Cooperative MIMO-OfDM Cellular System With

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1428 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 4, APRIL 2008

Cooperative MIMO-OFDM Cellular System withSoft Handover between Distributed

Base Station AntennasAntti Tolli, Student Member, IEEE , Marian Codreanu, Member, IEEE , and Markku Juntti, Senior Member, IEEE

Abstract Cooperative processing of transmitted signal fromseveral multiple-input multiple-output (MIMO) base stations(BS) is considered for users located within a soft handover (SHO)region. The downlink resource allocation problem with differentBS power constraints is studied for the orthogonal frequencydivision multiplexing system with adaptive MIMO transmission.Joint design of the linear transmit and receive beamformersin a MIMO multiuser transmission subject to per BS powerconstraints is considered. A solution for the weighted sum ratemaximization problem is proposed. The proposed algorithm isshown to provide a very efcient solution despite of the factthat the global optimality cannot be guaranteed due to thenon-convexity of the optimization problem. Moreover, efcientresource allocation method based on zero forcing transmission isprovided. The impact of the size of a SHO region, the overheadfrom the increased resource utilization, and different inter-cellinterference distributions due to the SHO are evaluated bysystem level simulations. Although the overhead from the SHOprocessing can be signicant, it can be mitigated by using spacedivision multiple access for users having an identical SHO activeset composition. The users located at the SHO region may enjoyfrom greatly increased transmission rates. This translates tosignicant overall system level gains from the cooperative SHOprocessing.

Index Terms Adaptive multiuser MIMO-OFDM, TDD,beamforming, convex optimization, geometric programming,second-order cone programming, cellular network, system levelanalysis, non-reciprocal interference.

I. INTRODUCTION

F UTURE broadband communication systems should pro-vide a wide range of services at a reasonable cost andquality of service (QoS), comparable to wireline technologies.The key radio techniques which have to be considered in de-veloping such systems include multiple-input multiple-output

Manuscript received December 29, 2006; revised May 17, 2007; acceptedJuly 4, 2007. The associate editor coordinating the review of this paper andapproving it for publication was M. Win. This research was supported by theFinnish Funding Agency for Technology and Innovation (TEKES), Nokia,Elektrobit, Tauno T onning Foundation, Nokia Foundation, Riitta & Jorma J.Takanen Foundation, Seppo S aynajakangas Foundation, KAUTE Foundationand Infotech Oulu Graduate School. Parts of this paper have been presentedat the 17th Annual IEEE International Symposium on Personal Indoor andMobile Radio Communications, Helsinki, Finland, September 2006, the IEEEGlobal Telecommunications Conference, November 2006, San Francisco,USA, and the IEEE International Conference on Communications, Glasgow,

Scotland, June, 2007.The authors are with the Centre for Wireless Communications, Univer-sity of Oulu, P.O. Box 4500, 90014 University of Oulu, Finland (e-mail:[email protected].).

Digital Object Identier 10.1109/TWC.2008.061124.

(MIMO) communication based on multiple antennas [1][5], multi-carrier modulation or orthogonal frequency divisionmultiplexing (OFDM), as well as adaptive modulation andcoding [6]. The spectral efciency of MIMO transmission canbe increased dramatically if channel state information (CSI)is available at the transmitter [7].

There has been increasing interest to consider network infrastructure based cooperative processing between base sta-tions (BSs) with a cellular system [8][14] or xed relaystations [15][18]. These types of systems have been consid-ered earlier for voice oriented code-division multiple access(CDMA) communications [19], [20]. More recently, [9][12], [21][23] studied the downlink sum rate and spectralefciency optimization for cooperative MIMO systems withperfect data cooperation between base stations. Although theBS cooperation naturally increases the system complexity,it has potentially signicant capacity and coverage benetsmaking it worth a more detailed consideration.

The sum capacity and the capacity region of MIMO down-link (DL) with per antenna or per BS power constraintswere recently discovered in [24] and in [25], [26], respec-tively. Furthermore, the minimum-power beamformer designfor multiple-input single-output (MISO) DL under per antennaor per BS power constraints was investigated in [25], where theoriginal DL problem was transformed into a dual uplink (UL)minimax optimization problem with an uncertain noise covari-ance. Convex optimization methods [27], such as second-ordercone programming [28], semidenite programming [29] andgeometric programming [30], are very powerful tools whichallow for efcient numerical solution for many signal process-ing and communications problems, e.g., [25], [31][35]. Inparticular, they were used to solve a wide range of optimaltransmit and receive beamformer design problems [36][39].

The purpose of this paper is to analyze the BS cooperationwith linear processing in more detail and to propose morepractical radio resource allocation solutions. We assume atime division duplex (TDD) system with adaptive MIMOOFDM transmission, where the modulation parameters in ULand DL can be adapted according to the channel conditions.The reciprocal DL channel can be estimated accurately duringthe previous UL transmission assuming that the frame length

is shorter than the channel coherence time; a frame refershere to a TDD frame which is divided into UL and DLtransmission parts. This assumption is mostly valid in envi-ronments with low mobility, e.g., in pedestrian metropolitan

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TOLLI et al. : COOPERATIVE MIMO-OFDM CELLULAR SYSTEM WITH SOFT HANDOVER BETWEEN DISTRIBUTED BASE STATION ANTENNAS 1429

BS

1

1

N T

BS

2

1

N T

CentralController

Optical bre

BSM

1

N T

1 N R1

user1

1 N Rk

userk

SHO region

Fig. 1. SHO system model

environments [40]. Furthermore, the served users should havesome minimum signaling in the UL direction to provide timelychannel estimates for the DL transmission. In order to attainthe CSI between all users and BS antennas in the cellularnetwork the channels should be jointly estimated at each BS.In practical TDD MIMOOFDM cellular systems, however,UL transmissions from distant users can be signicantly moreattenuated compared to the own cell users. Thereby, the joint channel estimation may be difcult if not impossible toimplement in practice.

We consider the somewhat more practical case where the joint cooperative processing of transmitted signal from severalMIMO BS antenna heads is restricted to an area where theusers have comparable signal strengths from adjacent BSantenna heads. We assume that cooperative signal processing

can be performed in a centralized manner so that the MIMOantenna heads are distributed over a larger geographical area(e.g., hundreds of meters), as illustrated for example in [14,Fig. 4]. The distributed antenna heads are then connectedto the central processing unit (controller) via radio overbre technology or wireless microwave links [13], [14], forexample. Similarly to the soft handover (SHO) feature in(W)CDMA systems [41], SHO region is dened for userswith similar received power levels from adjacent distributedBS antenna heads. Since the signal processing of the BSantenna heads is concentrated at one central controller, jointbeamforming from all the antennas belonging to the active

set can be performed to the user(s) within the SHO region,as seen in Fig. 1. The transmissions for other users outsidethe SHO region are seen as interference. In the following, thedistributed BS antenna heads are denoted as base stations forsimplicity.

