Optimizing Wireless Communication Systems Volume 1033 ||

Chapter 10Link Adaptation for MIMO-OFDM Systems

Darlan C. Moreira, Walter C. Freitas Jr., Cibelly A. de Araujo, and CharlesC. Cavalcante

10.1 Introduction

The paradigm of the design of a wireless system has changed. Since the use of thedimensioning for the “worst case”, which means to design the system to work onthe fading margin available when the channel has its poorest behavior, the driver ofthe optimization has evolved to a more suitable use of the available resources forperforming a reliable communication.

This approach is then called link adaptation (LA), when the system chooses theparameters which are the most suitable for usage in a certain channel condition.The always increasing demand for higher data rates, lower energy consumption,etc., requires that the system resources are utilized as efficiently as possible and LAtechniques are already a reality in any modern wireless communication systems toachieve that goal.

While many aspects of LA, such as usage of different modulations and code ratesfor providing better “protection” to data streams according to the channel condition,have already been understood, each system has a different set of “interesting param-eters” to be adapted in multiple dimensions and the trade-off between LA gains andsignaling overhead still provides challenges to be answered.

Typical dimensions used in LA procedure are modulation and coding. The choiceof the modulation allows the system to improve/decrease the spectral efficiency andthe code rate impacts the amount of redundancy inserted for error protection intodata frames. However, it is possible to envisage the exploitation of other features ofthe wireless system, for instance the spatial and frequency domains.

This chapter describes the use of transmission modes considering parameterswhich are important to the performance of a wireless system, in particular theextension of LA to the MIMO-OFDM case in fourth generation (4G) systems.

The rest of the chapter is organized as follows. The fundamentals of multiple-input multiple-output (MIMO) systems are presented in Section 10.2, where classicalMIMO schemes are described. Section 10.3 discusses the trade-off between thediversity and multiplexing gains that can be extracted from the MIMO channel

F. Cavalcanti, S. Andersson (eds.), Optimizing Wireless Communication Systems, 393DOI 10.1007/978-1-4419-0155-2 10, c© Springer Science+Business Media, LLC 2009

394 D. C. Moreira, W. C. Freitas Jr., C. A. de Araujo, and C. C. Cavalcante

and describes some hybrid MIMO schemes that are able to achieve both gainssimultaneously. The fundamentals of LA are described in Section 10.4 for a soft-input/soft-output (SISO) system and then extended to the MIMO-OFDM case.The summary of the chapter and envisaged research directions are discussed inSection 10.5.

10.2 Fundamentals of MIMO Transceiver Architectures

Higher transmission rates and better reliability are always desirable in communica-tion systems. However, according to information theory, to increase one, the otherhas to be decreased [27], unless we are willing to use more system resources, suchas power or bandwidth, which is not always possible.

In this context, the use of the spatial dimension through MIMO strategies ismandatory in the next generation systems, such as long-term evolution (LTE) andLTE-Advanced [3, 10]. By using the spatial dimension, more degrees of freedomcan be used to increase the data rates and/or the reliability of the system without theneed of more system resources.

10.2.1 Space Diversity/Spatial Dimension Gains

There are different types of gains that can be extracted from the spatial dimension,such as array gain, coding gain, diversity gain, multiplexing gain, etc. A MIMOsystem has the generic form shown in Fig. 10.1 and the gains actually extracted fromthe spatial dimension depend on how the MIMO encoder maps the input symbolsinto the coded symbols sent by each transmitter antenna and/or how the receptionprocessing is done.

Symbols MIMOEncoder

MIMODecoder

EstimatedSymbolsH

Fig. 10.1 Generic MIMO system.

The array gain refers to an average increase in signal-to-noise ratio (SNR) andis obtained when the receiver coherently combines the signal that arrives at the

10 Link Adaptation for MIMO-OFDM Systems 395

multiple receiver antennas. A similar gain, the coding gain, can be obtained whenthe transmitter encodes the symbols using, for instance, space–time codes, but notall space–time codes yield a coding gain. Both the array gain and the coding gainare seen in a graphic of bit error rate (BER), or similar measure, versus SNR as ashift to left in the curve when compared to a system without multiple transmitterantennas,10.1 as depicted in Fig. 10.2.

SNR

Err

orM

easu

re

Single antennaTransmission

With array gainWith diversity and

array gains

Fig. 10.2 Diversity gain versus array gain.

The diversity gain consists of increasing the reliability of the received informa-tion by combining the different versions of the faded signals. That is, since in MIMOsystems there are multiple links corresponding to the pairs of transmit and receiverantennas, the probability that all links are in a fade is low and by combining all linksthe resultant signal exhibits a lower fading (amplitude variation) when compared toa signal from a single link.

Different from the array/coding gain, the effect of the diversity gain is an in-crease in the curve slope for high SNRs as shown in Fig. 10.2. The more degreesof freedom/orders-of-diversity the MIMO system can take advantage of, the moreis the curves’ relative slope increase. Several MIMO strategies can be employed toextract a diversity gain from the channel and a common strategy in the literature isthe space–time codes, which will be presented in Section 10.2.2. It should be notedthat the maximum diversity gain that the (spatially uncorrelated) channel can pro-vide is given by Mr×Mt , where Mr is the number of receiver antennas [23, 38] andMt is the number of transmitter antennas [23, 38].

The multiplexing gain consists of increasing the transmission data rate by us-ing the spatial dimension to separate multiple data streams. That is, two or moredata streams are transmitted at the same time and frequency through the differenttransmitter antennas. Due to degree of freedom provided by the spatial domain thechannels of the different data streams are different and can be seen as signaturesused in the receiver to separate the streams as it will be described in Section 10.2.3.

However, a trade-off exists between diversity and multiplexing gains such thatincreasing one will decrease the other [38]. Also, it should be noted that the MIMO

10.1 Since their effect is the same (in the perceived SNR), coding gain and array gain will be usedinterchangeably.


architecture presented in most of the literature assumes a flat fading channel. Thisassumption can be well-motivated when using MIMO jointly with orthogonal fre-quency division multiplexing (OFDM), as discussed in Section 8.7.

10.2.2 Space–Time Coding

Considering a single-input multiple-output (SIMO) system and assuming a flat fad-ing channel, the channel vector h is given by

h = [h1,h2, . . . ,hMr ]T . (10.1)

For a transmitted symbol s, the received symbol vector is then given by

y = hs+v, (10.2)

where v is the considered noise, usually assumed additive white Gaussian noise(AWGN). In order to realize a receiver diversity gain and maximize the SNR thereceiver can perform a maximal ratio combining (MRC) [23, Chapter 5], i.e.,10.2

y = hHhs+hHv= ‖h‖2s+hHv,

(10.3)

where y is the Mr×1 receiver output.On the other hand, in a multiple-input single-output (MISO) system with multiple

antennas at the transmitter, the simplistic approach of transmitting the same signalfrom all transmitter antennas does not provide any diversity gain at the transmit-ter [23]. In this case, the received signal is a linear superposition of the transmittedsignals from all transmitter antennas plus noise. However, since the total transmitpower has to be divided among all antennas, no diversity gain is obtained and, there-fore, a more elaborate approach has to be used to extract a transmitter diversity gain.

