On the Applicability of MIMO Principle

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530 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 57, NO. 2, FEBRUARY 2009

On the Applicability of MIMO Principle to10-66GHz BFWA Networks: Capacity

Enhancement through Spatial Multiplexing and

Interference Reduction through Selection DiversityKonstantinos P. Liolis, Student Member, IEEE, Athanasios D. Panagopoulos, Member, IEEE,

Panayotis G. Cottis, and Bhaskar D. Rao, Fellow, IEEE

AbstractThis paper investigates the applicability of multiple-input-multiple-output (MIMO) technology to broadband fixedwireless access (BFWA) systems operating in the 10-66GHzfrequency range. In order to employ the MIMO principle atthese frequencies, the spatial channel benefits that may arisefrom the rainfall spatial inhomogeneity are more relevant since

multipath is insignificant. Therefore, a special MIMO/BFWAchannel may be implemented if every subscriber is equippedwith multiple antennas and communicates with multiple basestations. The exact relationship between conventional MIMO andthe proposed 10-66GHz MIMO/BFWA channels is established.Then, emphasis is put on two different topics from the field ofMIMO applications: (i) capacity enhancement for spatial multi-plexed MIMO/BFWA systems; and (ii) interference reduction forMIMO/BFWA diversity systems employing receive antenna selec-tion. More specifically, in the first case, a communication-orientedsingle-user capacity analysis of a 2 2 MIMO/BFWA spatialmultiplexing system is presented, the relevant optimal powerallocation policy is explored and useful analytical expressions arederived for the outage capacity achieved in the asymptoticallylow and high SNR regions. The effect of feedback on the capacityis investigated and quantified through Monte Carlo simulations.In the second case, a 2 2 MIMO/BFWA diversity system withreceive selection combining is considered and its efficiency tomitigate intrasystem/intersystem cochannel interference over thedownstream channel is studied from a propagation point ofview. A general analytical prediction model for the interferencereduction obtained by such a 22 MIMO/BFWA diversity systemis presented along with a numerical validation.

Index TermsBroadband fixed wireless access (BFWA),cochannel interference, multiple-input-multiple-output (MIMO),outage capacity, rain fading, selection diversity, spatial multiplex-ing, WiMAX.

Paper approved by A. Lozano, the Editor for Wireless Network Accessand Performance of the IEEE Communications Society. Manuscript receivedAugust 22, 2006; revised February 16, 2007. 50% of this work was supportedby UC Discovery grant nos. Cor02-10109 and Com04-10176.

K. P. Liolis was with the Digital Signal Processing Laboratory, Departmentof Electrical and Computer Engineering, University of California, San Diego(UCSD), La Jolla CA 92093-0407 USA. He is now with the Wireless & Satel-lite Communications Group, School of Electrical and Computer Engineering,National Technical University of Athens (NTUA), 9 Iroon Polytechniou Street,Zografou, Athens 15780, Greece (e-mail: [email protected]).

A. D. Panagopoulos and P. G. Cottis are with the Wireless & SatelliteCommunications Group, School of Electrical and Computer Engineering,National Technical University of Athens (NTUA), 9 Iroon Polytechniou Street,Zografou, Athens 15780, Greece (e-mail: [email protected]).

B. D. Rao is with the Digital Signal Processing Laboratory, Departmentof Electrical and Computer Engineering, University of California, San Diego(UCSD), La Jolla CA 92093-0407 USA.

Digital Object Identifier 10.1109/TCOMM.2009.02.060474

I. INTRODUCTION

BROADBAND fixed wireless access (BFWA) is employedfor the transmission of a plethora of high data rate

multimedia and IP services to stationary users over distances

of several km. It is a competitive alternative to relevantwireline technologies, such as digital subscriber line (xDSL)

and cable, and a promising, cost-effective solution to the socalled last-mile problem [1]. Recently, BFWA systems have

evolved and matured to the degree of being standardized by

the IEEE 802.16 Working Group in the U.S. as well as by

the ETSI HiperMAN Committee in Europe. On top of that,

the WiMAX forum was established to promote and certify

interoperable products based on the standards addressing the2-11GHz [2] and 10-66GHz [3] frequency ranges.

For the past decade or so, multiple-input-multiple-output(MIMO) wireless communication systems have received much

attention due to their promise of significantly higher data rates

compared to their single antenna counterparts at no cost of

extra transmit power and frequency spectrum [4], [5]. So far,

research on MIMO technology and, specifically, on its appli-

cability to BFWA systems has been mostly concerned with the

sub-11GHz band [1], [2] where the propagation conditions are

such that channel spatial multiplexing/selectivity is feasible.

Propagation phenomena in the 10-66GHz frequency range

are quite different than those encountered in the 2-11GHzrange. At frequencies above 10GHz, line-of-sight (LOS) be-

tween the base station (BS) and subscriber station (SS) is

deemed a practical necessity and higher antenna directivities

are exploited at the SS [6]. Multipath is insignificant, while

attenuation from atmospheric precipitation is more important.Rainfall is the dominant fading mechanism and exhibits sig-nificant spatial inhomogeneity within the distances of interest.

Although multipath is negligible, this paper investigatesthe applicability of MIMO technology to 10-66GHz BFWA

systems and proposes two different system architectures,

which promise significant performance gains over the rele-

vant single-input-single-output (SISO) cases. A key feature

of conventional MIMO systems operating below 10GHz is

their ability to turn multipath, normally a pitfall of wireless

transmission, into a benefit for the user. Multipath makes the

channel spatially selective [5]. At frequencies above 10GHz,

the required channel separability might arise from the spatial

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LIOLIS: ON THE APPLICABILITY OF MIMO PRINCIPLE TO 10-66GHZ BFWA NETWORKS 531

structure of the rainfall medium, if the BFWA network is

deployed in an analogous way to a generalized cell site

diversity system [7][14]. Cell site diversity is an efficientrain fade mitigation technique, which results in an inherent

waste of spectrum since the same amount of bandwidth should

be allocated to both BSs associated in order to implement

the switchover. However, the gains in terms of drastically

improved availability and coverage achieved when applied in a

BFWA system justify its use [7][14]. In the present paper, thegeneralized structure of a BFWA cell site diversity scheme is

considered to form a special MIMO communication channel.

Therefore, if every SS is equipped with multiple antennas and

communicates with multiple BSs, which subtend a large angle

to the SS, so that the spatial correlation due to rain is as lowas possible, a special MIMO/BFWA communication channel

is formed. The established multiple spatial sub-channels be-tween the transmitter and the receiver exhibit relatively low

correlation (ideally being independent), the resulting MIMO

channel becomes spatially selective and, hence, MIMO can be

considered to effectively exploit rainfall spatial inhomogeneity,

as well.In this paper, the differences between conventional MIMO

and the proposed 10-66GHz MIMO/BFWA channels are

demonstrated and their exact relationship is established. Then,

by drawing on the vast body of available MIMO literature,

emphasis is put on two different topics from the field of MIMO

applications to 10-66GHz BFWA networks:

(i) Capacity enhancement for spatial multiplexed

MIMO/BFWA systems;

(ii) Interference reduction for MIMO/BFWA diversity

systems employing receive selection combining.