In this paper, we consider transmitter optimization formultiuser MIMO downlink with linear processing both at thetransmitter and receiver, since this is a simple to implementand an important solution also in practical system design.Note that the sum capacity achieving schemes require non-linear precoding based on dirty paper coding (DPC) [26],[42]. We propose a general method for joint design of the

linear transmit and the receive beamformers for weighted sum rate maximization problem subject to per BS power constraints . The method can handle multiple antennas at BSsand mobile users, and any number of data streams is allowedper scheduled user. Furthermore, it can be easily modied

to accommodate supplementary constraints, e.g., per antennapower constraints or lower bounds for the SINR values of data streams, and the feasibility of the resulting optimizationproblems can be easily checked. Unlike the sum capacityachieving scheme, the optimization problems employed in thelinear multiuser MIMO transceiver design are not convex ingeneral. Therefore, the problem of nding the global optimumis intrinsically non-tractable. However, by utilizing the recentresults on the precoder design via conic optimization [39]and the signomial programming [30], we propose an iterativesolution where each step can be efciently solved by usingconvex optimization tools [43]. Even though each subproblemis optimally solved, the global optimality cannot be guaranteeddue to the non-convexity of the original problem. However,the simulation results demonstrate that the achieved locallyoptimal solutions are very efcient in several practicallyrelevant scenarios. The proposed framework can be extendedto other optimization criteria, such as maximization of theweighted minimum SINR per data stream subject to per BSpower constraints [44].

Furthermore, we put particular emphasis on generalizedzero forcing (ZF) transmission due to its simplicity [45], [46].It enables to decouple the data streams, and, as a result, allowsfor efcient implementation of the bit and power loading algo-rithms in practical systems. System level evaluation assessesthe impact of a realistic multi-cell environment (includingrealistic non-reciprocal inter-cell interference) on the cellularsystem performance. The impact of the size of the SHOregion, overhead from increased hardware and physical (time,frequency) resource utilization, different non-reciprocal inter-

cell interference distributions due to SHO are evaluated bysystem level simulations.The paper is organized as follows. In Section II, the

cellular MIMO-OFDM system model is presented. Section IIIconsiders the joint design of the linear transmit and receivebeamformers for weighted sum rate maximization subject toper BS power constraints. The cooperative processing in SHOwith ZF multiuser transmission is introduced in Section IV andthe relevant power optimization problems are derived. Sec-tion V describes the simulation environment and assumptions,and the results for theoretical mutual information studies andfor more practical link and system level simulation studies are

presented. Finally, conclusions are drawn in Section VI.The following notation is used. All boldface letters indicatevectors (lower case) or matrices (upper case). Superscripts()T , ()H , () 1 , ()1/ 2 stand for transpose, Hermitian trans-pose, matrix inversion and positive semidenite square root,respectively. We use Cm n to denote the set of mn complexmatrices. Matrix I signies identity matrix, 1 is an all onesvector, diag ( ) denotes the diagonal matrix with elements( ) on the main diagonal, [X ]i,j denotes the (i, j ) entryof the matrix X , and vec(X ) denotes the vector obtained bystacking the columns of the matrix X . The sets are indicatedby calligraphic letters and

|A|denotes the cardinality of the

set A. The notation h CN (0, h ) indicates that h iscircular symmetric Gaussian random vector with covariance h . (a)+ stands for max( a, 0). E{}, Tr{}and 2 denotestatistical expectation, the trace operator and the Euclidiannorm, respectively.



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I I . SYSTEM MODEL

The cellular adaptive MIMO-OFDM system consisting of N B base stations has N C sub-carriers, each BS has N T transmit antennas and user k is equipped with N R k receiveantennas. A user is served by M k BSs which dene the SHOactive set S k for the user k. The signal vector y k,c CN R kreceived by the user k at the subcarrier c can be expressed as

y k,c =bS k

ab,k H b,k,c

x b,k,c +i= k

x b,i,c

+bS k

ab,k H b,k,c x b,c + n k,c

= H k,c x k,c + i intrak,c + iinterk,c + n k,c , (1)

where x b,k,c CN T is the transmitted signal from the

bth base station to user k, x b,c CN T denotes the total

transmitted signal vector from the BS transmitter (TX) b,n k,c

CN (0, N 0 I N

R k) represents the additive noise sample

vector, and ab,k H b,k,c CN R k N T is the channel matrix from

the BS b to the user k with a large scale fading coefcientab,k . The elements of H b,k,c are normalized to have unitaryvariance.

The signal x k,c = x S k (1) ,k,c T, . . . , x S k (M k ) ,k,c TT

CM k N T transmitted for user k is distributed over M k basestations being in the SHO active set S k . The global channelmatrix H k,c CN R k M k N T for user k from all M k BSs isH k,c = aS k (1) ,k H S k (1) ,k,c , . . . , a S k (M k ) ,k H S k (M k ) ,k,c . (2)

The vectors i intrak,c = bS k ab,k H b,k,c i = k x b,i,c and

iinterk,c = bS k ab,k H b,k,c x b,c include the received intra- andinter-cell interference, respectively.

The transmitted vector for the user k is generated asx k,c = M k,c d k,c , where M k,c C

N T M k m k,c is the pre-coding matrix, d k,c = d1,k,c , . . . , dm k,c ,k,c

Tis the vector of

normalized complex data symbols transmitted at sub-carrier c,and mk,c min( N T M k , N R k ) denotes the number of activedata streams. M k,c can be further split into M k,c = V k,c P

1/ 2k,c ,

where V k,c = [v k, 1,c , . . . , v k,m k,c ,c ] contains the normalizedTX beamformers and P k,c = diag pk, 1,c , . . . , pk,m k,c ,ccontrols the powers allocated to each of mk,c streams.

The receiver (RX) is assumed to be equipped with a linearminimum mean square error (LMMSE) lter and the decisionvariables are generated as d k,c = W Hk,c y k,c . The weightmatrix W k,c C

N R k m k,c of the LMMSE lter is found byminimizing W k,c = arg min

W k,cE d k,c W Hk,c y k,c 2 and is

given as

W Hk,c = M Hk,c H Hk,c H k,c M k,c M Hk,c H Hk,c + Z k,c + R k,c 1

(3)

where Z k,c =i= k

H k,c M i,c M Hi,c HHk,c is the covariance ma-

trix of the intra-cell interference. It consists of transmissions tothe users i that have an identical SHO active set composition

with user k, S i = S k . The inter-cell interference-plus-noisecovariance matrix R k,c isR k,c =

bS k

a 2b,k H b,k,c E

x b,c x b,cH H Hb,k,c + N 0 I N R k (4)

R k,c is assumed to be known at the receiver and to remainunchanged during the transmission of a frame. In practicalTDD MIMOOFDM cellular systems, the ideal knowledge of R k,c also at the transmitter would require it to be reportedto the transmitter for each subcarrier and for each transmitteddata frame [47]. Therefore, in the system level studies weconsider a more practical case where R k,c is known onlyat the receiver. Note that the explicit estimation of R k,c isnot required in practice. Only the covariance of the totalreceived signal needs to be estimated, in addition to thedesired signal H k,c M k,c , as seen from (3). The channel matrixH b,k,c is assumed to be known at the transmitter in all cases.Furthermore, the TX signals are assumed to have a commoncarrier phase reference and the impact of the propagation delayfrom each of the transmitters to the intended users is ideallycompensated for at the BSs. We have studied the impact of the imperfect phase synchronization between the BS antennaheads in [48].

It is possible to serve several users having identical SHOactive sets S k in the same time-frequency transmission slotusing some space division multiple access (SDMA) methods.The SDMA can be used to improve the utilization of thephysical resources (space, time, frequency) by exploiting theavailable spatial degrees of freedom in a downlink multi-user MIMO channel, with an expense of somewhat increasedcomplexity. Each group of users with an identical SHO activeset composition forms a distinct user set and can be optimisedseparately. In the derivation in Sections III and IV, we restrictour focus to a single set of users A, where all users k Ahave an identical active set composition, S k = S i , k, i A.We denote by M = |S k | the SHO active set size, which iscommon to all users k A. Moreover, we focus on a lineartransmission scheme, where the transmitters can send up tomin( MN T , kA N R k ) streams / subcarrier.