The approach will depend on whether there is channel information available atthe transmitter or not. When the channel is known to the transmitter the power ineach transmitter antenna can be weighted appropriately by a weight vector w chosensubject to ‖w‖2 = Mt , where this restriction is necessary to ensure that the totaltransmit energy is not changed. The weight vector that maximizes the SNR is thengiven by [21]

w =√

MthH

‖h‖ . (10.4)

This solution is called maximal ratio transmission (MRT) and is similar to the MRC.The obtained gain corresponds in fact to a diversity gain plus a coding gain insteadof only a diversity gain. However, the assumption that the channel is known at thetransmitter can typically not be fully satisfied.

10.2 The channel h is assumed to be known at the receiver.


When the channel is not known to the transmitter, the most common approachin the literature is the space–time block codes (STBCs), which require channel in-formation only at the receiver. The transmit signal is encoded in a way to extractthe spatial diversity while at the same time it can be decoded by the receiver us-ing simple linear processing. However, due to the lack of channel knowledge at thetransmitter no coding gain is obtained and STBCs obtain only the diversity gain.10.3

A well-known STBC is the Alamouti scheme described in [4]. It encodes theinput signal onto two transmitter antennas and has the advantage of being a full-diversity code that requires only linear processing in the receiver. The Alamouticode has the advantage that it does not decrease the spectral efficiency compared tothe SISO case.

A full-diversity code extracts the maximum diversity gain that the MIMO chan-nel can provide, that is, Mt ×Mr. On the other hand, a full-rate code achieves themaximum multiplexing gain corresponding to min(Mt ,Mr) [23].

Given two transmit symbols s1 and s2, the space–time codeword matrix for theAlamouti scheme is given by

S =[

s1 s2

−s∗2 s∗1

],

where the rows correspond to the time slots, the columns correspond to the trans-mitter antennas, and∗ stands for complex conjugate. Hence, in the first time slot thefirst antenna sends the symbol s1 while the second one sends the symbol s2. Afterthat, the first antenna sends −s∗2 and the second one sends s∗1 in the subsequent timeslot.

The signal in the single receiver antenna for the two time slots is then given by,respectively, y1 and y2 such that y1 = h1s1 + h2s2 + v1 and y2 = −h1s∗2 + h2s∗1 + v2,where h1 is the channel between the first transmitter antenna and the receiver an-tenna, h2 is the channel between the second transmitter antenna and the receiverantenna, and v1 and v2 are zero mean circularly symmetric complex gaussian(ZMCSCG) noise. In matrix notation, the received signal can be written as

y =[

y1

y∗2

]=

[h1 h2

h∗2 −h∗1

][s1

s2

]+

[v1

v∗2

]. (10.5)

To decode the transmitted information the receiver only needs to multiply y by theconjugate transpose of the channel matrix in (10.5) yielding

[y1

y2

]=

[‖h1‖2 +‖h2‖2 0

0 ‖h1‖2 +‖h2‖2

][s1

s2

]+

[v1

v2

]. (10.6)

Note that this simple matrix multiplication is enough to decode the transmit-ted information, since y1 depends only on s1 and y2 depends only on s2. Also, theterm ‖h1‖2 +‖h2‖2 clearly shows that each transmitted symbol is amplified by bothchannel gains resulting in a diversity gain of two (two diversity branches).

10.3 The array gain can still be obtained if multiple antennas are used in the receiver.


In [33] STBCs for more than two transmitter antennas are proposed, but theyhave a code rate lower than one for any complex symbol constellation. The space–time codeword matrices for the H3, G3, and G4 schemes, presented in [33], and forthe Alamouti scheme, addressed as G2, are reproduced below.

SG2 =[

s1 s2

−s∗2 s∗1

], SH3 =

⎡⎢⎢⎢⎢⎣

s1 s2s3√

2−s∗2 s∗1

s3√2

s∗3√2

s∗3√2

−s1−s∗1+s2−s∗22

s∗3√2− s∗3√

2

s2+s∗2+s1−s∗12

⎤⎥⎥⎥⎥⎦ ,

SG3 =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

s1 s2 s3

−s2 s1 −s4

−s3 s4 s1

−s4 −s3 s2

s∗1 s∗2 s∗3−s∗2 s∗1 −s∗4−s∗3 s∗4 s∗1−s∗4 −s∗3 s∗2

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

, SG4 =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

s1 s2 s3 s4

−s2 s1 −s4 s3

−s3 s4 s1 −s2

−s4 −s3 s2 s1

s∗1 s∗2 s∗3 s∗4−s∗2 s∗1 −s∗4 s∗3−s∗3 s∗4 s∗1 −s∗2−s∗4 −s∗3 s∗2 s∗1

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

.

Another option to take advantage of MIMO channel properties and increase thereliability is to employ space–time trellis codes (STTCs) [32, 33], where the func-tions of symbol mapper and space–time encoder are combined into a single block.In fact, STBCs and STTCs are to space–time codes as block codes and trellis-codedmodulation are to channel coding. While STBCs extract only a diversity gain fromthe MIMO channel, STTCs can extract both diversity and coding gains yielding abetter BER performance.10.4 The disadvantage of STTCs is that they are more com-plex to encode (and more difficult to construct good codes) and decode comparedto the case for STBCs. While a linear decoder is used for STBCs, STTCs rely ona Viterbi decoder. These aspects explain the greater interest in STBCs compared toSTTCs.

10.2.3 Spatial Multiplexing

In the previous section the main goal was to increase reliability by using the spatialdimension to obtain a diversity gain. Herein the objective is to maximize the spectralefficiency by using the spatial dimension to obtain a multiplexing gain. The idea isto split the information and send it into Mt streams, where Mt is the number oftransmitter antennas and each stream is transmitted in a separate antenna.

10.4 Note that in both cases an array gain is also obtained when multiple receiver antennas areemployed.


This idea was initially proposed with different names. The structure of trans-mission/reception with multiple antennas is described in [24], and the vertical BellLabs layered space–time (VBLAST), described in [13], is an architecture to real-ize a multiplexing gain, with the constraint to operate with the same number ofantennas at the transmitter and the receiver. At the transmitter, the information isdivided into streams and sent through the different antennas with no special pro-cessing required. That is, the space–time codeword for the VBLAST scheme isgiven by

s =

⎡⎣s1

s2

s3

⎤⎦ . (10.7)

It is assumed that, for all detection algorithms, the received signal vector x, withdimension Mr×1, is expressed by

x = Hs+v, (10.8)

where H is the Mr×Mt MIMO channel matrix, s is the Mt × 1 transmitted signalvector, and v is the Mr × 1 noise vector. Since all streams are transmitted at thesame time and frequency, each element of the received signal vector x has contribu-tions from all transmitter antennas. Consequently, when decoding each stream thereceiver has to eliminate the interference from the other streams by using the spatialdimension. Some linear or nonlinear detection algorithms can be employed for thistask. Linear receivers are described in Section 10.2.3.1, which change only in theoptimization criterion for the filter calculation. Nonlinear receivers are describedin Section 10.2.3.2, where the main idea is to cancel the interference of alreadydetected streams, addressed as layers.

Another MIMO scheme similar to the VBLAST scheme and worth mentioninghere is diagonal Bell Labs layered space–time (DBLAST). Instead of Mt differentstreams, Mt copies of the same stream are transmitted where each copy is shiftedone time slot from the previous one. The space–time codeword for the DBLASTscheme is given by

S =

⎡⎣s1 s2 s3 − − ·· ·− s1 s2 s3 − ·· ·− − s1 s2 s3 · · ·

⎤⎦ . (10.9)

Even though the DBLAST scheme is similar to Bell Labs layered space–time(BLAST), it yields in fact a diversity gain instead of a multiplexing gain. Never-theless, it is described in this section instead of in Section 10.2.2 because of thissimilarity. As it can be seen in (10.9), there are some gap elements in the matrix S,which represent an absence of transmission. Because of these gaps not all symbolssee the same diversity.


