cost of system complexity, the system

capacity of FuTURE B3G TDD with OFDMA was only little larger than that of TDD/TDMA

4G schemes.

9.2 Throughput and Complexity

According to the common system configurations in Table 3, the bit error rate (BER) perfor-

mances of uncoded TDD/TDMA 4G, DoCoMo MIMO VSF-OFCDM, and FuTURE B3G

TDD, were evaluated in uncorrelatedMIMO channel scenarioswith 3 GPP VehicleA channel

profiles, where their corresponding radio frame structures were also implemented as shown

in Sect. 3. Assuming perfect channel knowledge had been estimated and complete system

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Fig. 11 System multiuser

diversity capacity normalized to

system bandwidth for for uplink

multiuser MIMO OFDM systems

with typical TDMA, OFCDM,

and OFDMA as access modes,

i.e., TDD/TDMA 4G, DoCoMo

MIMO VSF-OFCDM, FuTURE

B3G TDD, when the max total

capacity scheduler as shown in

Sect.8 was used with 32 users

schedules

0 2 4 6 8 10 12 14 16 18 204

6

8

10

12

14

16

18

20

22

24

SNR (dB)

Capacity(bits/s/Hz

)

TDD/TDMA 4GFuTURE B3G TDD with OFDMADoCoMo MIMO VSF-OFCDM with CDMA

synchronizations were achieved, the typical modulations such as quarter phase shift keying

(QPSK) and binary phase shift keying (BPSK), were used respectively to test the system

BERs. Here, the two-dimension spreading in DoCoMo MIMO VSF-OFCDM was only con-

ducted in time domain with spreading factor 32, and the spreading codes were obtained by

Walsh code generators.

Furthermore, the MUDs based on successive interference cancellation (SIC) or parallelinterference cancellation (PIC), were used for uplinks and downlinks in DoCoMo MIMO

VSF-OFCDM systems. To alleviate the complexity, the suboptimal subcarrier allocation cri-

teria [60], namely, the Product-criterion and the Sum-criterion were adopted for FuTURE

B3G TDD schemes. The computation complexity of the suboptimal approaches grows only

linearly with the number of users and the number of subcarriers.

When the round robin scheduler was used for multiple users scheduling schemes, the

simulated BERs results of for uplinks at base stations, were shown by Figs. 12, and 13 for

the modulations of BPSK and QPSK, respectively. Moreover, Figs. 14 and 15 displayed the

simulated BERs results for downlinks at terminals. As illustrated by these simulated results,

without multiuser interference, FuTURE B3G TDD and TDD/TDMA 4G have better perfor-mance than DoCoMo MIMO VSF-OFCDM. At any time, there was only one user that could

have access to base stations, TDD/TDMA 4G systems could achieve to best performance.

Furthermore, at high SNR, TDD/TDMA 4G could obtain about 1 dB signal noise rate gain,

when compared with DoCoMo MIMO VSF-OFCDM.

Subsequently, we also evaluated the system complexity in terms of system simulation

times for uplinks, which were described by Fig. 16. Clearly, as for DoCoMo MIMO VSF-

OFCDM, the complexityof receivers as base stations increaseswith proportion to thenumber

of users, while that of TDD/TDMA 4G and FuTURE B3G TDD system are kept unchanged

when the number of users increased. This could owe to the increase of multiuser signalinterference in the scenarios of DoCoMo MIMO VSF-OFCDM, which lead to more iterative

operations to cancel multiuser interferences. Thesimilar phenomenon could also be observed

at terminals when a larger number of users existed.

Now, let us check the throughputs achieved by the three typical multiuser MIMO OFDM

systemschemes forB3Gmobilecommunications, whenQPSKwas used in these simulations.