In the first case, attention is paid particularly to the single-

user capacity analysis of 2 2 MIMO/BFWA spatial multi-plexing systems. By properly modifying well-known capacity

formulas available in the MIMO literature [15], [16], useful

results for the outage capacity of the 10-66GHz MIMO/BFWA

systems are derived. The cases when the instantaneous channelis known or unknown at the transmit side are examined and

the effect of feedback on the capacity is investigated. Optimal

transmit power allocation policy along the spatial sub-channelsis also investigated, and analytical closed form expressions for

the outage capacity achieved in the asymptotically low andhigh SNR regions are also obtained.

In the second case, a 2 2 MIMO/BFWA diversity sys-tem employing receive antenna selection is considered, andinterference related issues are addressed from a propagationpoint of view. To this end, note that antenna selection is

a standard MIMO technique used to alleviate the high cost

and complexity associated with multiple RF chains while

retaining the potential MIMO performance gains [5]. Empha-

sis is put specifically on intrasystem/intersystem cochannel

interference (CCI) arising over the downstream channel of

such a 2 2 MIMO/BFWA system due to differential rainattenuation related to an adjacent BS [17]. These problems

are further aggravated due to the spatial inhomogeneity of

rainfall and constitute typical interference scenarios of rather

practical interest [18]. By applying selection combining atthe SS receiver, the proposed MIMO/BFWA system is shown

able to significantly mitigate CCI. An analytical prediction

model for the signal-to-interference ratio (SIR) improvement

achieved in the MIMO case with respect to the SISO one is

presented.In both the capacity and interference analyses presented

here for the respective MIMO/BFWA systems, the general

case of an ordered MIMO channel is successfully taken into

account. An analytical physical MIMO channel model is

assumed which effectively incorporates the rain fading effects.

This model is based on general assumptions about the rainprocess [8], [17], has inputs from the ITU-R rainmaps [19]

and, therefore, is flexible and can be applied on a global

scale. Thus, the capacity analysis for spatial multiplexed

MIMO/BFWA systems in this paper extends the work pre-

sented in [14], where the isomorphism between conventionalMIMO and BFWA cell site diversity channels was initially

addressed and primitive capacity results based on empirical

data appropriate only for balanced BFWA cell site diversity

channels were provided. Furthermore, the possible capacity

gain due to feedback is examined here. Useful analytical

closed form expressions for the outage capacity achieved in the

asymptotically low and high SNR regions are derived whichare extremely hard to obtain even in the well-established field

of MIMO theory [5]. Regarding the MIMO/BFWA selection

diversity systems under consideration, to the authors best

knowledge, the presented propagation-based interference anal-ysis is quite different than the conventional communication-

oriented approaches used in standard MIMO theory and is theonly analytical work reported up to now in the field of the

isomorphic BFWA cell site diversity systems. So far, most of

the available literature related to cell site diversity has ignored

interference related issues and focused only on the calculation

of SNR increase. In this regard, several prediction models,

both empirical (based on experimental propagation campaigns)[7], [10][12] and physical (based on general assumptions

about the rain process) [8], [9], have been proposed for the

characterization of the spatial correlation due to rain, as well.

The only work dealing with the possible SIR increase in a

cellular BFWA system employing cell site diversity is reportedin [13] and is based, however, on simulation results applicable

to a certain system case study.The rest of this paper is organized as follows. Section II

presents the MIMO/BFWA channel model assumed. Section

III provides a communication-based single-user capacity anal-

ysis for a spatial multiplexed 2 2 MIMO/BFWA system.An analytical propagation prediction model for the SIR im-

provement achieved in a 22 MIMO/BFWA diversity systememploying receive selection combining with respect to the

conventional SISO system is presented in Section IV. Useful

numerical results, obtained through Monte Carlo simulationsand analytical expressions for the outage capacity achieved in

the spatial multiplexing MIMO case and through the presented

analytical propagation model for the SIR enhancement in the

selection diversity MIMO case, are provided in Section V.

Conclusions are drawn in Section VI.

II. MIMO/BFWA CHANNEL MODEL

Fig.1 depicts the configuration of the downlink of a 2

2MIMO/BFWA channel. The interference scenario assumed is

illustrated, as well. The fixed SS is equipped with two highly


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Fig. 1. Downstream channel of a 22 MIMO/BFWA system and interferencescenario assumed. Base stations BS1 and BS2 transmit either independent data

streams (that is, MIMO spatial multiplexed system) or the same signal over themultiple (ideally) independent fading paths (that is, MIMO diversity system).

directive antennas (see Table I) and communicates with two

base stations, BS1 and BS2, subtending an angle to SS. is relatively large, so that the spatial correlation due torain is as low as possible. The length of each BSi-SS link

(i = 1, 2) is denoted by Li and the random variable (RV)associated with the rain attenuation induced along each path,

expressed in dB, is denoted by ARi. Regarding the interferencescenario under consideration, another BS (denoted by BS3),

which may belong to either the same or to a different BFWA

system, is located at a distance L3 from the SS and shares thesame frequency band with BS1 and BS2. Thus, intrasystemor intersystem CCI is created on the downlink of the 2 2MIMO/BFWA channel. BS1 and BS3 subtend an angle tothe SS. The RV associated with the rain attenuation on the

interfering path BS3-SS, expressed in dB, is denoted by AR3.Assuming that clear LOS exists between the SS and each

wanted BSi (i = 1, 2) and that the rain attenuation is the majorfading mechanism, the path gain for the BSi-SS link (i = 1, 2)is modeled as

gi L2i 10ARi/10 (i = 1, 2) (1)

That is, the total path loss along each wanted link BSi-SS

(i = 1, 2), expressed in dB, is

Ai = F SLi + ARi (i = 1, 2) (2)

where F SLi = 10log10 (4Lif /c)2

is the free space loss

along each link, c is the speed of light and f is the operat-ing frequency. The fundamental assumptions concerning the

modeling of the rain attenuation RVs ARi (i = 1, 2, 3) arethose analytically given in Appendix I. Of particular interest in

the present analyses is the lognormal distribution assumption

for the rain attenuation RVs, which is unconditional (that is,

both rainy and non-rainy periods are taken into account), andthe modeling of the spatial correlation coefficient due to the

rainfall medium ij ((i, j) = (1, 2) , (1, 3) , (2, 3)).