Different power constraints can be considered for the coop-erative BS processing [9], [23][26]. We consider two generalpower constraints: a sum power constraint for all M BSs inthe SHO active set S k and an individual power constraint foreach BS. The total power transmitted by the BS n isN C

c=1

Tr E x n,c x n,cH =

N C

c=1

TrkA

M [n ]k,c M[n ]k,c

H

=kA

N C

c=1

m k,c

i=1

v [n ]k,i,c22 pk,i,c (5)

where M [n ]k,c CN T m k,c is the pre-coder matrix of the user

k that corresponds to n th base station belonging to S k , i.e.,M [n ]k,c = [M k,c ][(n 1) N T +1 ,...,nN T ; 1,...,m k,c ], n = 1 , . . . , M .Similarly, v [n ]k,i,c C

N T is the transmit vector for the ith streamof user k from BS n , i.e., v [n ]k,i,c = [v k,i,c ](n 1) N T +1 ,...,nN T ,n = 1 , . . . , M ,

III . W EIGHTED SUM RATE MAXIMIZATION WITH PER BSCONSTRAINTS

In this section, we consider the problem of joint design of the linear transmit and receive beamformers for maximizingthe weighted sum of the rates of the individual data streams



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subject to per BS power constraints. The proposed methodcan handle multiple antennas at the BSs and mobile users,and an arbitrary number of data streams is allowed perscheduled user. In this section, the subcarrier index c isomitted to simplify the presentation, but the results can bestraightforwardly extended to multiple subcarriers similarly toSection IV. We consider a per data stream processing, wherethe central base station controller transmits S independent datastreams, S = min {MN T , kA N R k }. For each data streams , s = 1 , . . . , S , the base stations scheduler unit associates anintended user ks with the channel matrix H k s C

N R k s MN T .Notice that more than one stream can be associated to oneuser, therefore, the cardinality of the set of scheduled users,

A= {ks |s = 1 , . . . , S }, is less than or equal to S . We denethe normalized whitened channel matrix as H wk s = R

12k s H k s ,

i.e., R k s is ideally contained in H wk s .Let v s C

MN T , w s CN R k s and ps be arbitrary nor-

malized transmit and receive beamformers and the allocated

power for the stream s , respectively. The SINR of the datastream s can be expressed as

s = ps w Hs H wk s v s

2

1 + S i=1 ,i = s pi w Hs H wk s v i2 (6)

Similarly to (5), the total power transmitted by the n th BS isgiven by S s =1 ps v

[n ]s

22 , where v

[n ]s C

N T is the transmitvector for the data stream s associated with n th BS, i.e., v s =v [1]s

T, . . . , v [M ]s

T T. Assuming Gaussian codebook [49] for

each data stream, the weighted sum rate can be expressed as

R =S

s =1

s r s =S

s =1

s log(1 + s ) = logS

s =1

(1 + s ) s

(7)where r s and s are the rate and the SINR of the data stream s ,respectively. The weight vector, = [ 1 , . . . , S ]T , s 0, isused to give different relative importance to the data streams.It allows to compute the entire rate region achievable withthe linear processing [27]. = 1 corresponds to the usualsum rate maximization or best effort. Since R increases withrespect to each s and log() is a increasing function, theweighted sum rate maximization problem with per BS powerconstraints can be formulated as follows

maximize S

s =1 (1 + s ) s

subject to s ps

w Hs Hwk s

v s

2

1 + S

i =1 ,i = s pi

w Hs Hwk s

v i

2 , s = 1 , . . . , S S

s =1 ps-

- v [n ]s-

-

22 P n , n = 1 , . . . , M

w s 2 = 1 , v s 2 = 1 , ps 0, s = 1 , . . . , S (8)

where the variables are v s CMN T , w s C

N R k s , ps IR , s IR . It is easy to observe that at the optimal point of (8),the rst constraint holds with equality, thus the optimal valueof s represents the SINR of the data stream s .

The optimization problem (8) is not convex, and, hence, theproblem of nding the global optimum is intrinsically non-tractable. However, the problem (8) can be maximized withrespect to different subsets of variables by considering theothers xed. For instance, the maximum SINR receiver given

by [50]

w s =w s

w s 2, (9)

w Hs = ps v Hs H wHk sS

i=1

pi H wk s v i vHi H

wHk s + I

1

is optimal for any xed v s and ps . Furthermore, by xingv s and w s , (8) becomes a signomial problem [30], [33],[51]. The problem is not convex as such, but there areefcient methods for approximating the solution by usinggeometric programming [30], [33]. The procedure consists of searching for a close local maxima by solving a sequence of geometric programs which locally approximate the originalproblem. This procedure is known to converge fast (in a fewiterations) [30]. Finally, for xed w s and s we can nd amaximum reduction factor, common for all the per BS powerconstraints which preserves the SINR values s and, implicitly,the rate. This is given by the optimum that solves theproblem

minimize

s. t . s ps

w Hs Hwk s

v s

2

1 + S

i =1 ,i = s pi

w Hs Hwk s

v i

2 , s = 1 , . . . , S S

s =1 ps-

- v [n ]s-

-

22 P n , n = 1 , . . . , M -

- v s-

-

2 = 1 , ps 0, s = 1 , . . . , S (10)

where the variables are IR , ps IR , v s CMN T , s =

1, . . . , S . The solutions v s and ps do not directly increase theobjective of (8). However, they increase the power margin fora xed value of the objective, and hence, the saved power can

be used to increase the objective. This is realized by updatingv s and ps in (8) to the new values v s and ps / , respectivelyand increasing all s until all SINR constraints become tight.Notice that this is an ascent step since 1 for any w s and s that are feasible for (8).

The above observations suggest the following iterative op-timization algorithm.

Algorithm 1: Weighted Sum Rate Maximization Under perBS Power Constraints

1) Initialize v (0)s and p(0)s such that the per BS powerconstraints are satised. Compute the optimal w (0)s and (0)s according to (9) and (6), respectively. Let i = 1and go to Step 2.

2) Solve the problem (8) for the variables ps and s , byxing w s = w

( i 1)s and v s = v

( i 1)s , s = 1 , . . . , S .

Denote the solutions by ps and s .3) Solve the problem (10), where s = s and w s =

w ( i 1)s , s = 1 , . . . , S . Denote the solutions by , ps and v s . Update p

( i )s = ps / and v

( i )s = v s ,

s = 1 , . . . , S .4) Update w ( i )s and ( i )s according to (9) and (6), respec-

tively. Test a stopping criterion. If it is not satised, leti = i + 1 and go to Step 2, otherwise STOP.

Even though Algorithm 1 increases monotonically the objective of (8), there is no guarantee that the global optimumis found due to non-convexity of the problem. However, thesimulations in Sect. V-A show that the algorithm converges toa solution, which can be a local optimum, but is still efcient.



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Next, we present the algorithm used at Step 2 of Algo-rithm 1 , which solves the problem (8) for xed w s and v s .The objective of (8), f 0 ( 1 , . . . , S ) =

S s =1 (1 + s )

s isapproximated by a monomial function [30] m( 1 , . . . , S ) =c S s =1

a ss , near the point = ( 1 , . . . , S ), where the

parameters c and as of the best monomial local approximationare given by [51, Section IV. B, Lemma 1]

as = s s

1 + s, c =

f 0 ( 1 , . . . , S )S s =1

a ss

. (11)

By using the local approximation in the objective of (8), andignoring the multiplicative constant c which does not affect theproblem solution, we obtain the following iterative algorithm.