The throughputs of TDD/TDMA 4G, DoCoMo MIMO VSF-OFCDM and FuTURE B3G

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Fig. 12 System BER

performance for uplink multiuser

MIMO OFDM systems with

typical TDMA, OFCDM, and

OFDMA as access modes, i.e.,

TDD/TDMA 4G, DoCoMo


B3G TDD, when BPSK was used

for 32 users with 2 4 antennasconfigurations at terminals and

base stations, respectively

0 2 4 6 8 10 12 14 16

10-5

10-4

10-3

10-2

10-1

SNR (dB)

BitErrorRates

DoCoMo MIMO VSF-OFCDM

FuTURE B3G TDD

TDD/TDMA 4G

Fig. 13 System BER

performance for uplink multiuser

MIMO OFDM systems with

typical TDMA, OFCDM, and

OFDMA as access modes, i.e.,

TDD/TDMA 4G, DoCoMo


B3G TDD, when QPSK was used

for 32 users with 2 4 antennasconfigurations at terminals andbase stations, respectively

0 2 4 6 8 10 12 14 1610

-5

10-4

10-3

10-2

10-1

100

SNR (dB)

BitErrorRates


FuTURE B3G TDD

TDD/TDMA 4G

TDD, can reach to about 45, 56, and 52Mbps, respectively, and their corresponding spectrum

efficiency were 2.29, 2.85, and 1.97 bits/s/Hz. When 16-QAM modulation was adopted, their

spectrum efficiency were 4.58, 5.69, and 3.93bits/s/Hz. The spectrum efficiency of DoCoMo

MIMO VSF-OFCDM was inferior to that of FuTURE B3G TDD and TDD/TDMA 4G, as

the spreading in time-frequency domains increased the time and frequency diversity gains at

cost of system resource overheads. This results indicated that the proposed multiuser MIMO

OFDM system schemes with TDD/TDMA, i.e., TDD/TDMA 4G, can achieve comparable

system performance and throughputs with low complexity and radio resource overhead to

that of DoCoMo MIMO VSF-OFCDM and FuTURE B3G TDD.

9.3 Eigenmode Transmission Coupled with Spacetime Codes

Under spatially uncorrelated ITU vehicular A channels with Doppler frequencies of 200Hz,

we evaluate the system capacities and throughputs with and without considering spacetime

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Fig. 14 System BER

performance for downlink






B3G TDD, when BPSK was used



0 2 4 6 8 10 12 1410

-5

10-4

10-3

10-2

10-1

SNR (dB)

BitErrorRates


FuTURE B3G TDD

TDD/TDMA 4G

Fig. 15 System BER

performance for downlink






B3G TDD, when QPSK was used



0 2 4 6 8 10 12 14 1610

-5

10-4

10-3

10-2

10-1

100

SNR (dB)

BitErrorR

ates


FuTURE B3G TDD

TDD/TDMA 4G

codes, respectively. By the reason of terseness, the eigenmodes obtained for the two scenarios

are called spacetime eigenmodes and carrier eigenmodes, respectively. At transmitter, the

water-filling power allocation algorithm [76] is executed to adaptively adjust the transmit

powers for all the eigenmodes according to their fading coefficients.

Figure17 shows the system capacities for different signal noise ratios (SNR) when space

time codes are Alamouti Code, Space-Time Block Code (STBC) Xc3[80] and STBC Xh3 [80]

with code rates of 1, 0.5, and 0.75, respectively. According to Fig. 18, the code rates of space

time codes have significant effects on the system capacity when thespacetime

eigenmodesare constructed, i.e., the smaller the code rates, the larger the capacity difference between

carrier eigenmodes and spacetime eigenmodes. As the results pointed out in Sect. 7, this

phenomenon can owe to the increase of spacetime diversity gains with the decrease of code

rates, which lead to the reduction of data symbol transmit rates. At the same time, the scales

of system capacities for the carrier eigenmodes and the spacetime eigenmodes are eval-

uated by twenty time numerical simulation under the uncorrelated ITU indoor, pedestrian

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5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

Number of Users

Complexityintermsofsimulatio

ntimes(s)


FuTURE B3G TDD

TDD/TDMA 4G

Fig. 16 System complexity in terms of simulated times for typical multiuser MIMO OFDM systems with

typical TDMA, OFCDM, and OFDMA as access modes, i.e., TDD/TDMA 4G, DoCoMo MIMO VSF-

OFCDM, FuTURE B3G TDD, when QPSK was used for 32 users with 2 4 antennas configurations atterminals and base stations, respectively