TABLE ISUBSCRIBER STATION ANTENNA GAI N ACCORDING TO ETSI [21]

Angle relative to the antennaboresight (deg)

SS antenna gain relativeto the maximum (dB)

00

02

71-8

22-03

03-09

53-00104-081

Under the above assumptions together with the assumption

about frequency-flat fading, the resulting 22 MIMO/BFWAchannel matrix H is modeled as

H =

g1 exp(j1) 0

0

g2 exp(j2)

(3)

where l (i = 1, 2) are assumed uniformly distributed over[0, 2).

In (3), H is diagonal1 due to the high directivity of the

SS antennas (see Table I) and to the large enough angular

separation . Thus, the number of available paths betweenthe transmit and receive sides is limited to m, whereas in theconventional MIMO case, where the SS is usually equipped

with omnidirectional antennas and rich scattering environment

is assumed, it can be at most m2 resulting in higher diversitygain [4], [5]. Furthermore, the iid assumption of independent

identically distributed elements of H, often made in the

conventional MIMO case [4], [5], does not hold here. Instead,

there is relatively high spatial correlation due to the rainfallmedium. Moreover, since, in general, BS1 and BS2 are located

at different distances Li from the SS, the total path losses

Ai(i = 1, 2) along each BSi-SS link are not the same and,therefore, H is not normalized (that is, ordered MIMO system)

as usually assumed in the standard MIMO theory [4], [5].

The different path lengths Li(i = 1, 2) introduce alsoa propagation delay offset which, consequently, leads to

an asynchronism problem. This is an inherent problem ofdistributed communication systems, in general, and certainly

is not the case in conventional MIMO systems, where the

multiple transmit and receive antennas are collocated at the

transmitter and the receiver, respectively, and thus, the multiple

transmitted signals are simultaneously received [4], [5]. Sofar, the asynchronism problem has been treated mainly in

the context of distributed MIMO networks. Furthermore, evenin the extreme and much more challenging case of mobile

multi-satellite MIMO networks where the delay difference

is much larger and more variable, practical solutions to the

asynchronism problem have been proposed in the literature,

such as in [20]. More specifically, according to [20], matched

filters are first applied to the received signals for the detection

of the propagation delay offset, which is then fed to a timing

aligner. Subsequently, the proposed timing aligner eliminates

the delay offset by adjusting the timing of a signal parallel-to-serial converter. Therefore, it is feasible to tackle with and

solve the asynchronism problem at a cost of reasonably higher

1MIMO channels with diagonal channel matrix H are usually termed inthe MIMO literature as MIMO parallel channels [16].


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implementation complexity at the receiver. In the special

MIMO/BFWA channel under consideration, the delay offset

is reasonably fixed and the resulting asynchronism problemis assumed to be properly estimated at the SS receiver. This

rather practical issue, which addresses mainly the SS receiver

implementation, is out of the scope of the present paper and,

certainly, does not retract the detailed analyses and results

presented hereafter.

Although this work does not go into further details, it isworthwhile noting that the use of interference cancellation

techniques2 at the SS receiver can allow for smaller directivity

of the SS antennas and/or for closer placement of the BS1and BS2 with respect to the SS (that is, smaller angular

separation ). In either case, mutual self interferencebetween BS1 and BS2 is introduced at the MIMO channel, the

channel matrix H becomes non-diagonal and the interference

cancellation technique implemented at the SS receiver aimsto remove the non-diagonal components from the reference

transmitted signals. A similar analysis has been presented in

[20] concerning a 2

2 MIMO satellite network3 and its

application to the relevant terrestrial MIMO/BFWA case isleft for future work.

III. CAPACITY ENHANCEMENT IN SPATIAL MULTIPLEXED

MIMO/BFWA SYSTEMS

In this section, the interference problem depicted in Fig.1 is

not examined and emphasis is put particularly on the single-

user capacity enhancement achieved by a spatial multiplexed

2 2 MIMO/BFWA system. The two individual base stationsBS1 and BS2 in Fig.1 transmit independent data streams (that

is, spatial multiplexing [4], [5]). The channel matrix H is

assumed to be perfectly known to the SS receiver. At thetransmit side, both BS1 and BS2 are assumed either to haveperfect instantaneous channel knowledge (that is, channel

known (CK)) or to know only the long term rain fading

statistics (that is, channel unknown (CU)).4 In the latter case,

no communication between the two BSs is necessary, whereas

in the former one, communication between the BSs is required

for the optimal power allocation to the two sub-channels. This

communication is analogous to that between the BSs and

the mobile switching center in a conventional mobile cellular

communication system and can be realized through wired or

wireless links operating at a different frequency. Moreover,

feedback links between the SS and each BS i (i = 1, 2) shouldbe established, so that instantaneous channel state information

(CSI) becomes available at the transmit side. This resultsin higher system complexity. Therefore, for reasons related

to cost and practical implementation issues, the applicability

of the CK case is likely to be limited, unless a significant

capacity increase may be achieved through feedback. This

paper intends to provide insight in this regard.

2For instance, a possible interference cancellation technique can be eithera simple MMSE or a more advanced MMSE-SIC or Turbo-IC processing atthe receiver.

3The reference MIMO satellite system in [20] also serves to indicate the

use of MIMO in a non-traditional setting, that is, other than cellular or WLANscenario and, in that sense, is relevant to the work presented here.4Similar assumption on the CU case has also been made in [16].

Although H is random, the capacity of a sample channel

realization is first studied, that is, H is considered to be

deterministic. It is well known that capacity is achieved withGaussian code books, that is, the zero-mean 2 1 transmittedsignal vector s is a circularly symmetric complex Gaussian

vector [16]. The corresponding mutual information (in b/s/Hz)

for s having a covariance matrix Rss is given by

I = log2 detI2 + PT2N0

H Rss HH (4)and the capacity of the MIMO channel (in b/s/Hz) follows as[16]

C = maxRss

log2 det

I2 +

PT2N0

H Rss HH

(5)

In the equations above, the maximization is performed over all

possible input covariance matrices satisfying trace (Rss) =m = 2, I2 is the 2 2 identity matrix, PT is the totalaverage power available at the BSs transmitters, N0 is thenoise spectral density at the input of the SS receiver and the

superscriptH

denotes conjugate transposition.Eq. (5) gives the capacity of the deterministic 2 2 MIMO

channel matrix H. However, since rainfall introduces slow

fading into the channel, a useful statistic to characterize the

resulting fading channel is the outage capacity defined as [4]

P(C Cout,q ) = q (6)where Cout,q is the information rate guaranteed for(1 q)100% of the channel realizations.