10.2.3.1 Linear Detection

The linear receiver model is given by

y = Wx, (10.10)

where x is the received signal vector before filtering, y is the filtered signal vector,and the weight matrix W may be obtained by several optimization criteria.

The most direct optimization criterion is to nullify the interference when thenoise vector is a null vector, i.e.,

W = argmin E{‖Wx− s‖2} (10.11)

s.t.: Wx|v=0 = 0,

which yieldsW = (HHH)−1HH . (10.12)

This is the well-known zero-forcing (ZF) receiver, which works well in a relativenoiseless channel (high SNR). However, because of the constraint Wx|v=0 = 0 theZF receiver has a problem of enhancing the noise, which degrades its performancein noisy channels (lower SNR).

To overcome this limitation, a good strategy is to change the optimization crite-rion to the minimum-mean-square-error (MMSE), that is,

W = argmin E{‖Wx− s‖2}, (10.13)

which results in the following weight vector W [23]:

W =(

HHH+Mt

γIMt

)−1

HH , (10.14)

where γ is the SNR value and IMt is the Mt ×Mt identity matrix. Named after itsoptimization criterion, this receiver is known as the MMSE receiver. While theMMSE receiver does not usually eliminate the interference completely, it does notsuffer from the noise enhancement problem and it is more balanced than the ZFreceiver.

10.2.3.2 Nonlinear Detection

It is possible to substantially increase the performance of the receiver if nonlineardetection is employed. The successive interference cancellation (SIC) [23] detectionis an example of a nonlinear receiver where the first layer is detected with a linearreceiver, such as the ZF or MMSE receivers, producing an estimate s1. After that, thecontribution from layer 1 on the receive signal is estimated and cancelled, resultingin a signal x2.


In general, at the ith layer, the signal xi is expected not to have interference causedby the previous layers j < i. Therefore, based on the symbol estimate for ith layer,si, its contribution on the receive signal is estimated and subtracted from the receivesignal xi. This procedure results in a modified signal called xi+1 expressed as

xi+1 = xi− sihi, (10.15)

where hi is the ith column from the channel matrix H corresponding to the channelgains associated with the ith layer and sihi represents the estimated interferencefrom the ith layer. Finally, the receive signal xi+1 is interference free from the layers1, . . . , i. This signal acts as a feedback of the spatial filter for the next layer (i + 1).Figure 10.3 depicts the decoding of each layer by the SIC receiver.

+ + +

LD LD LD

h1 h2

x1 x2

−

s1 s2

−

xMt−1

−

sMt−1hMt−1 sMt

Fig. 10.3 SIC receiver.

If all decisions are correct, the interference is totally eliminated from the pre-vious detected symbols, resulting in better predictions for the following symbols.In Fig. 10.4 a comparison of the MMSE linear detection (LD) and SIC receivers isshown for each layer. As it can be seen from the figure, SIC has a better performanceand each successive detection iteration yields a different BER value. On the otherhand, LD is performed in a single step and all layers have the same BER value.

Fig. 10.4 Comparison ofthe LD and SIC layers fortheVBLAST scheme withMt = Mr = 4.

10–6

10–5

10–4

10–3

10–2

10–1

100

0 2 4 6 8 10 12 14 16 18

BE

R

Eb/N0 [dB]

SIC LayersLD Layers

SIC Layers

LD Layers


Furthermore, in the SIC detector, if a layer has a low SNR and an error oc-curs in its detection, this error will be propagated to the subsequent layers even ifthey have higher SNR. This problem can be mitigated by properly ordering thelayer detection in SIC, which is then denoted as ordered successive interferencecancellation (OSIC). The layers are ordered in decreasing order of SNR such that thefirst detected layer corresponds to the layer with highest SNR. Figure 10.5 comparesthe BER behavior for different SNR values using LD, SIC, and OSIC detectors.

Fig. 10.5 Comparison of LD,SIC, and OSIC receivers fortheVBLAST scheme withMt = Mr = 4.

10–4

10–3

10–2

10–1

0 2 4 6 8 10 12 14 16 18

BE

R

Eb/N0 [dB]

VBLAST LD N = 4VBLAST SIC N = 4

VBLAST OSIC N = 4

10.2.4 Channel State Information (CSI)

As already mentioned in Sections 10.2.2 and 10.2.3, the channel must be knownat the receiver to decode the coded information or to separate the different datastreams when STBC or multiplexing is used, respectively. On the other hand, whenthe channel is also known in the transmitter, the capacity can be further increased bya non-uniform power allocation among the transmitter antennas or some kind of pre-coder technique [23]. However, due to the channel variation in time, frequency, andspace inherent to wireless systems, it is difficult to have this information availableat the transmitter.

In time division duplex (TDD) systems it is usually assumed that the channel isapproximately the same in both ways: downlink and uplink. Since in these systemsthe downlink and uplink channels usually correspond to the same frequency bandswith only a time separation, this assumption is justified provided that the time sepa-ration is lower than the coherence time of the channel. Therefore, the transmitter canacquire information about the direct channel by using information from the reversechannel.10.5

On the other hand, this assumption is not valid in frequency division duplex(FDD) systems, since the downlink and uplink channels have a frequency sepa-

10.5 It should be noted, however, that while the propagation channel is the same the RF circuitrywill differ between the receive and transmit branches. Hence, RX/TX branch calibration is requiredfor TDD systems to be able to exploit this channel reciprocity.


ration greater than the coherence bandwidth of the channel. In such systems thechannel must be estimated in the receiver and some kind of feedback channel mustexist to report the channel conditions to the transmitter. However, this requiresthat additional control information must be sent to the transmitter using availableresources.10.6

In this context, the methods can be classified regarding the amount of CSI infor-mation: full CSI where the channel is required to be known at the receiver and atthe transmitter [8] and partial CSI where the channel is known only at the transmit-ter or receiver [25]. The latter method is also referred to as side information. FullCSI methods require a large amount of feedback information in order to provideto the transmitter all channel characteristics estimated at the receiver. The partialCSI methods decrease the quantities by using limited versions of the feedback in-formation. Some methods use a set of precoders from which, according to a suitablecriterion, one is selected to be used at some time [35]. Other strategies are based onthe use of statistical measurements which can be passed to the transmitter less often.These methods are also known as dynamic CSI [36].

Another way to reduce the required feedback is the method based on channelquality indicator (CQI), which is a measure that comprises the information about thechannel state in order to transmit a reduced amount of data for a selection/estimationof the best parameters to use the channel [20]. Some commercial systems, such ashigh-speed packet access (HSPA), use methods for prediction of CQI in order toreduce the interference in the uplink due to those frequent transmissions [11].

Other systems under development, such as the 3GPP LTE, are going to use somekind of schemes which do not require calibration. These transceivers have a set ofprecoders, called codebook, and use a criterion to select, according to the channelestimate, the best precoder [1]. Hence, only the index of the precoder is transmitted.This reduces a lot of the feedback information and makes the process completelyadaptive. The precoder is selected every time the channel is estimated. Strategies ofthis type are discussed in detail in Chapter 12.

With channel state information available in both the transmitter and the receiverthe capacity can be increased with a non-uniform power allocation among the trans-mitter antennas [23] optimized to maximize the capacity, such as the water fillingalgorithm. Alternatively, the reliability can be increased if the non-uniform powerallocation is optimized to maximize the SNR, such as the weight vector, given by(10.4), mentioned in Section 10.2.2.