0 5 10 15 20 25

5

10

15

20

25

30

SNR (dB)

Capacity(bits/s/Hz)

Alamouti Code r = 1 for carrier eignmodesAlamouti Code r = 1 for space-time eignmodesSTBC X(h,3) r = 0.75 for carrier eignmodesSTBC X(h,3) r = 0.75 for space-time eignmodesSTBC X(c,3) r = 0.5 for carrier eignmodesSTBC X(c,3) r = 0.5 for space-time eignmodes

Fig. 17 Capacity curves of the proposed TDD/TDMA 4G systems when the carrier eigenmodes and space

time eigenmodes are conductedfor thespacetime codes with differentcode rates, under spatiallyuncorrelated

ITU vehicular A channels with Doppler frequencies of 200 Hz

and vehicular A channel scenarios, respectively. Then, these scale factors are averaged out

to 1.9526, 4.4807, and 3.5509, when Alamouti Code, SpaceTime Block Code (STBC)Xc

3and STBC Xh3 are considered, respectively. However, this doesnt mean the throughputs of

carrier eigenmodes are larger than that ofspacetime eigenmodes, as showed in the following

simulation results.

Furthermore,whenspacetime codes areAlamoutiCode, SpaceTimeBlock Code(STBC)

Xc3 and STBC Xh3 with code rates of 1, 0.5, and 0.75, respectively, the throughputs for dif-

ferent signal noise ratios (SNR) are given in Fig. 18, where the modulation order of data

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Fig. 18 Throughput curves of

MIMO OFDM systems when the

carrier eigenmodes and

spacetime eigenmodes are

conducted for the spacetime

codes with different code rates,

where different powers are

allocated to different eigenmodes

according to water-filling scheme

with given target BER 106

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

9

SNR (dB)

Throughput(bits/s/H

zl)

Alamouti Code r = 1 for carrier eignmodesAlamouti Code r = 1 for space-time eignmodesSTBC X(c,3), r = 0.5 for carrier eignmodesSTBC X(c,3), r = 0.5 for space-time eignmodesSTBC X(h,3), r = 0.75 for space-time eignmodesSTBC X(h,3), r = 0.75 for carrier eignmodes

symbols in carrier eigenmodes is fixed unchanged in a spacetime codeword. However, the

adaptive modulation is only performed on the data symbols of spacetime codes, for the

case ofspacetime eigenmodesother than carrier eigenmodes, as the data symbols carried

by spacetime codes in carrier eigenmodes are transported by multiple carrier eigenmodes,

simultaneously. Due to adaptive modulation of data symbols for spacetime eigenmodes,

the larger throughputs are achieved than that ofcarrier eigenmodes, as showed in Fig. 18,

while the throughputs also increase with the code rate of spacetime codes, at the SNR above

15dB. What is more, the ratios between the numbers ofcarrier eigenmodes and spacetime

eigenmodes are 1, 3, and 2 for Alamouti Code, SpaceTime Block Code (STBC)Xc3 and

STBCXh3 , respectively. Consequently, the link adaptation technique with a few eigenmodes

can be implemented effectively in spacetime eigenmodes.

9.4 Performance with Link Adaptation

In order to evaluate performance of TDD/TDMA 4G systems with link adaptation, classicalwater-filling scheme [77], greedy scheme [81], equal power allocation [83] and the scheme

given in this paper are numerically simulated. When the SNR at receiver is lower than 15 dB,

the modified water-filling power allocation algorithm can achieve better performance than

that of classical water-filling scheme and equal power allocation schemes, but inferior to that

of greedy power allocation scheme. However, different from greedy scheme, the modified

water-filling power allocation method is conducted in only two steps.