A. Instantaneous Channel Unknown at the Transmit Side (CU)

Based on the standard MIMO theory for conventional

MIMO systems, in the absence of instantaneous CSI at thetransmitter, it is reasonable to choose s to be spatially white,that is, Rss = I2. This implies that the transmitted signalsare independent and equi-powered. The capacity of MIMO

channels (in b/s/Hz) achieved with this covariance matrix is

given by [15], [16]

CCU = log2 det

I2 +

PT2N0

HHH

=2

i=1

log2

1 +

PT2N0

i

(7)

where i(i = 1, 2) are the positive eigenvalues of the matrixHH

H. However, in the special MIMO/BFWA case examined

in this work, the two spatial sub-channels do not experience

the same path loss due to unequal path lengths Li(i = 1, 2).Therefore, power should not be equally allocated to the

two sub-channels but should be determined according to the

SNR on each link. Hence, a reasonable choice for the input

covariance matrix is

Rss =

p 00 2p

(8)

where p reflects the transmit power to the strongest sub-channel (strong eigenmode) (for example, the BS1-SS link if

L1 L2) and is a function of the nominal SNR values underclear sky conditions, SN RCS i (i = 1, 2). Based on the path


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gain model in (1), the SN RCS i (i = 1, 2) values, expressedin dB, are related through

SN RCS1 SN RCS2 = 20 log10 (L2/L1) (9)By properly modifying (7), p can be determined as a solutionto the following optimization problem for the ergodic capacity

CCU = max0p2

E

1 log

21 +p PT2N0 1+

E2

log2

1 + (2 p) PT2N0 2

(10)

where Ei [] denotes the expected value with respect tothe RV i(i = 1, 2). The expectation operation in (10) isperformed over long term periods including both raining and

non-raining events and, thus, justifies the channel unknown

assumption made here [16]. Moreover, the unconditional log-

normal distribution (that is, including both raining and non-

raining time) for the rain attenuation RVs ARi(i = 1, 2) isadopted here (see Appendix I). Therefore, the averaged values

in (10) refer to both rainy and clear sky conditions and so, the

ergodic capacity expressed there covers both the rainfall andthe clear-sky channel states.

In the equal link length case, the solution to the constrainedoptimization problem in (10) reduces to the already known

solution related to (7) [15], [16]. In the more general case

of L1 < L2 assumed here, the problem can only be solvednumerically over the whole SNR range. Ifpopt is the solutionto (10) and the assumptions about channel modeling are taken

into account, the instantaneous capacity achieved is given by

Eq. (11), see top of next page.

In the special cases of asymptotically low and asymptoti-

cally high SNR, analytical solutions to (10) can be derived (see

Appendix II). For low SNR values, it is shown that the totaltransmit power is exclusively allocated to the strongest sub-

channel (that is, popt = 2), whereas for high SNR values, thetotal transmit power is equally allocated to each sub-channel

(that is, popt = 1). Based on these analytical solutions to (10)and the channel modeling assumed, useful analytical closedform expressions for the outage capacity of the fading MIMO

channel H can be obtained for the special cases of asymp-

totically low and high SNR. Considering the transformation

given in (34), which relates the lognormal rain attenuation

RVs ARi to the normalized normal RVs ui(i = 1, 2), and aftersubstitution of (11) into (6) and some straightforward algebra,

the following expressions for the outage capacity achieved in

the asymptotically low and high SNR regions are obtained,respectively by Eqs. (12) and (13) at the top of the next page,

where erfc () is the complementary error function, fU1 (u1)is the normal density function, and uA, uB are analyticallygiven by Eqs. (14) and (15) (see next page). The rest of the

parameters encountered in (12)(15) are analytically given inAppendix I.

B. Instantaneous Channel Known at the Transmit Side (CK)

If the instantaneous channel is known at the BSs transmit-

ters, the transmit power can be optimally allocated to thetwo parallel spatial modes via the waterfilling algorithm

[16] so as to maximize the mutual information I and achieve

the capacity C. Taking the previous assumptions about chan-nel modeling into account and applying the waterfilling

solutions opti (i = 1, 2), the following expressions for theinstantaneous capacity achieved are obtained

CCK =

2i=1

log2

1 + opti

PT2N0

l

=2

i=1

log2

1 + 0.5 opti SN RCS i 10AmR2/10

(16)

Since the waterfilling solutions are complicated non-linear

functions of i (i = 1, 2), the distribution of the CCK isintractable. Thus, an analytical closed form expression for the

outage capacity of the fading MIMO channel H is hard to

obtain, even in the special cases of asymptotically low and

high SNR. Nevertheless, CCK can be simulated for any givenchannel realization H and the corresponding outage capacitycan be numerically computed for any channel.

IV. SIR IMPROVEMENT IN SELECTION DIVERSITYMIMO/BFWA SYSTEMS

In this section, the interference scenario depicted in Fig.

1 is considered and the possible SIR increase offered by a

MIMO/BFWA diversity system with receive antenna selection

is studied from a propagation point of view. The two individual

base stations BS1 and BS2 in Fig.1 are assumed now to

transmit the same signal over the (ideally) independent fading

paths BSi-SS (i = 1, 2) (that is, diversity [4], [5]). To alleviatethe high cost and complexity associated with multiple RF

chains, the dual-antenna SS receiver is equipped with onlyone RF chain, and performs antenna selection [5]. Therefore,

the SS receiver chooses the path with the highest SNR andperforms detection based on the signal from the selected path

(that is, selection diversity or else selection combining).

Regarding the interference analysis, rainfall is taken into

account. In this respect, the signal leakage due to differential

rain attenuation (DRA) from the adjacent BS3 is considered to

be the dominant cause of the SIR degradation [17]. It is shown

that selection combining employed at the dual antenna SS

receiver makes the proposed MIMO/BFWA diversity system

able to significantly mitigate CCI arising over the downstream

channel. The SIR improvement achieved in the 2 2 MIMOcase with respect to the SISO one is quantified through the

analytical prediction model presented hereafter.Due to selection combining at the dual antenna SS receiver,

the minimum total path loss Ai along each wanted link BSi-SS (i = 1, 2) determines the output of the combiner at everyinstant. The system becomes unavailable whenever A1 > Mand A2 > M, where M is the diversity system margin asdetermined in [8]. The event related to the MIMO diversity

system availability is mathematically expressed as

= (min {A1, A2} < M) (17)However, due to selection diversity, it is clear that

= 1 21 2 = (18)


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CCU = log2

1 + 0.5 popt SN RCS1 10AR1/10

+ log2

1 + 0.5 (2popt) SN RCS2 10AR2/10

(11)

P (CCU Cout,q ) = 12

erfc

(ln

10log10

SN RCS12Cout,q1

ln (AmR1))/

2SaR1

= q (12)

P(CCU Cout,q ) = 12

+uA

du1fU1 (u1) erfc

uB n12u1

2 (1 2n12)

= q (13)

uA =

ln

10log10 (0.5 SN RCS2) 10log10

2Cout,q 1 ln (AmR2) /SaR2 (14)

where

i = (Al < M, Ai < Aj ) ((i, j) = (1, 2) , (2, 1)) (19)

is the event that the SS is serviced by BSi (i = 1, 2). Therefore

P() = P(1) + P(2) (20)