10.3 Advanced MIMO Transceiver Architectures

The potential for multiple antennas to provide link robustness can be traced back toMarconi’s experiments in Pohdu [7]. The same idea of Marconi is still considered incurrent wireless systems. The maximal diversity order of a MIMO channel can be

10.6 Feedback reduction is an intense research topic to reduce the drawback of expensive chan-nel state information (CSI) reporting. See [22] for an overview of limited feedback in wirelesscommunication systems.


achieved by space–time code schemes. However, in such schemes a capacity loss isnecessarily present. In counterpart, strategies designed to obtain capacity increasein MIMO channels are far away from the maximal diversity order. The inter-relationabout these two main possible gains in the MIMO channel was shown in the seminalpaper of Zheng and Tse [38].

10.3.1 The Trade-Off Between Multiplexing and Diversity Gains

In [38], Zheng and Tse provided a simple expression relating the two main possiblegains in MIMO wireless channels given by

d(r) = (Mt − r)(Mr− r), (10.16)

where r ∈Z is the multiplexing gain represented in a high SNR scenario and definedas

r = limSNR→∞

R(SNR)logSNR

, (10.17)

and d is the diversity gain defined as the error probability of a given space–timecode. A fixed rate R is related with the multiplexing gain r by

R = r logSNR. (10.18)

Thus, the diversity gain could be expressed as

d =− limSNR→∞

Pe(SNR)logSNR

. (10.19)

As a consequence of (10.16), the maximal diversity and multiplexing gains in aMIMO wireless channel are, rmax = min(Mt ,Mr) and dmax = MtMr, respectively, asillustrated in Fig. 10.6. In the literature most of the space–time code transceiverswere proposed aiming to obtain just one of these upper bounds.

By the analysis of the trade-off proposed by Zheng and Tse transceivers thatachieve higher diversity gain necessarily achieve a lower multiplexing gain, andvice versa. Furthermore, due to the variation of the wireless channel caused by fad-ing the system could benefit from a specific gain depending on the channel state,suggesting that schemes adapting between diversity and multiplexing gains shouldbe considered.

10.3.2 MIMO Transceiver Structure Design

The use of multiple transmit and receiver antennas may result in great capacitygains. Indeed, in a rich scattering environment the deployment of antenna arrays atboth link ends results in a capacity that increases almost linearly with the minimum


Fig. 10.6 Illustrative resultsof the MIMO channel trade-off of [38].

…

…

Div

ersi

tyga

in

Multiplexing gain

(0, MtMr)

(1, (Mt − 1)(Mr − 1))

(r, (Mt−r)(Mr−r))

(r−1,⎪Mt−Mr⎪)

(r, 0)

number of antennas [13, 34]. MIMO antenna systems may also provide diversitygain, which is a measure of robustness against fading [30]. There is, however, thetrade-off discussed in Section 10.3.1, in which the diversity gain can only be in-creased if the multiplexing gain is decreased, see [38]. The conventional systemsdescribed in Sections 10.2.2 and 10.2.3 lie in extreme points in the trade-off curve,Fig. 10.6, as they only provide multiplexing or diversity gains. In this section, wedescribe some approaches which lie in intermediate points in the trade-off curve,providing both types of gains at the same time.

The idea of a transceiver structure aiming to achieve both spatial gains, diversityand multiplexing, was first proposed by Tarokh et al. in [31]. The authors com-bined STTC and array processing by partitioning antennas at the transmitter intosmall groups. The signal transmitted in each group of antennas goes through a givenSTTC. At the receiver, the signals from each STTC are separated by a nonlinearprocessing technique that suppresses signals transmitted from other groups of an-tennas, by treating them as interference. Then, the STTCs are individually decoded.Tarokh et al.’s idea involves a fixed transmission structure in [31], where the authorsdid not consider adapting the transmitter to the channel conditions.

Since wireless channel is random, the use of a fixed structure designed to theworst-case propagation scenarios would represent a waste of the resources in morefavorable situations. In the following, a structure that combines traditional space–time codes and multiplexing schemes to capture both diversity and multiplexinggains as presented in [31] is described, where a family of structures makes the adap-tation to more (or less) diversity and multiplexing in accordance with the channelstate. These structures are called hybrid MIMO transmit scheme (HMTS).

In general, the transmission process of HMTSs can be divided in layers, similarto VBLAST. However, in contrast to VBLAST, in the HMTS case a layer mayconsist of the stream of symbols at the output of a STBC, which is sent to a groupof antennas, or of an uncoded stream, which is transmitted from a single antenna.Based on this concept of layers, HMTS transceiver schemes combine pure diversity


schemes (e.g., STBC) with pure spatial multiplexing schemes (e.g., VBLAST). InHMTS, some layers are space–time coded across two, three, or four antennas. Forthe remaining layers, a VBLAST approach is used. With this idea, hybrid MIMOschemes achieve a compromise between spatial multiplexing and transmit diversitygains. The basic idea behind these structures is to combine array processing andspace–time coding, as first presented in [31].

In the remainder of this section some specific HMTSs are presented. The nota-tion for a particular HMTS is based on the notation of the STBC used by the spe-cific scheme (e.g., alamouti space–time block code (STBC) (G2) or 3 transmitterantenna STBC (G3)), while each uncoded stream following the VBLAST schemeis denoted with an additional label for the hybrid according to +1. For example, thescheme designed for three transmitter antennas consisting of two layers, one space–time coded with the G2 scheme and another uncoded layer following the VBLASTscheme, is denoted G2+1.

10.3.2.1 Hybrid Scheme Designed for Three Transmitter Antennas

This HMTS, whose structure is shown in Fig. 10.7(a), employs three transmitterantenna elements with two spatial multiplexing layers. A standard G2 (Alamouti’s)space–time block code is used for the first layer; the other layer is not space–timecoded, similar to the VBLAST approach. In the G2+1 scheme, the transmitted sig-nals can be organized in the equivalent space–time coding matrix:

SG2+1[k,k +1] =[

s1 s2 s3

−s∗2 s∗1 s4

], (10.20)

where the spatial dimension varies column-wise and the temporal dimensionrow-wise.

From (10.20), it can be seen that K = 4 information symbols (two from each mul-tiplexing layer) are transmitted in T = 2 consecutive time slots. Thus, the effectivespectral efficiency of this scheme is equal to η = 2 · log2 M bps/Hz, where M is themodulation order.

10.3.2.2 Hybrid Schemes Designed for Four Transmitter Antennas

The second HMTS, called G2+G2, is shown in Fig. 10.7(b). It employs four trans-mitter antenna elements with two vertically layered G2 block code schemes. Ob-serve that the four transmitter antennas are divided into two space–time codinggroups of two antennas each. The transmitted signals can be organized in an equiv-alent space–time coding matrix given by

SG2+G2[k,k +1] =[

s1 s2 s3 s4

−s∗2 s∗1 −s∗3 s∗4

]. (10.21)


12s

11s

1s ST coderG2

ST coderG3

lellaraP - laireS 2s

12s

13s

11s

1

2

s

s

s

s

(a) HMTS G2 + 1 with one STBC G2and two multiplexing layers.

ST coderG2

Seri

al -

Par

alle

l

s

s

12s

11s

12s

11s

ST coderG2 22s

21s

1s

2s

1s

2s

3s

(b) HMTS G2 + G2 with two STBC G2and two multiplexing layers.

(c) HMTS G3 + 1 with one STBC G3and two multiplexing layers.