Algorithm 2: Geometric optimization step under per BSpower constraints

1) Let the initial SINR guess, = ( ( i 1)1 , . . . , ( i 1)S )

2) Solve the following geometric program,

maximize S s =1 s s1+ ss

s. t . (1 ) s s (1 + ) s , s = 1 , . . . , S g 1s,s p 1s s +

S k=1 ,k = s gs,k pk g

1s,s p 1s s 1,

s = 1 , . . . , S S s =1 ps v

[n ]s

22 P n , n = 1 , . . . , M (12)

where the variables are s , ps and gs,k = w Hs H wk s v k2

are xed values. Denote the solution by ps and s . If max s | s | > set = ( 1 , . . . , S ) and go toStep 2, otherwise STOP.

The geometric program (12) approximates the originalsignomial problem (8) around the point = ( 1 , . . . , S ). Therst set of inequality constraints of (12) are called trust regionconstraints [30] and they limit the domain of variables s in aregion where the monomial approximation is accurate enough.The constant < 1 controls the desired approximationaccuracy and a typical value is = 0 .1 [30].

Now, we focus on Step 3 of Algorithm 1 . First, observethat the change of variable m s = ps v s denes a bijectivemapping between the sets {( ps , v s ) | ps IR+ , v s 2 =1, v s CMN T }and m s CMN T . Thus, we can solve (10)for m s

CMN T , and then recover the optimal ps and v s .Furthermore, by replacing the positive variable by 2 weobtain the following equivalent reformulation of (10)

minimize 2

s. t . s w Hs H

wk s m s

2

1 + S i =1 ,i = s w Hs H wk s m i2 , s = 1 , . . . , S

S s =1 m

[n ]s

22 2P n , 0, n = 1 , . . . , M (13)

Notice that the objective 2 can be replaced by since for 0, minimizing 2 is equivalent to minimizing . More-over, the constraints of (13) can be expressed as generalizedinequalities with respect to the second-order cone [27], [28],[39]. Thus, the problem (13) can be further reformulated as asecond-order cone program (SOCP) and it can be efcientlysolved numerically by using a standard optimization software[43], [52]. By modifying the approach presented in [39,

Section IV.B] to accommodate per BS power constraints, weobtain the following equivalent SOCP formulation

minimize

s. t .

1 + 1 s w Hs H wk s m sM HH wHk s w s1

K 0, s = 1 , . . . , S

P nvec(M [n ]) K 0, n = 1 , . . . , M

(14)where M = [ m 1 , . . . , m S ], M [n ] = [m

[n ]1 , . . . , m

[n ]S ], and K

denotes the generalized inequality with respect to the second-order cone [27], [28], i.e., for any x IR and y C

n ,[x, y T]T K 0 is equivalent to x y 2 . Let us denotethe solution of (14) by , m s , s = 1 , . . . , S . The solutionof (10) is given by = 2 , v s = m s / m s 2 , ps =

m s22 , s = 1 , . . . , S . Note that (14) provides a minimum-

power beamformer design under per BS power constraints

for MIMO DL with xed receivers. This is equivalent to themethod proposed in [25], where the original DL problem wastransformed into a dual UL minimax optimization problemwith an uncertain noise covariance.

The optimization problem in (8) can be easily modied toaccommodate supplementary constraints, e.g., per antenna orsum power constraints, or minimum SINR values for someof the data streams ( s mins ). The modied problem withminimum SINR constraints can be directly solved using theproposed algorithm, if it is feasible under the initial beam-former conguration obtained at the Step 1 of Algorithm 1 ,i.e., (0)s

mins . The feasibility of the modied optimization

problem with any minimum SINR constraints can be easilychecked by iterating between problem (10) with xed s = mins and (9). If the resulting 1, then the problem isfeasible and the resulting beamformer conguration can beused as a feasible starting point for Algorithm 1 .

IV. COOPERATIVE ZERO FORCING PROCESSING IN SHO

A. Multiuser Zero Forcing Solution for SHO

Block diagonalization (BD) of multiple user channels com-bined with coordinated TX-RX processing and schedulingbetween users is a simple but efcient zero-forcing method[45]. An iterative BD method was originally proposed in [46],[53], and we later extended it in [54] to include joint user,bit and power allocation and a method to compensate forthe impact of a nite number of iterations. The iterative BDalgorithm [46], [53] is briey presented for the consideredsystem scenario in Algorithm 3 .

Algorithm 3: Iterative BD Decomposition1) Let a scheduling algorithm dene the number of streams

mk,c allocated for each user k A. Initialize F( i )k,c

matrix to include the dominant mk,c left singular vectorsof H wk,c . Let i = 1 .

2) Set H k,c = F ( i )k,cH

H wk,c , dene Ak = A\{k} andH k,c = [ H TA k (1) ,c . . . H TA k ( |A k | ) ,c ]T .3) Set V k,c to be the orthogonal basis for the null space

of H k,c so that H k,c V i,c = 0 for i = k.



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4) Perform SVD of H k,c = H wk,cV k,c = U k,c

12

k,c VHk,c ,

and let U k,c and V k,c represent the rst mk,c leftand right singular vectors of H k,c , respectively. SetF ( i+1)k,c = U k,c and check the stopping criterion. If it isnot satised, let i = i + 1 and go to Step 2, otherwiseSTOP.

The pre-coding matrix M k,c for user k is now dened asM BDk,c =

V k,c V k,c P12k,c = V

BDk,c P

12k,c (15)

where the diagonal matrix P k,c = diag p1,c , . . . , pm k,c ,ccontrols the powers allocated for each of the mk,c eigen-modes. As a result, the multiple-access interference (MAI)is eliminated between users, i.e., F Hk,c H

wk,c M

BDi,c = 0 for

i = k and the channel for user k is diagonalized toF Hk,c H

wk,c M

BDk,c =

BD 12k,c P

12k,c , where the diagonal matrix

BDk,c = diag k, 1,c , . . . , k,m k,c ,c includes the rst mk,ceigenvalues of k,c of user k. Note that in case of |A|= 1the above procedure is replaced by the well-known single userMIMO-OFDM precoder design [3], [4], [7].

B. Weighted Sum Rate Maximization with Cooperative ZF Transmission

In this section, we provide the power allocation for max-imizing the weighted sum rate with multiuser zero forcingprocessing under an individual power constraint for each BS.In [37], similar treatment was also provided for a singleuser MIMO transmission. With ZF processing the problemof maximizing the weighted sum of rates of the data streams

under per BS power constraint in (8) is reduced to

maximize N 1C kA

N C

c =1

m k,c

i =1

k,i log2 (1 + k,i,c pk,i,c )

s. t .kA

N C

c =1

m k,c

i =1

-

- v [n ]k,i,c

-

-

22 pk,i,c P n , n = 1 , . . . , M

pk,i,c 0, k A, i = 1 , . . . , m k,c , c(16)

where the variables are pk,i,c , k A, i = 1 , . . . , m k,c ,c = 1 , . . . , N C and P n is the power constraint on the BS n .The weights, k,i 0, k, i , are used to prioritize differentlythe data streams of different users. It is easy to observe thatthe objective function of (16) is concave and all the inequalityconstraints are afne. Thus, the problem (16) is a convexanalytic centering problem [27, Chapt. 8.5.3], and it can beefciently solved numerically by using standard optimizationsoftware packages, e.g., CVX [43], SeDuMi [52]. Under thesum power constraint, P sum and with equal user priorities, thesum rate is maximized by the well known water-lling powerallocation [49], pk,i,c = ( 1/ k,i,c )+ , where the waterlevel, , is chosen such that the sum power constraint holdswith equality, i.e., kA

N Cc=1

m k,ci=1 pk,i,c = P sum .