Taking the previous assumptions about channel modelingand the interference scenario depicted in Fig.1 into account,

the SIR ratios under rain fades SI Ri(i = 1, 2) are expressed(in dB) by

SI Ri = SI RCS i ARi + AR3 (21)

where SI RCS i(i = 1, 2) are the nominal SIR values underclear sky conditions being analytically given by

SI RCS i = SI Ri GR (i) (i = 1, 2) (22)

In (22), GR () is the assumed normalized directional gain ofthe SS antennas according to the ETSI standard [21] given

in Table I, and i(i = 1, 2) are the off-axis angles in theradiation pattern of the SS antennas, formed by the interfering

and the wanted links. From Fig.1, it follows that 1 = and2 = . SI Ri (i = 1, 2) are the relevant SIR valuesof the interfered links BS1-SS and BS2-SS when i = 1

0, and

correspond to the nominal CCI levels. Their interrelationship

for i = 1, 2 is defined through (9) by simply interchangingthe SI RCS i and SI Ri .

In (21), the difference ARi AR3(i = 1, 2) is known asDRA [17]. The SIR is a random process due to the spatial

inhomogeneity of the rainfall medium. When DRA becomes

sufficiently large, severe CCI problems may arise aggravating

the SIR distribution. To deal with the statistical behavior of

the SIR, the Acceptable Interference Probability (AIP) [22],

[23] is introduced, which, in the light of the considerations of

the present analysis, is expressed as

AIP = P (SIR < r, ) = P (SI R1 < r, 1)

+ P (SI R2 < r, 2) = P1 + P2 (23)

In (23), r (in dB) is the non-exceedance level of the SIR at thereceiver input of the SS. r and AIP constitute a pair of usefuldesign specifications concerning interference. Every user mustcomply with these specifications, given the quality of service

(QoS) related to the system availability event .Considering the transformation given in (34), which relates

the lognormal rain attenuation RVs ARi to the normalizednormal RVs ui(i = 1, 2, 3), and the channel model assumed,the probabilities Pi(i = 1, 2) encountered in (23) after somestraightforward algebra are expressed as

Pi =

uDiuCi

du1

+u1

du2fU1U2 (u1, u2)

1 1

2erfc

uEi 3/1,2

23/1,2

(i = 1, 2) (24)

where fU1U2 (u1, u2) is the two-dimensional normal jointdensity function.

For i = 1, 2, the rest of the parameters encountered in (24)are (see next page for Eqs. (26) and (28)).

uCi = [ln (xi) ln (AmRi)] /SaRi (25)

uDi = [ln (M F SLi) ln (AmRi)] /SaRi (27)Furthermore, the statistical parameters 3/1,2 and 3/1,2 are

the parameters of the conditional distribution of the normal

RV 3 given the other two 1, 2, and their analytical

uB = ln(10log10 (0.5SN RCS1) + 10 log10

1 + 0.5SN RCS2 10AmR2 exp(u1SaR2)/1010log10 2Cout,q 1 0.5SN RCS2 10AmR2 exp(u1SaR2)/10 ln (AmR1) /SaR1 (15)


7/12


xi =

0 r > SIRCS iSI RCS i r SIRCS i + F SLi M < r SI RCS iM F SLi r SI RCS i + F SLi M

(26)

uEi = [ln(exp (ui SaRi) AmRi SI RCS i + r) ln (AmR3)] /SaR3 (28)

TABLE IIRAI N ATTENUATION DISTRIBUTION PARAMETERS

Atlanta,GA

f=25GHz

(L1,L2)=(3,4)km

L3=5km

Atlanta,GA

f=25GHz

(L1,L2)=(3,3)km

L3=5km

Atlanta,GA

f=42GHz

(L1,L2)=(3,4)km

L3=5km

Singapore

f=25GHz

(L1,L2)=(3,4)km

L3=5km

(1 1

,m aR RA S ) (0.0130, 2.0179) (0.0131, 2.0179) (0.0845, 1.7429) (0.0612, 1.7587)

(2 2

,m aR RA S ) (0.0183, 1.992) (0.0131, 2.0179) (0.1186, 1.7133) (0.0859, 1.7292)

(3 3

,m aR RA S ) (0.0239, 1.9679) (0.0239, 1.9679) (0.1551, 1.6867) (0.1124, 1.7028)

12 (=50o) 0.7076 0.7443 0.7076 0.7076

12 (=90o) 0.5651 0.5994 0.5651 0.5651

12 (=100o) 0.5423 0.5759 0.5423 0.5423

expressions in terms of the logarithmic correlation coefficients

nij ((i, j) = (1, 2) , (1, 3) , (2, 3)) (see Appendix I) can befound in [23].

The analytical prediction model presented above for the SIR

improvement can also be applied in cellular configurations

commonly assumed for BFWA networks [24]-[26]. In fact,multi-user interference analyses based on the AIP consid-

eration and concerning SISO/BFWA systems with cellularstructure have been performed by the authors in [22] and

[23], which deal with the CDMA- and the TDMA-based

versions of the same BFWA system, respectively. The presentanalysis has been performed for the single-user scenario of the

proposed 2 2 MIMO/BFWA diversity system. However, itsincorporation in multi-user scenarios such as that considered

in [22], [23] is feasible but out of the scope of this paper.

V. NUMERICAL RESULTS AND DISCUSSION

The analyses presented have been applied for the predic-

tion of possible capacity improvement and SIR improvement

achieved by the proposed 2 2 MIMO/BFWA spatial multi-plexing and selection diversity systems, respectively, over therelevant SISO cases. Depending on the simulation scenario

assumed, the 2 2 MIMO/BFWA channel operates at either25GHz or 42GHz, and is located in either Atlanta, GA or Sin-

gapore, where different rain climatic conditions are observed.

The lognormal statistical parameters AmRi, SaRi(i = 1, 2, 3)along with the spatial correlation coefficient due to rainfall 12(see Appendix I) concerning the rain attenuation distribution

for the cases examined are given in Table II.

First, numerical results obtained through Monte Carlo sim-

ulations over 10000 channel realizations are provided con-

cerning the outage capacity achieved by the proposed spatial

multiplexed 2 2 MIMO/BFWA system.Fig. 2 shows the 0.1% outage capacity of the special 2

2

MIMO/BFWA channel for both cases of CU and CK vs. the

SNRCS1 (that is, clear sky SNR of strong eigenmode). The

0 5 10 15 20 25 300

2

4

6

8

10

12

14

SNRCS1

(dB)

0.1

%O

utage

Capac

ity

(b/s/Hz

)

SISO BFWA

2x2 MIMO BFWA CU

2x2 MIMO BFWA CK

Fig. 2. 0.1% outage capacity vs. SNR for a spatial multiplexed 2 2MIMO/BFWA system when instantaneous channel is either known or un-known at the transmit side (SISO case is also plotted for comparison).