(d) HMTS G2 + 1 + 1with one STBC G2and three multiplexing layers.

lellaraP - laireS

lellaraP - laireS

ST coderG2

Fig. 10.7 Architecture of the HMTS transmitters.

From (10.21), it can be shown that K = 4 information symbols (two from each mul-tiplexing layer) are transmitted in T = 2 consecutive time slots. Thus, the effectivespectral efficiency of this scheme is equal to η = 2 · log2 M bps/Hz. Compared tospace–time code for four transmitter antenna elements (which has a code-rate of1/2), the G2+G2 scheme achieves four times the data symbol rate.

Figure 10.7(c) depicts the third HMTS considered in this work. The four trans-mitter antennas are now divided into two multiplexing layers, where the first oneconsists of three antennas that are space–time coded using a G3 code [30]. Theequivalent space–time coding matrix for this hybrid scheme is given by

SG3+1[k, . . . ,k +7] =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

s1 s2 s3 s5

−s2 s1 −s4 s6

−s3 s4 s1 s7

−s4 −s3 s2 s8

s∗1 s∗2 s∗3 s9

−s∗2 s∗1 −s∗4 s10

−s∗3 s∗4 s∗1 s11

−s∗4 −s∗3 s∗2 s12

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

. (10.22)


From (10.22), K = 12 information symbols (four from the first layer and eight fromthe second one) are transmitted in T = 8 consecutive time slots. Thus, the effec-tive spectral efficiency of this scheme is equal to η = 1.5 · log2 M bps/Hz. Thisrepresents three times the spectral efficiency of G4.

The fourth HMTS scheme is called G2+1+1 and is depicted in Fig. 10.7(d).Again, four transmitter antennas are employed. As it can be seen from the figure,this scheme consists of three spatial multiplexing layers; the first layer is space–time coded using G2, and the remaining ones are transmitted using VBLAST. Theequivalent space–time coding matrix for the G2+1+1 scheme is given by

SG2+1+1[k,k +1] =[

s1 s2 s3 s4

−s∗2 s∗1 s5 s6

]. (10.23)

In this HMTS, K = 6 information symbols (two from the first layer and four from theuncoded ones) are transmitted in T = 2 consecutive time slots. Thus, the effectivespectral efficiency of this scheme is equal to η = 3 · log2 M bps/Hz. Compared to aspace–time code with four transmitter antennas (which has a code-rate of 1/2), thishybrid scheme achieves six times the data rate. Furthermore, the G2+1+1 schemeoffers a 50% increase in spectral efficiency compared to the G2+G2 scheme.

In Fig. 10.8(a) and (b), the performance of BER versus SNR among the VBLASTand HMTS MIMO schemes for three (Fig. 10.8(a)) and four transmitter antennas(Fig. 10.8(b)) in a Rayleigh MIMO channel model, respectively, are illustrated. Allschemes consider binary phase-shift keying (BPSK) modulation. In the receiverSTBC uses maximum likelihood (ML) detection and the hybrids and VBLASTschemes use the nonlinear detector OSIC. Since the STBC presents hardly any biterrors in this scenario, the corresponding curves are not shown in Fig. 10.8(a) and10.8(b).

According to these figures, the performance of the HMTS is between the twoextremes VBLAST and STBC. In general, HMTS outperforms VBLAST withrespect to robustness and outperforms STBC with respect to multiplexing gain, thusgenerating more diverse opportunities for considering an adaptive MIMO schemeinstead of just selecting between pure diversity and multiplexing schemes.

Table 10.1 summarizes the multiplexing and diversity orders of the MIMOtransceivers. The diversity order is shown for each layer under both linear and SICdetectors. When considering a STBC that has just one layer, the diversity order isbased on the ML detection. Looking at the table we can clearly identify the trade-offbetween diversity and capacity. For example, the STBC G4 can achieve a diversityorder of 4Mr, but only achieves a symbol rate of 1/2 symbol per channel use. On theother hand, VBLAST achieves a rate of 4 symbols per channel use, but with low di-versity order. The HMTS resides between the two extremes, maximal diversity order(e.g., STBC designed for four transmitter antennas) and maximal multiplexing or-der (e.g., VBLAST). Clearly, HMTSs are inherently flexible structures which can beadapted to the channel conditions, providing more diversity if the channel is in deepfade or more rate if the channel is experiencing good conditions for multiplexedtransmission.


Table 10.1 Summary of MIMO transmission schemes.

SchemeAchievable diversity order per layer Spectral efficiency

ηηη (bps/Hz)Linear detection SIC

VBLAST(4Tx-MrRx)

Mr−3 Mr−3 Mr−3 Mr−3 Mr−3 Mr−2 Mr−1 Mr min(Mt ,Mr)log2 M

G2+1+1(4Tx−MrRx)

2(Mr−2) Mr−3 Mr−3 – 2(Mr−2) Mr−1 Mr – 3 · log2 M

G2+1(3Tx−MrRx)

2(Mr−1) Mr−2 – – 2(Mr−2) Mr – – 2 · log2 M

G2+G2(3Tx−MrRx)

2(Mr−2) 2(Mr−2) – – 2(Mr−2) 2Mr – – 2 · log2 M

G3+1(4Tx−MrRx)

3(Mr−1) Mr−3 – – 3(Mr−1) Mr – – 1.5 · log2 M

H3(3Tx−MrRx)

3Mr – – – – – – – 3/4 · log2 M

G3(3Tx−MrRx)

3Mr – – – – – – – 0.5 · log2 M

G4(3Tx−MrRx)

4Mr – – – – – – – 0.5 · log2 M

0 2 4 6 8 10 12 14 16 1810−3

10−2

10−1

100

SNR

BE

R

HybridVBLAST

(a)

0 5 10 15 2010−6

10−5

10−4

10−3

10−2

101

SNR

BE

R

VBLAST

Hybrid 1Hybrid 2

(b)

Fig. 10.8 Performance comparison of MIMO schemes with (a) three and (b) four transmitterantennas.

10.3.3 An Added Degree of Freedom

Once the operation of a MIMO system is adapted to provide gains of both diversityand multiplexing, the number of degrees of freedom is higher compared to classicalMIMO systems.

In this sense, if the possibility of exploiting a layered approach to achieve bothdiversity and multiplexing gains is considered, a MIMO system with Mt transmit-ter antennas can be divided into several combinations, with each such combination


being dependent on the criterion to be optimized and the conditions of the MIMOchannel experienced by the considered user.

This approach thereby offers an additional degree of freedom, namely the abilityto adapt between different structures. Clearly, the higher the number of transmitterantennas, the higher the flexibility of choosing different structures or the possiblecombinations of them.

This new free parameter can play a very important role when we consider thechannel information to perform transceiver optimization. This will be discussed indetail in the following section.

10.4 Link Adaptation in Multiple Signal Dimensions

In Section 10.4.1 the basic idea of link adaptation is presented, while the inclusion ofthe spatial dimension is described in Section 10.4.2. Section 10.4.3 presents aspectsrelated to OFDM and Section 10.4.4 includes the multiuser aspect to the problem oflink adaptation.

10.4.1 Fundamentals of Link Adaptation: Modulation and CodingSchemes

Due to the channel variation inherent to wireless systems, changing the transmissionparameters to match the current channel condition promotes a more efficient useof the available resources than just designing the system to function in a worst-case scenario. The collection of techniques that try to solve the problem of makingefficient use of (radio) resources is referred to as link adaptation (LA). As a moreexplicit example, the set of algorithms and protocols governing adaptive modulationand coding is often referred to as LA.