Inspired by the earlier work in [23], we also provide asimple heuristic algorithm which nd a suboptimal, but still

efcient, power allocation for the problem (16) with equal userpriorities. Similar to the sum power constraint case, we imposea water-lling power allocation, pk,i,c = ( 1/ k,i,c )+ , butthe water level is increased until one of the BSs reachesits power constraint. The water level can be efciently found

by using a bisection method [27], where in each iteration wesimply check all the per BS power constraints. In the caseof equal power constraints for all the BS, i.e., P n = P T ,n = 1 , . . . , M , the nal TX power is allocated such that theBS with strongest reception at the receiver is using the fullpower P T while the other BSs are using power less than P T . Itwill be shown in Section V-A that the heuristic method resultsin almost the same mutual information as (16).

C. Practical Considerations

Previous sections dealt with maximizing the mutual infor-mation with per BS power constraints. In practical systems, thenite granularity imposed by the nite set of modulation andcoding schemes (MCS) makes the bit and power optimizationproblems non-convex, and solutions similar to (8) are difcultif not impossible to obtain. We consider greedy bit andpower loading algorithms that try to maximize the achievablespectral efciency for a certain quality of service criteria,such as target frame error rate (FER). In order to guaranteethe per BS power constraints, the same heuristic solution asin the previous subsection is proposed. Basically, the onlydifference to an original single link algorithm, such as theHughes-Hartogs algorithm [55], is that the per BS powerconstraints, which are function of v [n ]k,i,c as in (5), are includedin the stopping criterion. Similarly to the previous section, theiterative process (bit and power loading) is continued until oneof the BSs in S k reaches its power constraint.In the numerical evaluation, a low complexity bit and powerloading algorithm requiring a low signalling overhead (LSO)is used [56]. In [54], we extended the LSO algorithm to theadaptive multiuser MIMO-OFDM system with ZF processing.Two iterations in Algorithm 3 were shown to be sufcient toachieve most of the gains from the iterative BD decomposition.The throughput degradation of the LSO relative to the optimalHughes-Hartog (HH) algorithm for a xed target frame errorrate (FER) was shown to be small while the signalling over-head was N C times reduced. See [54], [56] for more details.Note that a solution based on joint TX-RX design similar to(8) would require a new design of the bit and power loadingalgorithm, and hence, it is not considered in this paper.

In previous sections, we assumed that the inter-cell in-

terference R k,c was perfectly known at the transmitter andit could be incorporated into the whitened channel matrixH wk,c = R

12k,c H k,c . However, without R k,c known at the trans-

mitter the optimum pre-combiner obtained from the whitenedchannel matrix H wk,c cannot be computed [47]. Therefore, weuse a sub-optimal but still efcient design of the pre-coder,which relies on the channel knowledge only. The procedureto compute the sub-optimal pre-combining matrix per user isexactly the same as that in Section IV-A, except that H k,cis used in the algorithms instead of H wk,c . Due to the non-reciprocal interference at the receiver, inter-stream interferenceis not completely removed by the LMMSE receiver operation.

The SINR per sub-channel can no longer be controlled at thetransmitter but it is affected by the structure of R k,c [47].Therefore, a simple closed-loop algorithm that we introducedin [47] is used for compensating the effect of the interferencenon-reciprocity at the transmitter. This, combined with the



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interference suppression at the receiver (LMMSE), was shownto result in nearly the same performance as in the ideal case(R k,c known at the transmitter) [47].

V. S IMULATION RESULTS

The simulated OFDM system was based on HIPER-LAN/2 [57] and IEEE 802.11a assumptions, where the numberof subcarriers in the OFDM air interface is N C = 64 and thecyclic prex length is 16 samples. Except in the system levelstudies, the channel delay taps were considered independent of each other with a power delay prole specied by ETSI BRANChannel A [57], and the elements of the channel matrices weremodelled as i.i.d. Gaussian random variables. The number of both TX and RX antennas was xed at 2, {N T , N R k }= {2, 2}.For simplicity, we assume that all the base stations have equalmaximum power limit P T , i.e. P n = P T n . The impact of the following three power constraints are studied.

Sum power constraint : All M BSs in S k have perfectpower cooperation in addition to the data cooperation.This provides an unrealistic upper bound, where thepooled maximum available power is always P sum =MP T , while the antenna array gain from having MN T transmit antennas depends on the RX power differencesbetween the BSs.

Per BS power constraint : Available power can be in-creased up to M times depending on the RX powerdifference between BSs. Also, the antenna array gainfrom having MN T transmit antennas depends on the RXpower difference.

Shared single BS power constraint : The same total TX

power is used as in the single link case, i.e., P sum = P T is shared between M BSs and only the antenna arraygain is available.

A. Mutual Information Results

The mutual information for 2-branch SHO with differentpower constraints is studied. The impact of the inter-cellinterference is omitted for simplicity, i.e., R k,c = N 0 I . Fig. 2illustrates the single user ergodic mutual information for dif-ferent received power imbalance values = a2S k (2) ,k /a

2S k (1) ,k

and for 0 dB and 20 dB single link SNRs. S k (1) is the BSwith the strongest reception at the terminal and the single link SNR is dened as SNR = P T a2S k (1) /N 0 . As already shownin [37], the single user ( |A|= 1 ) rate optimization reduces to(16), where k,i,c and v k,i,c are the squared singular valuesand the right singular vectors of R

12

k,c H k,c , respectively.Fig. 2 shows that the performance of the proposed heuristic

method is close to the optimal solution (16) with per BS powerconstraints. Moreover, the gain from the joint processingquickly diminishes as the imbalance between the received BSpowers increases, especially at low SNR values. On the otherhand, the highest SHO gains are achieved at low SNR range,where the achievable rate can be even doubled. The achievable

rate with sum power constraint provides an unrealistic upperbound assuming that the BSs can share their TX powers.Sum power constraint with innite power imbalance (-Inf) isequivalent to the single link transmission with 3 dB higherSNR.

Inf 20 10 6 3 02

3

4

5

Rx power imbalance [dB]

E r g o d

i c M u

t u a l

I n f o r m a

t i o n

[ b i t s / s / H z ]

Inf 20 10 6 3 010

12

14

16

18

SHO, sum powerSHO, per BS power (opt.)SHO, per BS power (heur.)SHO, single BS powerSingle link capacity

SNR = 20 dB

SNR = 0 dB

Fig. 2. Single user ergodic mutual information of {N T , N R k , N C , M k } ={2, 2, 64, 2} system at 0 dB and 20 dB single link SNR.

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

User 1 rate [bits/s/Hz]

U s e r

2 r a

t e [ b i t s / s / H z ]

BC capacity region, sum powerBC capacity region, per BS powerLin. rate points, sum powerLin. rate points, per BS powerLin. rate region, sum power

Lin. rate region, per BS powerEqual weight points, sum powerEqual weight points, per BS power

Fig. 3. Broadcast capacity region and rate region with linear processing for{N T , N R k , N C , M } = {2, 2, 1, 2} system at 10 dB single link SNR with-3 dB RX power imbalance between BSs.