0 5 10 15 20 25 300

10

20

30

40

50

60

70

SNRCS1

(dB)

Re

lative

Capac

ity

Ga

indue

toFee

dbac

k(%

)

=100o

(12

=0.5759)

=50o

(12=0.7443)

0.1% Outage Capacity

1% Outage Capacity

Fig. 3. Relative capacity gain due to feedback vs. SNR in a spatialmultiplexed 22 MIMO/BFWA system effect of capacity outage probabilityq and angular separation .

system is located in Atlanta, GA whereas the assumed path

lengths and separation angle are L1 = 3km, L2 = 4km,and = 100 (that is, 12=0.5423), respectively. For thesake of comparison, the capacity of the SISO case is also

plotted. As can be seen, at low SNR levels, all three curvesfor SISO, MIMO-CU and MIMO-CK cases coincide with each

other. Therefore, exclusive power allocation to the strongest


8/12


0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

SNRCS1

(dB)

1%

Ou

tage

Capac

ity

(b/s/Hz

)

Atlanta,GA f=25GHz

Atlanta,GA f=42GHz

Singapore f=25GHz

Analytical Solutions (Eq.(12))

Analytical Solutions (Eq.(13))

Fig. 4. 1% outage capacity vs. SNR for a spatial multiplexed 2 2MIMO/BFWA system when instantaneous channel is unknown at the transmitside effect of operating frequency f and climatic conditions over theserviced area.

sub-channel (which is always the case in SISO channels) is

the optimal choice and, so, there is a slight capacity gain of

both MIMO cases over the SISO one. As the SNR increases,

the two curves of MIMO-CU and MIMO-CK cases coincide

with each other but diverge notably from the SISO one. Thus,

equal power allocation becomes the optimum choice and the

capacity gains of both MIMO cases over the SISO one turn

out to be significant.

To investigate the effect of feedback on capacity, Fig. 3

depicts the relative capacity gain of the MIMO-CK case over

the MIMO-CU one vs. the SNRCS1 for two different capacityoutage probabilities q, 0.1% and 1%, and two different angularseparations, = 50 and 100 (that is, 12=0.7443 and0.5759, respectively). The system is located in Atlanta, GA

whereas the assumed path lengths are equal, L1 = L2 = 3km.As can be seen, the relative capacity gains yielded by instanta-

neous CSI are higher at low SNR and decrease asymptotically

to zero as the SNR increases. This is because the waterfilling

solution converges to equal power allocation as the SNR

increases [5]. It is also observed that the relative capacity gain

due to feedback decreases as the capacity outage probability

q increases. This can be intuitively explained as follows: As

q increases, whether or not the BSs allocate optimally thetransmitted power along the two sub-channels, the probabilitythat both sub-channels being in outage increases. Therefore,

the power allocation strategy employed in the CU case seems

to be a more reasonable choice at higher values ofq. However,it is shown that at higher capacity outage probabilities q,even at low SNR, feedback does not result in significant

capacity gains, that is, there is no reason to increase system

complexity by establishing the required feedback links. This

can be attributed to the relatively high spatial correlation

coefficient 12 between the rain induced attenuations AR1,AR2. It can be seen that as decreases (from 100

to 50),12 increases correspondingly (from 0.5759 to 0.7443), andthe capacity gain due to feedback decreases.

Fig. 4 shows the dependence of the 1% outage capacity

2 4 6 8 10 12 14 16 18 2010

6

105

104

103

102

101

SIR level (dB)

Accep

tableInterference

Pro

ba

bility

(AIP)

f=25GHz, pavail

=99.9%

(L1,L

2,L

3)=(3,4,5)km

f=25GHz, pavail

=99.99%

(L1,L

2,L

3)=(3,4,5)km

f=42GHz, pavail

=99.9%

(L1,L

2,L

3)=(3,4,5)km

f=42GHz, pavail

=99.9%

(L1,L

2,L

3)=(1,1,3)km

SISO BFWA

2x2 MIMO BFWA

Fig. 5. AIP vs. SIR level in a 2 2 MIMO/BFWA diversity system withreceive antenna selection (SISO case is also plotted for comparison). Effectof system availability pavail and operating frequency f.

achieved by a 22 spatial multiplexed MIMO/BFWA systemon both the climatic conditions and the operating frequency.

The separation angle and path lengths assumed are the same

as in Fig. 2. Since q = 1%, there is no significant capacitygain due to feedback over the whole range of SNR (see also

Fig. 3) and hence, only the MIMO-CU case is examined.

Furthermore, together with the results obtained via Monte

Carlo simulations, the corresponding results obtained from

the analytical expressions given in Eqs. (12) and (13) for the

special cases of asymptotically low and asymptotically highSNR, respectively, are also plotted. The agreement observed

between the analytical and the simulation results is very good.Since the rain conditions in Atlanta, GA, are lighter than

those observed in Singapore, rain fading is less severe and the

outage capacity achieved by a 2 2 MIMO/BFWA locatedin Atlanta, GA, is higher compared to the one achieved by

a similar system in Singapore. Moreover, as the operating

frequency increases, the rain fading increases correspondingly

and, hence, the capacity achieved decreases.

In the following, the proposed analytical propagation model

predicting the SIR increase achieved in a 22 MIMO/BFWAdiversity system with receive antenna selection is numerically

verified, and the effect of various geometrical and operational

system parameters on the downstream SIR distribution isexamined.

In Fig. 5, the AIP is plotted vs. the SIR level for twodifferent values of system availability pavail, 99.9% and99.99%, and for two different operating frequencies f, 25GHzand 42GHz. For the sake of comparison, a 22 MIMO/BFWAdiversity system and the relevant SISO one are examined. Both

systems are located in Atlanta,GA whereas the other param-

eters assumed for the interference scenario are L1 = 3km,L2 = 4km, L3 = 5km, = 30

, = 90 and SI R1 =20dB. Due to rain, an SIR degradation is observed becomingmore severe as either pavail or f increase. This furtherindicates that BFWA systems operating at higher availabilitiesor higher frequencies are more sensitive to interference. The

SIR improvement achieved in the 22 MIMO/BFWA diversity


9/12


10 20 30 40 50 60 70 8015

20

25

30

35

40

45

50

55

(deg)

SIR

leve

l(dB)

SIR*1=15dB

SIR*

1=25dB

clearsky

2x2 MIMO BFWA

SISO BFWA

Fig. 6. SIR level in a 2 2 MIMO/BFWA diversity system with receiveantenna selection vs. angular separation (SISO and clear-sky cases arealso plotted for comparison) effect of nominal CCI level.

system over the SISO one is significant, especially for high

pavail and high f. Moreover, since BFWA systems operatingat higher frequencies are characterized by smaller cell radii, an

interesting result to look at is the performance of the proposed

2 2 MIMO/BFWA diversity system under such conditions.Therefore, the case where f = 42GHz, L1 = L2 = 1km,L3 = 2km, and pavail = 99.9% (the rest parameters assumedare the same) is also plotted in Fig. 5. It can be seen that

the SIR degradation is less severe in that case. However,

even at smaller distances, the proposed system architecture

results in sufficient SIR improvement, which can be even more

significant at higher availability pavail.