The main idea is that when the radio link is in a deep fade the system shouldadapt to a set of transmission parameters that increase reliability. On the other hand,when the channel condition is favorable the system should select a set of transmis-sion parameters that increase the data rate and therefore result in a higher spectralefficiency. Alternatively, in cases where power is a more important resource, thepower could be decreased when the channel condition is favorable and vice versa,while keeping the data rate constant.

10.4.1.1 Adaptive Modulation and Coding (AMC)

As an example of LA, adaptive modulation and coding (AMC) has been widely in-vestigated in the literature [9, 15, 17]. In fact, sometimes the terms “link adaptation”and “adaptive modulation and coding” are used interchangeably, but any parameterthat is limited and whose value influences system performance according to channel


condition can be considered for adaptation. Furthermore, it is even possible to adaptdifferent sets of parameters over different time scales.10.7

As an illustration, in Fig. 10.9 the various modulation and coding schemes(MCSs) for an enhanced data rate for GSM evolution (EDGE) system [2] areillustrated. The link adaptation is performed by changing the MCS according tothe carrier-to-interference ratio (CIR) so that the system “stays on the LA curve” tomaximize the throughput. Likewise, with the increased interest in MIMO strate-gies, the antenna elements used for MIMO transmission become important toadapt [12, 14] in such a way that a joint adaptation is performed over the modu-lation, coding and antenna scheme parameters.

Fig. 10.9 MCSs for an EDGEsystem.

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

MCS 1MCS 2MCS 3MCS 4MCS 5MCS 6MCS 7MCS 8MCS 9

LA

Thr

ough

put

(kbp

s)

C/I (dB)

MCSs for Link Adaptation in EDGE systems (3 km/h)

For a good performance of this LA process, it is necessary that the (estimated)rate of channel variation is known by the transmitter and this rate of variation inthe time and frequency domains will dictate how often the estimated informationmust be updated. Hence, if the channel is changing faster than it can be reliablyestimated and fed back to the transmitter, the adaptation will perform poorly [16].While the channel variation is not a problem for systems with low mobility, it canbecome a critical factor in systems with high mobility [26]. As an example, in HSPAsystems [10] the link adaptation takes place every 2 ms and, therefore, a channelquality indicator (CQI) must be fed back to the transmitter at least 500 times persecond.

10.4.1.2 Link Adaptation Criteria

Two important aspects may be highlighted in LA:

• The set of parameters that can be adapted• The optimization criteria and channel quality metrics used

10.7 For instance, some parameters could be adapted according to path loss and shadowing whileothers could be adapted according to fast fading.


Both of them vary according to the application, but the optimization criteria usuallyreflect a desire to increase the spectral efficiency.

As for metrics, the quality of the channel may be measured by the estimated SNRin the receiver, the idea is making the choice of the transmission mode based on theestimated SNR and the transmitter is assumed to have at its disposal a pre-definedtable containing the best transmission modes for each SNR interval. While the ideais simple, it has the practical limitation of requiring a good estimation of the SNRand good approximations of the BER for each scheme, which is not always a simpletask, especially in scenarios with interference.

Regarding the pre-defined table, the switching points from one mode to anotherare the crossing points in curves such as “BER versus SNR”, “Spectral Efficiencyversus SNR”, etc., as depicted in Fig. 10.10. That is, “choose the most spectrallyefficient mode if it has a BER lower than a specified threshold”.

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35 40

G2+1 with 4-PSKG2+1 with 16-QAM

VBLAST with 4-PSKVBLAST with 16-QAMVBLAST with 64-QAM

MCAS Performance

SNR

Spec

tral

Effi

cien

cy

Switching Points

Fig. 10.10 An example of a spectral efficiency versus average SNR curve for different modulationsand MIMO schemes.

Another metric that can be used for LA is based on the consecutive successor failure of transmissions. After a specific number of consecutive successfultransmissions, the transmission mode is increased.10.8 Besides the consecutive suc-cess transmission counter, the mode increase may also be triggered by a timecounter. This time counter is used for increasing the mode when a specified timeout

10.8 The transmission mode is increased in the sense that it is changed to a more spectral efficientone, while when it is decreased it is changed to a more robust one.


period has expired even if the success counter did not reach a specified threshold.This has been demonstrated to increase the system performance in a system withhigh load [6], since in this case the difficulties to reach the “increase mode thresh-old” are due to collisions instead of bad channel quality. That is, increasing thetransmission mode does in this case actually result in more successful transmissionsby reducing the probability of collisions due to the lowered transmission time.

Similarly, after a specific number of consecutive failed transmissions is reachedthe transmission mode is decreased. This method of LA is called automatic repeatfall-back.

In both of the previous cases, the optimized criterion is the capacity or, equiva-lently, the spectral efficiency. As a restriction, a minimum robustness is necessary toallow the usage of a given transmission mode. An alternative optimization criterioncan be the transmit power, that is, choosing the transmission mode that requires thelowest transmit power for the channel conditions, usually for a minimum throughputrestriction.

10.4.2 Adaptation Between Multiple MIMO Schemes

When the spatial dimension is added to the problem of LA the main idea of choosingthe best parameters is the same but the metric is different. To clarify this aspect,note that in Fig. 10.9 the modulation and coding rate were adapted according to themetric of C/I. With MIMO, using a metric such as SNR is not clear since for thesame channel condition the resultant SNR seen by the receiver (after decoding theinformation) is different according to which MIMO scheme was used.

In Fig. 10.10 the spectral efficiency versus SNR for different modulation andMIMO schemes in a curve that resembles Fig. 10.9 is shown. Note, however, thatwhile it seems that the situation “hasn’t changed”10.9 from the SISO case, manyimportant aspects of a MIMO system cannot be shown in this simple example inFig. 10.10. Other factors such as correlation among the transmitter and/or receiverantennas must be accounted for by a channel quality metric, since the SNR alonedoes not capture any ill-conditioning of the channel matrix.

An important metric that should be considered in the MIMO case is the condi-tion number of the correlation matrix of the channel H, which gives an insight intothe performance potential of the considered MIMO channel. For instance, when thechannel has a low rank, which usually represents a line-of-sight (LOS) scenario re-sulting in a high condition number, the user would be starved of diversity (multiplex)gain and an STBC (VBLAST) scheme is not appropriated, even if the SNR is low(high). In fact, it may even be better to fall back to the SIMO case to avoid dividingthe power among the transmitter antennas, instead of trying to extract a diversity(multiplex) gain that the correlated channel cannot provide.

10.9 The resulting throughput or spectral efficiency is plotted against a metric of C/I or SNR fordifferent parameter configurations and the one with highest spectral efficiency is chosen.


From [23, Chapter 4], the capacity of a MIMO channel in the absence of channelknowledge at the transmitter is given by

C = log2 det

(IMr +

Es

MtN0HHH

), (10.24)

where Es is the transmit power and N0 is the noise power spectral density.Equation (10.24) may then be used as a metric of the channel quality with the ad-vantage that the SNR and the condition number are taken into account implicitly.However, the capacity presents an upper bound on the throughput of the channeland does not cover any aspect of suboptimal decoding or STBC schemes that do notachieve the capacity bound in (10.24) [26].

The time variation of the channel is another important issue to be considered.Each MIMO scheme has some assumption of time period for which the channel isconsidered constant. Therefore, if the Doppler frequency is high a MIMO schemeoffering the potential for a high diversity gain may perform worse than a schemeoffering lower diversity gain, simply due to time variation of the channel.