Next, we consider a multiuser case where two SHO users(labelled as u = 2 ) are served simultaneously by two BSsin a at fading scenario. Furthermore, we assume that they

have identical large scale fading coefcients for simplicity,i.e., aS 1 (1) ,1 = aS 2 (1) ,2 and aS 1 (2) ,1 = aS 2 (2) ,2 . First, theimpact of beamformer initialization on the behavior of thelinear weighted sum rate maximization algorithm is studied.Due to non-convexity of the original optimization problem (8),different initial beamformer congurations {v

(0)1 , . . . , v

(0)S }used in Algorithm 1 may end up in different local optima.

The behavior of the linear Algorithm 1 is illustrated inFig. 3 for 2-user channel, where rate pairs correspondingto different weight vectors are plotted with both sum andper BS power constraints. Equal weights are assigned to allstreams associated with one user. For each weight vector,

ten rate pair points are generated each with a random linearTX beamformer initialization. The rate region with linearprocessing is then plotted as a convex hull of the achievablerate pairs. Furthermore, the rate pairs corresponding to theequal user weights are indicated. The rate regions are plotted



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0 5 10 15 20 25 30 35 40 45 505

5.2

5.4

5.6

5.8

6

Number of random Tx beamformer initializations [n init]

E r g o d

i c S u m

R a t e

[ b i t s / s / H z ]

Sum capacity, per BS powerlin. max rate (random), sum powerlin. max rate (QR), sum powerlin. max rate (random), per BS powerlin. max rate (QR), per BS power

0 5 10 15 20 25 30 35 40 45 5012.5

13

13.5

14

14.5

E r g o d

i c S u m

R a t e

[ b i t s / s / H z ]

0 dB single link SNR

10 dB single link SNR

Fig. 4. The impact of the beamformer initialization on the ergodic sumrate of {N T , N R k , N C , M } = {2, 2, 1, 2} system with 0 dB RX powerimbalance at 0 dB and 10 dB single link SNR.

for a single random channel realization per user. All thepoints deviated from the boundary of the convex hull are localoptima. Note that the at parts in the rate regions are onlyachievable via time sharing. Moreover, the capacity regionwith per BS and sum power constraints, computed as in [25],are plotted as the absolute upper bounds of the scenario.

Fig. 4 depicts the ergodic 2-user sum rate as a functionof the number of random beamformer initializations. The bestout of n init random Tx beamformer initializations was selectedfor each channel realization. The imbalance between the BSs

is xed at 0 dB and single link SNRs are 0 dB and 10dB. The ergodic sum rate is depicted for the weighted sumrate maximization algorithm ( Algorithm 1 labelled as lin.max rate) with sum power and per BS power constraintsand with weight vector = 1 . Moreover, the sum capacitywith per BS power constraint is plotted as the absolute upperbound of the scenario. A large number of randomly choseninitializations increases the probability to nd a solution closeto the global optimum for each channel realization. It isseen from Fig. 4 that the impact of the initial beamformerconguration is relatively small and the gain achieved fromdrawing randomly several initial points saturates rapidly to

a xed value. We studied also a different approach wherethe initial transmit beamformers were obtained by applyingthe orthogonal-triangular QR decomposition to the set of dominant right singular vectors of user channels. The singularvectors were ordered in a descending order according to theirsingular values. The unitary vectors from the resulting Qmatrix were used as initial beamformers. As shown in Fig. 4,the QR based initialization method produces a very efcientstarting point, e.g., more than two random initializations arerequired to produce higher ergodic sum rate.

Figs. 5 and 6 illustrate the ergodic mutual information fordifferent power imbalance values, and for 0 dB and 10 dB

single link SNRs, respectively. The ergodic 2-user sum rateis depicted for the proposed algorithm with QR based initial-ization and the corresponding ZF method (Section IV) withdifferent power constraints. The single user case ( u = 1 ) withand without SHO is also included for comparison. The sum

20 10 6 3 02

2.5

3

3.5

4

4.5

5

5.5

6


E r g o d

i c M u t u a l

I n f o r m a

t i o n

[ b i t s / s / H z ]

SHO (u=2), sum capacity, sum powerSHO (u=2), sum capacity, per BS powerSHO (u=2), lin. max rate, sum powerSHO (u=2), lin. max rate, per BS powerSHO (u=2), ZF PL, per BS power (opt.)SHO (u=2), ZF PL, per BS power (heur.)SHO (u=2), ZF FL, per BS power (opt.)SHO (u=1), per BS power (opt)Single link capacity

Fig. 5. Ergodic sum rate of {N T , N R k , N C , M } = {2, 2, 1, 2} system at0 dB single link SNR.

20 10 6 3 04

6

8

10

12

14

16


E r g o d

i c M u

t u a l

I n f o r m a t

i o n

[ b i t s / s / H z ]

SHO (u=2), sum capacity, sum powerSHO (u=2), sum capacity, per BS power

SHO (u=2), lin. max rate, sum power

SHO (u=2), lin. max rate, per BS power

SHO (u=2), ZF PL, per BS power (opt.)

SHO (u=2), ZF PL, per BS power (heur.)

SHO (u=2), ZF FL, per BS power (opt.)

SHO (u=1), per BS power (opt)

Single link capacity

Fig. 6. Ergodic sum rate of {N T , N R k , N C , M } = {2, 2, 1, 2} system at10 dB single link SNR.

capacity bounds shown in Figs. 4, 5 and 6 are not generallyachievable with a linear transmission strategy. However, theproposed weighted sum rate maximization algorithm achievemore than 90 percent of the sum capacity with per BS power

constraints and a single sum power constraint. Note that theresulting ergodic sum rates for the proposed algorithm can bestill slightly improved if a few random initializations for eachchannel realization are allowed as seen in Fig. 4.

The zero forcing solution, labelled as ZF, is depicted fortwo scenarios: fully loaded case {m1 , m 2}= {2, 2}, labelledas FL, and partially loaded case, labelled as PL, where thebest allocation of mk among possible combinations {m1 , m 2}= [{2, 2}, {2, 1}, {1, 2}, {1, 1}] is selected for each channelrealization. It is seen from the gures that the zero forcing withfull spatial load (FL) performs rather bad, especially at lowSNR range. Even with large imbalance (

20 dB) both users

are intended to be served with two streams. This obviouslyreduces the achievable rate even below the single link capacity.The zero forcing with partial loading performs reasonablywell even at low SNR and approaches the weighted sum ratemaximization algorithm ( Algorithm 1 ) at high SNR. Again,



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Inf 20 10 6 3 01

1.5

2

2.5

3


S p e c t r a

l E f f i c i e n c y

[ b i t s / s / H z ]

Inf 20 10 6 3 04

4.5

5

5.5

SHO, sum powerSHO, per BS power (heur)SHO, single BS powerSingle link

SNR = 12 dB

SNR = 0 dB

Fig. 7. Single user spectral efciency (SEFF) of {N T , N R k , N C , M k } ={2, 2, 64, 2} system with LSO algorithm and with 10% FER target at 0 dBand 12 dB single link SNR.

the heuristic power loading solution performs almost as goodas the optimal method (16). The ZF method with heuristicpower loading and with partial spatial loading is used in thefollowing link and system level studies due to its simplicityand good performance. It also enables to decouple the datastreams, and hence, allows for an efcient implementation of the bit and power loading algorithms in practical systems.