In Fig. 6, the SIR dependence on is examined fortwo different nominal CCI levels SI R1, 15dB and 25dB.The parameters assumed for the interference scenario are

L1 = 3km, L2 = 4km, L3 = 5km, = 90, f = 25GHz,

AIP = 0.001% and pavail = 99.99% whereas the system islocated in Atlanta, GA. As expected, an SIR improvement

is observed as SI R1 increases. It is also clear that theSIR values achieved by a 2 2 MIMO BFWA diversitysystem under rain fades get closer to the clear sky ones when

compared to those achieved by a relevant SISO system. As

an illustration, for = 30 and SI R1 = 15dB, the SIRvalue achieved at the receiver input of the SS under clear sky

conditions is 37dB, whereas in the cases of a SISO/BFWAand a 22 MIMO/BFWA system, it is 25.27dB and 28.59dB,respectively.

Finally, Fig. 7 quantifies the SIR improvement achieved

by a 2 2 MIMO/BFWA diversity system employing re-ceive antenna selection with respect to the relevant SISO

one. Specifically, the CCI Reduction Level, defined as the

difference (in dB) between the SIR non-exceedance levels

at the receiver input of the SS for the MIMO and for the

relevant SISO case, is plotted vs. the angular separation for AIP = 0.01% and 0.001%, and for two different climaticconditions. The operating frequency, pavail and nominal CCIlevel are 25GHz, 99.99%, and SI R1 = 20dB, respectively,

40 60 80 100 120 140 160 1800

1

2

3

4

5

6

7

8

(deg)

Co

Channe

lInterference

Re

duc

tion

Leve

l(dB)

Singapore

Atlanta,GA

AIP=0.001%

AIP=0.01%

Fig. 7. CCI reduction level achieved in a 2 2 MIMO/BFWA diversitysystem with receive antenna selection vs. angular separation . Effect ofAIP level and climatic conditions over the serviced area.

while the rest of the parameters employed are the same as

those assumed in Fig. 6. As the AIP decreases or as increases, the achieved CCI reduction level becomes higher.

Moreover, it is obvious that the SIR enhancement obtained in

Singapore is much higher than that in Atlanta, GA, due to the

corresponding heavier rain conditions.

VI . CONCLUSIONS

In this paper, the novel applicability of MIMO technology

to 10-66GHz BFWA networks is examined. By drawing on the

vast body of available MIMO literature, an interesting mixturebetween communication-based and propagation-based analy-

ses is presented for two different cases of MIMO applications

to BFWA systems operating in the 10-66GH frequency range:

capacity improvement in spatial multiplexed MIMO/BFWA

systems; and SIR enhancement in MIMO/BFWA diversity sys-

tems with receive antenna selection. Both capacity and inter-

ference analyses assume an analytical physical MIMO/BFWAchannel model. This model takes into account the effect of

rain fading, has inputs from the ITU-R rainmaps, can beapplied on a global scale and can successfully incorporate the

general case of an ordered MIMO system. The differences

between conventional MIMO and the proposed 10-66GHz

MIMO/BFWA channels are pointed out and the exact rela-

tionship is established.

Useful results are obtained for the outage capacity of a

spatial multiplexed 2 2 MIMO/BFWA system. Significantcapacity gains over the relevant SISO case have been demon-

strated, especially for high SNR levels. Based on analytical

closed form expressions and Monte Carlo simulations, it is

shown that exclusive power allocation is the optimal strategy

at low SNR, whereas equal power allocation is optimal at high

SNR. The effect of feedback on the outage capacity is also

investigated and it is shown that a capacity gain exists only

when the capacity outage probability q is low (for example,q = 0.1%). This further implies that no additional complexityin terms of feedback links and communication links between


10/12


the two BSs is worthwhile at reasonably higher values of q(for example, q 1%).

Emphasis is also put on 2 2 MIMO/BFWA diversitysystems with receive antenna selection and their ability to

combat intrasystem/intersystem CCI arising over the down-stream channel. A general analytical propagation model for

the calculation of the SIR improvement achieved is presented,

which is flexible and can incorporate the influence of various

geometrical, climatic and operational system parameters on theSIR distribution. The proposed model is tested numerically

and it is shown that the SIR increase obtained by a 2 2MIMO/BFWA diversity system can take values of several

dB depending on the operating frequency, system availability,

nominal CCI level, angular separations, acceptable interfer-

ence level, and climatic conditions existing over the serviced

area.

By drawing on the vast body of MIMO literature currently

available, the relationship between conventional MIMO andthe proposed MIMO/BFWA channels may be used to obtain

additional insight into the analysis and design of 10-66GHz

BFWA networks.

APPENDIX A

RAI N FADING MODEL

The fundamental assumptions for the modeling of rainattenuation are as follows:

(i) The specific rain attenuation AR0 (in dB/km) in termsof the point rainfall rate R (in mm/hr) is given by

AR0 = aRb (29)

where the constants and b depend upon operating frequency,incident polarization, temperature, and raindrop size distribu-

tion [28].

(ii) Including the non-raining time, the lognormal distribu-

tion is adopted for the distribution of the unconditional point

rainfall rate R and the rain attenuations ARi(i = 1, 2, 3) [8],[9], [17].

(iii) The spatial correlation coefficient of the specific rainattenuation 0 between two points within the rain medium isgiven by the semi-empirical expression [29]

0 (z1, z2) =G

G2 + d2 (z1, z2)(30)

0 is a function of the distance d (z1, z2) =z21 + z

22 2z1z2 cos between two converging radio

links, while G is a characteristic distance ranging from 0.75to 3 km [29].