Note also that while switching among different MCASs can provide extensiveperformance gains, the necessary rate of feedback information is larger than what isrequired when only MCSs are adapted. Therefore, the impact of this feedback mustbe observed on the overall system [18] and research on limited feedback strategiesis becoming even more relevant as discussed in Chapter 12.

10.4.3 Frequency Diversity: Link Adaptation for OFDM

OFDM is an important technique to transform a wideband frequency-selective chan-nel into several narrowband flat fading channels. In this sense, the spectrum is di-vided into N smaller portions called subcarriers. Again, we can profit from thisparameter to select the best way (according to some criterion) to use the systemresources. Hence, the link adaptation can be done separately for each subcarrier[19, 28, 29, 37] or for blocks of subcarriers. Each block is then either a group com-posed by consecutively located subcarriers or non-consecutively located subcarriers.This choice will depend on the process of allocation/assignment of the subcarriersfor the user.

In Fig. 10.11, a scheme with five subcarriers from the same user is illustratedwhere we can see the amplitude of subcarriers in time and frequency domains. Thetransmit parameters can then be adapted according to the channel variations in bothdomains.

While the use of OFDM increases the flexibility of LA, some drawbacks arisesuch as an increase in the amount of feedback information needed to perform therequired tasks for LA. If the link adaptation is executed per block of subcarriers,the system must consider metrics that represent the channel quality for all subcar-riers in a block. Obviously, link adaptation based on blocks requires less feedbackinformation than link adaptation based on individual subcarriers.


Fig. 10.11 An example ofamplitude variation in termsof time and subcarriers. Subcarrier

TimeA

mpl

itud

e

10.4.4 Multiuser Diversity: Channel-Aware Subcarrier Assignment

The overarching goal for link adaptation is to select the best set of transmissionparameters for a given user considering its channel conditions. Similar to that goal,channel-aware subcarrier assignments can be seen as selecting the best set of usersto allocate subcarriers according to their channel state information.

From the discussion in Section 10.4.3, the whole bandwidth may be allocated toonly one user, but in the present subcarrier assignment scenario, the whole band-width will be shared among all users. Each subcarrier (or each block of subcarriers)is allocated to only one user and since each user undergoes different fading con-ditions, the system may exploit this difference to obtain to a multiuser diversityby allocating the subcarrier to the “best user”. Following the idea of LA, the “bestuser” corresponds to the user with the best channel. In Fig. 10.12 the concept ofmultiuser diversity is illustrated where three different users experience differentchannel conditions and the “best user” choice is based on channel gain amplitude.For this specific example, the system throughput is maximized and it has a specialfeature where the system data rate is derived from the user’s best channel state ratherthan average one.

However, if the subcarrier assignment is just a part of a global resource allocationother metrics such as fairness must also be taken into account. Some cost functionsand optimization problems have been proposed in the literature [19, 28, 29, 37] inorder to assign subcarriers and to adapt link parameters.

In [28, 29], the main goal is to maximize system throughput while maintainingan acceptable BER. In these papers, adaptive modulation is used as a parameter inthe cost function thus taking into account user fairness and the type of used service(best effort).

As the subcarrier assignment is dependent on the current CSI, the amount ofrequired CSI is proportional to the number of users and subcarriers. When the uplinkand downlink channels use different frequency bands, like in FDD systems, the CSImust be reported to the transmitter and this feedback information becomes another


Fig. 10.12 An example ofa link adaptation using themultiuser diversity.

Am

plit

ude

Time

User 1User 2User 3

Best Channel

important topic of study [5, 37]. In TDD systems, having calibrated receive andtransmit RF branches, feedback information can be significantly reduced, as thebase station can predict the CSI from the uplink measures. In [37] a channel-awareALOHA-based assignment is proposed, where users send their CSI when they areabove a pre-defined threshold. Similarly, in [5], thresholds are defined and userswhich are above these thresholds are allowed to send CSI, where the main differencecompared to [37] is that in [5] thresholds are established for the employed resourceallocation algorithms.

10.5 Summary

Link adaptation is essentially a very useful feature to facilitate adaptation of thesystem parameters to the channel variations. Although modulation and coding arethe classical system parameters involved in link adaptation, the adaptation of thespatial dimension parameters resulting from the employment of multiple antennaelements for transmission and/or reception is a very active research area, the resultsfrom which are being exploited in the current and future generations of wireless sys-tems. The adaptation possibility of the frequency dimension parameters by meansof subcarrier assignment is another research area that continues to be developed.

In this chapter, the main solutions for the problem of link adaptation were dis-cussed. Both spatial and frequency dimensions were presented with their respectivebenefits and drawbacks. In Section 10.2.1, the discussions centered around the twomain gains provided with spatial dimension: spatial diversity, which improves linkreliability, and spatial multiplexing which increases the system spectral efficiency.The associated increase of the feedback signaling and the trade-off between diver-sity and multiplexing were also discussed.

Link adaptation using the frequency dimension was presented and a solution tak-ing advantage of the offered potential for multiuser diversity was described that


used subcarrier assignments on a per-user basis where the subcarriers were assignedaccording to the channel gain distribution over the population of users.

Future research efforts, relevant for the problem of multi-antenna link adaptation,are needed within the areas outlined below:

• Different antenna schemes present different resulting signal-to-noise-plus-interference ratio (SNIR), thus such a metric is not a unique option for the se-lection of the transmission modes to be chosen. Different criteria/metrics forswitching among the modes are then an open problem for LA when MIMO isconsidered.

• Regarding the selection of the transmission modes, it is still not clear how much,or what kind of, information is needed for performing a correct choice. This issuepoints to the problem of limited feedback information.

• When considering multiple dimensions, the granularity of the set of parametersallows the use of a high number of possibilities. However, the adaptation of pa-rameters may benefit from updates using different time scales for different pa-rameters. A possible solution would then define “fast” and “slow” adaptationprocedures for different sets of parameters. How to define those modes is still aquestion.

• The MIMO-OFDM system is a very rich environment due to the frequency andspace domains. Those domains can be employed to better exploit the conditionsof the channel when considering frequency and space diversities. This fact maylead us to a configuration of parameters which is different from one subcarrierto another. For instance, one subcarrier could better exploit the channel (moresuitable for transmission) using two antennas and another subcarrier using threeantennas. How can this scenario be managed?

• The increasing interest of distributed antenna systems captures also the atten-tion of resource allocation and LA. However, transmission modes, signaling, andwhat kind of metrics to be used are still not defined. This is also a foreseen re-search direction.