B. Link Level Results

In this section, the single user (

|A|= 1 ) link level per-

formance for 2-branch SHO with different power constraintsis studied in terms of achievable spectral efciency. Again,the impact of inter-cell interference is omitted for simplicity,i.e., R k,c = N 0I . In the link level simulations, one codedOFDM frame consists of 8 OFDM symbols. Modulation andcoding schemes (MCS) used in the simulations were QPSK,16QAM and 64QAM, all turbo encoded and punctured to rate= 1/2. The minimum codeword length is lmin = 500 bits [56]and the SNRs required by each MCS to achieve the desiredtarget FER = 10% in AWGN channel are: 1.8 dB, 7.1 dB and11.6 dB, respectively. Fig. 7 illustrates the achievable spectralefciency for different power imbalance values and for 0 dBand 12 dB single link SNRs. With small power imbalance theSHO gains can be rather signicant. There is very little gainfrom the SHO at low SNR and with a high imbalance betweenBSs since the TX power is concentrated on the strongesteigenmode(s) only. However, the weaker BS has in generallarger contribution on the weaker eigenmode(s). Thus, SHOcan provide considerable gains at high SNR even with a largeimbalance, as the strongest eigenmode(s) become saturatedand more power is poured on the weaker eigenmode(s).

C. System Level Evaluation

A realistic multi-cell environment with 57 cells (19 3-sector antenna sites) was used for the system level evaluation.Fig. 8 illustrates the simulation scenario. It is assumed forsimplicity that the cooperative SHO processing of transmittedsignal is possible between any of the 57 BSs. Okumura-Hata

BS1

BS2

BS 3BS

4BS

5

BS 6

BS7

BS8

BS9

BS10

BS11

BS12

BS13

BS14

BS 15

BS16

BS17

BS18

BS19

BS20

BS21

BS22

BS23

BS 24

BS25

BS26

BS27

BS28

BS29

BS30

BS31

BS32

BS33

BS34

BS35

BS36

BS37

BS38

BS39

BS40

BS41

BS 42

BS43

BS44

BS45

BS46

BS47

BS48

BS49

BS50

BS51

BS52

BS53

BS54

BS55

BS56

BS57

Xcoordinate [m]

Y c o o r

d i n a

t e [ m ]

1500 1000 500 0 500 1000 1500

1500

1000

500

0

500

1000

1500Traced user locationsTraced users in SHO

Fig. 8. System level simulation scenario.

propagation model is used and the effect of antenna patternsis included in the path loss calculations [58]. The shadowingfactor is a log-normal random variable with mean of 0 dB andthe standard deviation of 6 dB.

Independent time-continuous fading process is simulatedfor each MIMO antenna transmitter-receiver pair includingboth the desired links H b,k , b S k and the most dominantinterference links b S k for each terminal k dropped inthe system. The channel coefcients are generated by a stan-dardized geometric stochastic channel model, 3GPP/3GPP2SCM model [58] with urban micro scenario. The simulationrun consist of D user drops where K users are randomlyuniform distributed within the geographic area of the systemin the beginning of each drop [58]. Only the center site usersdata is recorded for the statistics. Large scale mobility is notmodelled, but the time-continuous fading is emulated for thestationary users during a drop. An example distribution of some of the traced user locations is also shown in Fig. 8.

Universal frequency reuse one is assumed. The multipleaccess scheme is time division multiple access (TDMA),

where each user is assigned a xed length transmission slotwithin a DL TDD frame. The number of DL slots is set to24, each slot corresponding to 8 OFDM symbols. The samelink parameters are used as in Section V-B. Parameter K isadjusted such that different target average DL loads (time slotoccupation) are achieved. A simple dynamic transmission slotallocation scheme is used. It is assumed that the BS(s) areaware of each users received pilot power levels from all theadjacent cells and the user allocations in the adjacent cells.A user is allocated to a time slot within the DL TDD framewhere the resulting SINR is the highest. The SINR is denedas the ratio between the average RX power from the strongest

cell in S k and the average other-cell interference power. Theresulting user allocation tables are maintained xed during onesimulation drop. The BS TX power is xed to 33 dBm. Onlythose center site users with an average SINR more than 0 dBare traced for the statistics while the others are declared to



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be in the outage (dropped). The user locations are identicalbetween the simulation cases in order to make the resultscomparable.

Depending on the simulation case, the users having identicalSHO active set composition can be served within the sametime slot using the ZF SDMA method from Section IV-Awith two iterations and the joint user, bit and power allocationalgorithm from [54]. In order to simplify the simulationsetup, the SDMA is not considered for users assigned to asingle cell only ( |S k | = 1 ). For the single user transmission,we use the original LSO algorithm from [56]. The closed-loop interference non-reciprocity compensation algorithm ableto follow the time-continuous changes in the interferencestructure, is applied for each traced user in order to maintainthe target quality of service ( 10% FER) at the receiver [47]. Italso compensates for the residual MAI caused by the limitednumber of iterations in Algorithm 3 .

1) Single User TDMA Solution: First, the system levelimpact of the proposed SHO scheme is studied for the casewhere only one user can be allocated to a single time slot,i.e., SDMA between users having identical S k is not allowed.Fig. 9 illustrates the blocking and the total outage (blocking+ dropping) probability versus the system load with differentSHO parameters. The load is dened such that each user iscounted only in the cell where it is associated with, i.e., inthe cell with the highest received power. Due to the fact thatthe active SHO connection requires a physical resource (timeslot) allocated at each participating BS, the actual load withthe SHO can be signicantly larger than without the SHO.Typically, the overhead from the SHO varies between 20-50%

depending on the parameters used. Thus, the blocking prob-ability can be dramatically increased if the SHO parameters:SHO window, maximum SHO active set (AS) size, are toolarge. On the other hand, the dropping probability is decreasedcompared to the case without the SHO. Thus, the total outageprobability with the SHO can be even less than the one withoutthe SHO (Fig. 9). It must be noted, that the dropping criteriaused in these simulations (0 dB SINR) is rather strict since forthe channel allocation in the beginning of each user drop weassume that all the interfering BSs are transmitting with fullpower P T . Also, the SINR after receiver processing can besignicantly higher than the pre-processing SINR. Note that

the blocking probability depends also on the frame parameters(total number of slots), i.e., the larger the channel pool thelower the call blocking and vice versa.

The cumulative distribution function (CDF) of spectralefciency (SEFF) per user with different SHO window sizes( 3 dB and 6 dB) and power constraints is plotted in Fig.10. All the traced users are included in the statistics. Themaximum SHO active set size is limited to three in this case.The load used in the simulations in Fig. 10 corresponds to30% time slot occupation without the SHO. It is seen from thegure that signicant system level gains from the cooperativeSHO processing are available, especially with a large SHO

window. However, the 6 dB SHO window becomes too largewhen the load increases further from 30% due to the increasedoutage probability (Fig. 9).

The impact of two different power constraints is alsocompared in Fig. 10. The per BS power constraint implies

10 20 30 40 50 600

2

4

6

8

10

B l o c k

i n g

[ % ]

10 20 30 40 50 600

5

10

15

Load [%]

B l o c k

i n g +

D r o p p

i n g

[ % ]

AS size 3, 3dB SHO windowAS size 2, 3dB SHO windowAS size 3, 6dB SHO windowAS size 2, 6dB SHO windowno SHO

Fig. 9. The blocking and the total outage probability as a function of thesystem load, TDMA only.