(iv) The rain attenuations along the three converging links

ARi(i = 1, 2, 3) (concerning the two wanted signals andthe interfering one, respectively) are positive RVs following

the joint lognormal distribution. The lognormal statistical

parameters (that is, mean value and variance) of these RVs

AmRi, SaRi (i = 1, 2, 3) can be calculated from

S2aRi = ln

1 +

XiL2i

exp

b2S2r

1

(31)

AmRi = aRbmLi exp

b2S2r S2aRi

2

(32)

where Rm, Sr are the point rainfall rate lognormal statisticalparameters estimated through appropriate regression fitting

analysis on local rainfall data or on rainfall data coming fromthe ITU-R rainmaps [19]. In (31) and (32)

Xi = 2LiG sinh1

LiG

+2G2

1LiG 2

+ 1

(i = 1, 2, 3) (33)

(v) Considering the transformation

ui = [ln (ARi) ln (AmRi)] /SaRi (i = 1, 2, 3) (34)the lognormal RVs ARi are related to the normalized normalRVs ui (i = 1, 2, 3). The logarithmic correlation coefficientnij ((i, j) = (1, 2) , (1, 3) , (2, 3)) for each pair of normalRVs (ln ARi, ln ARj ) is given by Eq. (35) on next page, where

ij =Xij

XiXj(36)

with

Xij =

Li0

Lj0

0 (z1, z2) dz1, dz2

((i, j) = (1, 2) , (1, 3) , (2, 3)) (37)

In (35) and (36), ij is the correlation coefficient for eachpair of lognormal RVs (ARi, ARj ). Specifically, 12 is thecorrelation coefficient of rather interest in the present analysis,

and the one usually referred to throughout this work.

APPENDIX BANALYTICAL SOLUTIONS TO THE CONSTRAINED

OPTIMIZATION PROBLEM (10)

Considering the well-known approximations log2 (1 + x) x log2 e when x 0, and log2 (1 + x) log2 x whenx 1, along with the assumptions about channel modeling,the following useful analytical solutions to the constrained

optimization problem expressed through (10) come up for the

particular cases of asymptotically low and asymptotically high

SNR, respectively.

Low SNR region, see Eqs. (38) and (39) on next page.

popt = 2 (40)

High SNR region, see Eq. (41) on next page.

CCUp

=1

p 1

2p = 0 (42)

popt = 1 (43)

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(exp(S2aRi) 1)exp

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1

(35)

CCU EAR1p log2 e 0.5 SN RCS1 10AR1/10

+EAR2 (2

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log2 e

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SN RCS1 10AR1/10

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SN RCS2 10AR2/10

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SN RCS1 10AR1/10

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Konstantinos P. Liolis (S04) was born in Athens,Greece in September 1981. He received the Dipl.-

Eng. degree in electrical and computer engineeringfrom the National Technical University of Athens(NTUA), Greece, and the M.Sc. degree in electricalengineering from the University of California, SanDiego (UCSD), USA, in July 2004 and December2005, respectively. He is currently working towardshis Ph.D. degree at NTUA. From September 2004to December 2005, he was Research Assistant at theUCSDs California Institute for Telecommunications

and Information Technology (Cal-IT2), San Diego, USA. From June 2006 toJanuary 2008, he was Communication Systems Engineer at the EuropeanSpace Agency, Research and Technology Centre (ESA/ESTEC), Noordwijk,The Netherlands. Since February 2008, he has been R&D Systems Engineer atSpace Hellas SA, Athens, Greece. His research interests include mobile/fixedwireless and satellite communications with emphasis on their physical layerdesign and analysis, and their propagation channel modeling. He has published

more than 15 papers in international journals and conference proceedings,he has numerous technical contributions to DVB-SH, mobile DVB-RCS andITU-R standardization bodies, and he has participated in several EU, ESAand US funded R&D projects in these areas. Mr. Liolis is member of theTechnical Chamber of Greece. He received the 3rd place Best Student PaperAward in the 2006 IEEE Radio and Wireless Symposium.

Athanasios D. Panagopoulos (S98, M02) wasborn in Athens, Greece on January 26, 1975. Hereceived the Diploma Degree in Electrical andComputer Engineering (summa cum laude) and theDr. Engineering Degree from National TechnicalUniversity of Athens (NTUA) in July 1997 andin April 2002. From May 2002 to July 2003, heserved the Technical Corps of Hellenic Army. InSeptember 2003, he joined School of Pedagogicaland Technological Education, as part-time AssistantProfessor. From January 2005 to May 2008, he was

head of the Satellite Division of Hellenic Authority for the Information andCommunication Security and Privacy. Since May 2008, he is Lecturer in theSchool of Electrical and Computer Engineering of NTUA. He has publishedmore than 110 papers in international journals and conference proceedings.He is the recipient of URSI General Assembly Young Scientist Award in2002 and 2005. His research interests include radio communication systemsdesign, wireless and satellite communications networks and the propagationeffects on multiple access systems and on communication protocols. Heparticipates to ITU-R and ETSI Study Groups and he is member of TechnicalChamber of Greece. He serves on the editorial boards of the HindawiINTERNATIONAL JOURNAL OF ANTENNAS AND PROPAGATION and ElsevierPHYSICAL COMMUNICATION and since October 2008 as an Associate Editorof IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION.

Panayotis G. Cottis was born in Thessaloniki,Greece, in 1956. He received the Dipl. (mechani-cal and electrical engineering) and Dr.Eng. degreesfrom the National Technical University of Athens(NTUA), Greece, in 1979 and 1984, respectively,and the M.Sc. degree from the University of Manch-ester, (UMIST), Manchester, U.K., in 1980. In 1986,he joined the School of Electrical and ComputerEngineering, NTUA, where he has been a Professorsince 1996. He has published more than seventy

papers in international journals and transactions. Hisresearch interests include electromagnetic scattering, microwave theory andapplications, wave propagation in anisotropic media, wireless networks, andsatellite communications. Dr. Cottis is member of the Technical Chamber ofGreece. From September 2003 to September 2006, he was the Vice Rectorof NTUA.

Bhaskar D. Rao (S80-M83-SM91-F00) receivedthe B.Tech. degree in electronics and electrical com-munication engineering from the Indian Instituteof Technology, Kharagpur, India, in 1979 and theM.S. and Ph.D. degrees from the University ofSouthern California, Los Angeles, in 1981 and 1983,respectively. Since 1983, he has been with the Uni-versity of California at San Diego, La Jolla, wherehe is currently a Professor with the Electrical andComputer Engineering Department. His interests are

in the areas of digital signal processing, estimationtheory, and optimization theory, with applications to digital communications,speech signal processing, and human-computer interactions.His paper receivedthe best paper award at the 2000 speech coding workshop and his studentshave received the student paper awards at both the 2005 and 2006 InternationalConference on Acoustics, Speech and Signal Processing as well as the beststudent paper award at NIPS 2006. He also received the graduate teachingaward from the graduate students in the Electrical Engineering departmentat UCSD in 1998. He was elected to the IEEE Fellow grade in 2000 forhis contributions in high resolution spectral estimation. Dr. Rao has been amember of the Statistical Signal and Array Processing technical committeeand the Signal Processing Theory and Methods technical committee ofthe IEEE Signal Processing Society. He is currently a member of theSignal Processing for Communications technical committee and serves onthe editorial board of the EURASIP S IGNAL PROCESSING JOURNAL.

Documents

On the Applicability of MIMO Principle