Subsequently, according to CSI at transmitter, transmit power is firstly adaptively allo-

catedamongdifferent eigenmodes as detailed in Sect.7, then adaptive modulation andcoding

(AMC) is performed to fit for current channel states for given special BER requirements. Thefour differentpower allocation strategies as showed aboveareused to conduct adaptive power

allocation. Figure 19 shows the system spectrum efficiency achieved by different power allo-

cation schemes, and the spectrum efficiency of modified water-filling scheme is inferior to

that of other three schemes at high SNR, as great diversity gain can be achieved under the

case of TDD/TDMA 4G systems. The greedy scheme can obtain the best results, while the

classical water-filling and equal power allocation scheme obtain the same results. Although

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Fig. 19 Spectrum efficiency of

TDD/TDDMA 4G system with

the improved water-filling power

allocation scheme, classical

water-filling, greedy scheme,

equal power allocation schemes,

when the carrier eigenmodes and



codes

0 5 10 15 20 25 300

2

4

6

8

10

12

14

SNR of every Receive Anntena (dB)

SpectralEfficency(bits/s

/Hz)

CacapcityWater-Filling Power AllocationEuqal Power AllocationGreedy Power AllocationModified Water-Filling Power Allocation

Fig. 20 System BER of

TDD/TDMA 4G systems, when

the carrier eigenmodes and



codes, and different powers are

allocated to the improved

water-filling power allocation

scheme, classical water-filling,greedy scheme, equal power

allocation schemes with given

target BER < 103

0 5 10 15 20 25 3010

-3

10-2

10-1

SNR (dB)

BER

Water-Filling Power Allocation

Equal Power Allocation

Greedy Power Allocation

Modified Water-Filling Power Allocation

the modified water-filling power allocation scheme can not achieve the best results, its simple

implementation can win its application in TDD/TDMA 4G systems.

Finally, as showedin Fig. 20, thecorresponding BERresults of above systemconfiguration

with requirement of BER < 103, is given by simulating the TDD/TDMA link performancethrough Matlab 7.0 simulink blocksets.

10 Conclusions

The combination of MIMO and OFDM has emerged as a promising solution for future

high-rate wireless communication systems. Based on the state-of-the-art review of MIMO

and OFDM technologies, we further discussed the specific limitations of existing techniques

designed for multiuser MIMO OFDM systems in broadband wireless mobile channel scenar-

ios, i.e., bad performance and extreme complexity of multiuser detectors for rank-deficient

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multiuserMIMO OFDM systems with CDMA asaccessmodes,extreme challenges of spatial

MIMO channel estimators in rank-deficient MIMO OFDM systems, and exponential growth

complexity of optimal sub-carrier allocations for OFDMA-based MIMO OFDM systems.

Furthermore, in fast doubly selective fading mobile channel scenarios, these issues will pose

great challenges to multiuser MIMO OFDM systems.Up to now, several typical multiuser MIMO OFDM systems for next generation mobile

communications with OFDMA and CDMA as access modes, i.e., FuTURE B3G TDD and

DoCoMo MIMO VSF-OFCDM, were given in recent literatures. However, many different

field tests were only conducted in the scenarios similar to that of wireless local networks, and

few test results in fast doubly selective fading mobile channel scenarios. Herein, aiming at

the internal specification limitations of these typical next generation mobile communication

schemes, we proposed the multiuser MIMO OFDM systems with TDD/TDMA as access

methods for next generation mobile communication candidates.

With TDD/TDMA, many intractable issues could be avoided or alleviated, such as multi-

user interferences, channel estimationoverhead with larger number users, optimal sub-carrier

allocations for OFDMA-based schemes. In this paper, the proposed TDD/TDMA 4G sys-

tems were dedicately designed for fast mobile channel environments. Furthermore, we also

displayed the design of Stainer channel training sequence for rank-deficient MIMO OFDM

systems. With eigenmodes with spacetime codes, system performances of TDD/TDMA 4G

systems were analyzed in terms of the pairwise error probability and system capacity with

multiuser diversity under different schedulers.

Acknowledgments The authors would like to express their thanks to the reviewers for their helpful and

insightful comments and suggestions that improved the quality of this paper. This work was supported in

part by grants from the National High Technology Research and Development Program (863) project ofChina under grant No.2006AA01Z258, a grant from National Nature Science Foundations (NSF) China under

contract 60602034, and partly by Huawei, TD-Tech, LGE and Samsung.

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Multiuser MIMO OFDM Based TDD TDMA for Next Generation Wireless Communication Systems