1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SEFF per user [bits/s/Hz]

P r o

b a b

i l i t y S E F F >

A b s c i s s a

SHO, 3dB, shared single BS powerSHO, 3dB, per BS powerSHO, 6dB, shared single BS powerSHO, 6dB, per BS powerno SHO

Fig. 10. CDF of the spectral efciency per user with 30% system load andmax. AS size 3.

that the power consumption at BSs may be increased due tothe SHO overhead. Any BS in S k can use up to P T TX powerper time slot depending on the users received signal strength,imbalance between the SHO BSs, etc. Also, more inter-cell

interference is potentially generated. Therefore, it is interestingto compare it to the case where the power consumption ismaintained the same on average, independent of the SHOparameters used. The shared single BS power constraint doesnot increase the power consumption at the transmitters even if the SHO overhead is high, since the TX power P T of a singleBS is shared between M k transmitters. Also, the inter-cellinterference generated from a single BS is reduced with thesame ratio. In spite of generating more inter-cell interference,the per BS power constraint results in better overall systemperformance.

Obviously, the users located at the SHO region may enjoy

from greatly increased transmission rates, as depicted in Fig.11. The spectral efciency of those users that are outside of the SHO region is slightly reduced due to the increased inter-cell interference. However, the net performance improvementis clearly positive as seen from Fig. 10.



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1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SEFF per user [bits/s/Hz]

P r o

b a b i l i t y S

E F F >

A b s c i s s a

SHO, shared single BS powerSHO, per BS powerSHO, per BS power (SDMA)no SHO

Fig. 11. CDF of the spectral efciency per SHO user with 30% system load,max. AS size 3 and 3 dB SHO window.

10 20 30 40 50 600

2

4

6

8

10

B l o c k

i n g

[ % ]

10 20 30 40 50 600

5

10

15

Load [%]

B l o c k

i n g +

D r o p p i n g

[ % ]

AS size 3, 3dB SHO windowAS size 2, 3dB SHO windowAS size 3, 6dB SHO windowAS size 2, 6dB SHO windowno SHO

Fig. 12. The blocking and the dropping probability as a function of thesystem load, SDMA for SHO users.

2) Multiuser SDMA for SHO: Now, the SDMA betweenusers having an identical S k is enabled. The channel allocationalgorithm is slightly modied for the SDMA. Still, the newuser is allocated to the time slot where the resulting SINR

is the highest. For each new user k, the allocation table ischecked for whether there are any earlier allocated users iwith the same active set composition, S k = S i . If the availableSINR in the slot of the i th user is larger or equal than the bestfree slot, then the user k is allocated to the same slot with theuser i. The maximum number of users per time slot is limitedto M , and MN T kA mk,cc . The number of beamsallocated per user mk,c depends on the loading algorithm [54].Fig. 12 illustrates the outage probability of the system withdifferent SHO parameters. The probability of nding a userwith the same SHO active set composition depends on thesystem load and on the SHO parameters used. The largest

improvement in terms of reduced total outage is achievedwith a large SHO window, where the probability for suchan occurrence can be up to 40%. The SDMA reduces alsothe inter-cell interference by concentrating the transmissionson fewer time slots. Therefore, it decreases the dropping

probability as well. The overall outage probability is hencereduced in all SHO cases below the case without SHO.

Fig. 11 depicts also the spectral efciency distribution forthe case where the SDMA is enabled. Some performancepenalty from using the ZF method from Section IV-A is causedby its inherent noise amplication property [45], [54]. Also,the TX power is shared between the users allocated to thesame time slot. However, the overall reduction is rather smallresulting from the fact that the fading is independent at eachBS antenna site. At the same time less inter-cell interference isgenerated. Therefore, the total spectral efciency with SDMA(not shown) remains somewhat unchanged to the curves shownin Fig. 10.

VI . CONCLUSION

The joint cooperative processing of transmitted signal fromseveral MIMO BSs was considered for users located withina SHO region. The system level gains and trade-offs fromthe cooperative SHO processing were investigated. The math-ematical framework for the SHO based MIMO-OFDM systemwas derived and the joint design of linear TX and RXbeamformers in a MIMO multiuser transmission accordingto the weighted sum rate maximization criterion and subjectto per BS power constraints was considered. The proposedalgorithm was shown to provide very efcient solutions de-spite of the fact that there is no guarantee of achieving theglobal optimum due to the non-convexity of the optimizationproblem. Moreover, practical and efcient resource allocationmethods based on generalized ZF transmission were provided.

The impact of the size of the SHO region, overhead from theincreased hardware and physical (time, frequency) resourceutilization, and different non-reciprocal inter-cell interferencedistributions due to the SHO were evaluated by system levelsimulations. Although the overhead from the SHO processingcan be signicant, it can be mitigated by using zero forcingSDMA for users having an identical SHO active set compo-sition. Also, the dropping probability is decreased, and thus,the total outage probability with the SHO can be less thanwithout the SHO depending on the parameters used. The userslocated at the SHO region may enjoy from greatly increasedtransmission rates. This translates to signicant overall sys-

tem level gains from the cooperative SHO processing. Theproposed soft handover scheme can be used to provide moreevenly distributed service over the entire cellular network.

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Antti T olli (S03) received his M.Sc. (Tech.) degreein electrical engineering from University of Oulu,Oulu, Finland in 2000. From 1998 to 2003 heworked for Nokia Networks, IP Mobility Networksdivision as Research Engineer both in Finland andSpain. In 2003 he joined the Centre for WirelessCommunications (CWC) at University of Oulu, Fin-land where he is currently working toward the Dr.Tech. degree. His main research interests are inradio resource management for broadband wirelesscommunications with special emphasis on resource

allocation for multiuser MIMO-OFDM cellular systems.

Marian Codreanu (S02) was born in Bucharest,Romania in 1974. He received the M.Sc. (E.E.)degree from the University Politehnica of Bucharest,Romania in 1998. From 1998 to 2002 he was

Assistant at Telecommunications Department at Uni-versity Politehnica of Bucharest, Romania. In 2002he joined the Centre for Wireless Communications(CWC) at University of Oulu, Finland where he iscurrently working toward the Ph.D degree. His back-ground is in wireless communications and signalprocessing and his areas of interest includes mul-

tidimensional adaptive radio link, multi-carrier communications and MIMOtechniques.

Markku Juntti (S93-M98-SM04) received hisM.Sc. (Tech.) and Dr.Sc. (Tech.) degrees in Elec-trical Engineering from University of Oulu, Oulu,Finland in 1993 and 1997, respectively.

Dr. Juntti has been with Telecommunication Lab-oratory and Centre for Wireless Communications,University of Oulu in 199298. In academic year199495 he was a Visiting Scholar at Rice Uni-versity, Houston, Texas. In 19992000 he was withNokia Networks. Dr. Juntti has been a Professorof Telecommunications at University of Oulu since

2000. His research interests include communication and information theory,signal processing for wireless communication systems as well as theirapplication in wireless communication system design. He is an author or co-author in some 150 papers published in international journals and conferencerecords as well as in book WCDMA for UMTS published by Wiley.

Dr. Juntti is an Associate Editor for IEEE Transactions on Vehicular Technology . He was Secretary of IEEE Communication Society FinlandChapter in 1996-97 and the Chairman for years 2000-01. He has beenSecretary of the Technical Program Committee (TPC) of the 2001 IEEEInternational Conference on Communications (ICC01), and the Co-Chair of the Technical Program Committee of 2004 Nordic Radio Symposium. He isa Co-Chair of the TPC of 2006 IEEE International Symposium on Personal,Indoor and Mobile Radio Communications (PIMRC 2006).

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