References

1. 3GPP: Performance evaluation of codebook-based precoding. Tech. rep., 3GPP, TSG RANWG1 #46 meeting R1-062208 (2006). URL http://www.3gpp.org

2. 3GPP: Radio link control/medium access control (RLC/MAC) protocol. Tech. rep., 3GPP,TS 44.060 V8.1.0 (2008). URL http://www.3gpp.org

3. 3GPP: Requirements for further advancements for E-UTRA (LTE-advanced) (release 8).Tech. rep., 3GPP. TSG RAN (2008). URL http://www.3gpp.org

4. Alamouti, S.: A simple transmit diversity technique for wireless communications. IEEEJournal on Selected Areas in Communications 16(8), 1451–1458 (1998)

5. de Araujo, C.A., Cavalcante, C.C., Freitas Jr., W.C.: Pre-processing effects for limited CSIfeedback in scheduling algorithms using cross-layer issues. In: Proceedings of the XXVBrazilian Telecommunications Symposium (SBrT2007). Recife, Brazil, vol. 1 (2007)

6. Bazzi, A., Diolaiti, M., Pasolini, G.: Link adaptation algorithms over IEEE8o2. 11WLANs in collision prone channels. In: IEEE 63rd Vehicular Technology Conference

http://www.3gpp.org

http://www.3gpp.org

http://www.3gpp.org


(VTC 2006-Spring), vol. 3, pp. 1176–1181. Melbourne, Vic. (2006). DOI 10.1109/VETECS.2006.1683020

7. Belrose, J.S.: A radioscientist’s reaction to Marconi’s first transatlantic experiment – revisited.In: IEEE Antennas and Propagation Society International Symposium, vol. 1, pp. 22–25.Boston, MA, USA (2001)

8. Biglieri, E., Caire, G., Taricco, G.: Limiting performance of block-fading channels with mul-tiple antennas. IEEE Transactions on Information Theory 47(4), 1273–1289 (2001)

9. Catreux, S., Erceg, V., Gesbert, D., Heath Jr., R.W.: Adaptive modulation and MIMO cod-ing for broadband wireless data networks. IEEE Communications Magazine 40(6), 108–115(2002). DOI 10.1109/MCOM.2002.1007416

10. Dahlman, E., Parkvall, S., Skold, J., Berming, P.: 3G Evolution HSPA and LTE for MobileBroadband. Elsevier, Oxford, UK (2007)

11. El-Atty, S.M.A., Skoutas, D.N., Rouskas, A.N.: Reducing CQI signalling overhead inHSPA. Research Letters in Communications, vol. 2008, Article ID 982805, 5 pages (2008).DOI 10.1155/2008/982805

12. Forenza, A., Pandharipande, A., Kim, H., Heath Jr., R.W.: Adaptive transmission scheme se-lection for mimo systems. In: Wireless World Research Forum (WWRF12). Toronto, Canada(2004)

13. Foschini, G.J.: Layered space-time architecture for wireless communications in a fading envi-ronment when using multiple antennas. Bell Labs Technical Journal 1(2), 41–59 (1996)

14. Freitas Jr., W.C., Cavalcanti, F.R.P., de Almeida, A.L.F., Lopes, R.R.: Exploiting dimensionsof the MIMO wireless channel: multidimensional link adaptation. In: IEEE 61st VehicularTechnology Conference (VTC 2005-Spring). Stockholm, Sweden, vol. 2, pp. 924–928 (2005).DOI 10.1109/VETECS.2005.1543441

15. Glisic, S.G.: Advanced Wireless Communications. Wiley, West Sussex, UK (2004)16. Goldsmith, A.: Wireless Communications. Cambridge University Press, New York, USA

(2005). DOI 10.2277/052183716217. Hanzo, L., Munster, M., Choi, B.J., Keller, T.: OFDM and MC-CDMA for Broadband Multi-

User Communications, WLANs and Broadcasting. Wiley, West Sussex, UK (2003)18. Heath Jr., R.W., Love, D.J.: Multimode antenna selection for spatial multiplexing systems with

linear receivers. IEEE Transactions on Communications 53(6), 962–968 (2005)19. Hottinen, A., Heikkinen, T.: Subcarrier allocation in a multiuser MIMO channel using

linear programming. In: Proceedings of 14th European Signal Processing Conference(EUSIPCO2006). Florence, Italy (2006)

20. Jeon, S.Y., Cho, D.H.: An enhanced channel-quality indication (CQI) reporting scheme forHSDPA systems. IEEE Communications Letters 9(5), 432–434 (2005)

21. Lo, T.K.Y.: Maximum ratio transmission. IEEE Transactions on Communications 47(10),1458–1461 (1999). DOI 10.1109/26.795811

22. Love, D.J., Heath Jr., R.W., Lau, V.K.N., Gesbert, D., Rao, B., Andrews, M.: An overviewof limited feedback in wireless communication systems. IEEE Journal on Selected Areas inCommunications 26(8), 1341–1365 (2008). DOI 10.1109/JSAC.2008.081002

23. Paulraj, A., Nabar, R., Gore, D.: Introduction to Space-Time Wireless Communications.Cambridge University Press, Cambridge, UK (2003)

24. Paulraj, A.J., Kailath, T.: Increasing capacity in wireless broadcast systems using distributedtransmission/directional reception (DTDR).URL http://www.freepatentsonline.com/5345599.html

25. Roh, J.C., Rao, B.D.: Multiple antenna channels with partial channel state information at thetransmitter. IEEE Transaction on Wireless Communications 3(2), 677–688 (2004)

26. Sandell, M.: Link adaptation for MIMO systems using reliability values. In: Wireless Com-munications and Networking Conference, 2006. WCNC 2006. IEEE, vol. 3, pp. 1608–1613.Las Vegas, NV, USA (2006). DOI 10.1109/WCNC.2006.1696528

27. Shannon, C.E.: A mathematical theory of communication. The Bell System Technical Journal27, 379–423, 623–656 (1948)

http://www.freepatentsonline.com/5345599.html


28. Song, G., Li, Y.G.: Cross-layer optimization for OFDM wireless networks – Part I: theoreticalframework. IEEE Transactions on Wireless Communications 4(2), 614–624 (2005)

29. Song, G., Li, Y.G.: Cross-layer optimization for OFDM wireless networks – Part II: algorithmdevelopment. IEEE Transactions on Wireless Communications 4(2), 625–634 (2005)

30. Tarokh, V., Jafarkhani, H., Calderbank, A.R.: Space-time block codes from orthogonal de-signs. IEEE Transactions on Information Theory 45(5), 1456–1467 (1999). DOI 10.1109/18.771146

31. Tarokh, V., Naguib, A., Seshadri, N., Calderbank, A.R.: Combined array processing and space-time coding. IEEE Transactions on Information Theory 45(4), 1121–1128 (1999)

32. Tarokh, V., Naguib, A., Seshadri, N., Calderbank, A.R.: Space-time codes for high data ratewireless communication: performance criteria in the presence of channel estimation errors,mobility, and multiple paths. IEEE Transactions on Communications 47(2), 199–207 (1999).DOI 10.1109/26.752125

33. Tarokh, V., Seshadri, N., Calderbank, A.R.: Space-time codes for high data rate wireless com-munications: performance criterion and code construction. IEEE Transactions on InformationTheory 44(2), 744–765 (1998). DOI 10.1109/18.661517

34. Telatar, I.E.: Capacity of multi-antenna gaussian channels. European Transaction on Telecom-munications 10, 585–595 (1999). DOI 10.1002/ett. 4460100604

35. Visotsky, E., Madhow, U.: Space-time transmit pre-coding with imperfect feedback. IEEETransactions on Information Theory 47(6), 2632–2639 (2001)

36. Vu, M., Paulraj, A.: On the capacity of MIMO wireless channels with dynamic CSIT. IEEEJournal on Selected Areas in Communications 25(7), 1269–1283 (2007)

37. Xue, Y., Kaiser, T., Gershman, A.B.: Channel-aware ALOHA-based OFDM subcarrier as-signment in single-cell wireless communications. IEEE Transactions on Communications 55,953–962 (2007). DOI 10.1109/TCOMM.2007.896071

38. Zheng, L., Tse, D.N.C.: Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels. IEEE Transactions on Information Theory 49(5), 1073–1096 (2003). DOI10.1109/TIT.2003.810646

Documents

Optimizing Wireless Communication Systems Volume 1033 ||