Multiuser Successive Maximum Ratio Transmission (MS-MRT) for Video Quality Maximization in Unicast and Broadcast MIMO OFDMA-Based 4G Wireless Networks

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TVT.2014.2298249, IEEE Transactions on Vehicular Technology

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Multiuser Successive Maximum Ratio Transmission(MS-MRT) for Video Quality Maximization in

Unicast and Broadcast MIMO OFDMA based 4GWireless NetworksNikhil Gupta and Aditya K. Jagannatham

Abstract—In this work, we propose a novel low-complexitybeamforming algorithm for Multiuser Successive Maximum Ra-tio Transmission (MS-MRT) towards space-division multiplexingto achieve video quality maximization in the downlink of amultiuser (MU) multiple-input multiple-output (MIMO) OFDMAbased 4G wireless network. We compare the performance of thisalgorithm in terms of system throughput and video quality withthe two popular precoding techniques namely Block Diagonal-ization (BD) and Successive Optimization (SO). We also compareits performance with the generalized versions of these two algo-rithms termed Coordinated Transmit-Receive Processing (CTR)-BD and CTR-SO algorithms respectively. Further, we proposean extension of the MS-MRT scheme to broadcast scenarios,termed Broadcast Successive Maximum Ratio Transmission (BS-MRT), which computes the optimal Broadcast beamformingvector to maximize the video quality at each of the broadcastgroup members while maintaining orthogonality to the previouslyscheduled user groups. We also demonstrate that the proposedMS-MRT, BS-MRT schemes can be naturally adapted to thecontext of various multiuser OFDMA scheduling algorithms suchas proportional fairness (PF), Round Robin (RR) to name a few,to maximize video quality through optimal scheduling in thepresence of a large number of users. We discuss implementationsof the proposed MS-MRT scheme in association with thesescheduling algorithms for multiuser unicast and broadcast videotransmission scenarios. The simulation results presented in thiswork rely on the rate models derived using the JSVM (JointScalable Video Model) software developed by the Joint VideoTeam (JVT) and are thus readily applicable in practice. Thepresented results clearly demonstrate the ability of the proposedalgorithm to maximize the video quality in comparison tothe other competing multiuser MIMO precoding techniques.Further, employing the proportional fair scheduling algorithm inconjunction with the MS-MRT results in an overall enhancementin the received video quality compared to the Round Robin andMax-Rate algorithms.

I. INTRODUCTION

The recent evolution of 4G wireless networks has led to agreat demand for high speed broadband services over wireless

Copyright (c) 2013 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

The authors are with the Department of Electrical Engineering, Indian In-stitute of Technology, Kanpur, UP 208016, India (e-mail: [email protected],[email protected]).

This work is supported by research grants from the Department of Scienceand Technology (DST) India under the IU-ATC Project in Next GenerationNetworks (DST/EE/20120275), and IIMA-IDEA Telecom Center of Excel-lence (IITCOE/EE/20120301).

networks. In such 4G wireless networks, video transmissionis a highly popular service that requires fast and reliable datatransfer, with QoS constraints. One of the major technologiesthat has made this possible is orthogonal frequency division formultiple access (OFDMA) [1], which employs narrowband or-thogonal subcarriers for the transmission of parallel bitstreams,thus multiplexing several users over a wideband spectrum.Further, its unique IFFT/FFT architecture eliminates the inter-symbol interference resulting from frequency-selective fadingin wireless networks, while limiting the processing complex-ity. Deployment of multiple-input multiple-output (MIMO)systems additionally enhances the throughput through spatialmultiplexing, a scheme which essentially allows the transmis-sion of several independent information streams over parallelMIMO modes.

The above mentioned techniques can be readily appliedto 4G MIMO wireless systems to increase the data rate.Further, as the subscriber density increases in such networks,it is essential to multiplex an increasing number of users onthe limited spectral bandwidth. In such scenarios, Multiuser(MU) MIMO systems, with each user device possessingmultiple antennas, have been shown to be ideally suitedto support multiple users simultaneously. However, this canlead to an increase in the noise level of the system due tothe interference at the receiver from the signal intended forother users. In this context, several beamforming schemeshave been proposed for directional transmission of signals,thus facilitating the transmission of multiple streams to theusers, while simultaneously minimizing interference. Severalbeamforming techniques have been proposed in literature toaccomplish the above task.

In this scenario, the optimal transmission rate is achievedby Dirty Paper Coding (DPC) as described in [2], though thehigh complexity of such an algorithm makes it prohibitive inpractical scenarios. An analysis of various related techniqueshas been presented in [3]. It has been shown that zero-forcing based beamforming, which nulls the interference tothe unintended users, is a readily implementable sub-optimalbeamforming technique for MU-MIMO systems [4]. In [5],[6], the authors have proposed several novel beamformingtechniques such as Block Diagonalization (BD) and SuccessiveOptimization (SO) to reduce the co-channel interference inMIMO systems. However, in both these schemes, all theavailable modes of the selected users are employed, resulting



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in poor rates for other competing users. For instance, a userpossessing a large number of antennas can occupy a dispro-portionately large fraction of the spatial modes available atthe base station. In such scenarios, single mode beamformingcan result in fair transmission by simultaneously multiplexinga large number of users. In [7], the authors have suggesteda framework for Coordinated Transmit-Receive Processing, abeamforming technique based on [8], which not only supportssingle mode beamforming, but also generalizes the BD andSO algorithms to scenarios where the total number of receiveantennas exceeds the number of transmit antennas at thebase station. However, this technique is based on an iterativeprocedure to compute the optimal beamformers, resulting in ahigh computational complexity. In [5], authors have suggesteda non-iterative framework for CTR. However, it employs aheuristic method for the selection of the receive beamformers,which yields sub-optimal results.

Towards this end, similar to linear processing schemes suchas BD and SO, in this paper, we propose a low-complexitymultiuser beamforming algorithm based on maximum ratiotransmission [9], specifically targeted towards video qualitymaximization in 4G MIMO-OFDM wireless networks. Sim-ilar to successive optimization, it nullifies the interferenceto all the previously scheduled users from the successivelyscheduled users. Further, since it is based on beamformingemploying a single mode to each selected user, it is able toschedule a large number of users, thereby resulting in highervideo quality and improved QoS in high subscriber densityscenarios. This leads to enhanced end user video experiencewhen compared to the Block Diagonalization and SuccessiveOptimization techniques [10], [5]. Moreover, it employs thestrongest available mode for transmission to the user, leadingto higher user rates, and hence, better video quality whencompared to the non-iterative version of CTR [5]. The iterativeversion provides an additional marginal improvement in thevideo quality as compared to MS-MRT at the expense of veryhigh computational complexity. Thus, MS-MRT provides anattractive multi-user multi-antenna scheduling algorithm witha performance close the one given by the globally optimalbeamformer computation. The results also demonstrate thatthe proposed algorithm provides higher system throughput, ascompared to the other techniques.

Further, for broadcast scenarios, we develop an extension ofthe MS-MRT scheme, termed Broadcast Successive MaximumRatio Transmission (BS-MRT), which maximizes the net videoquality received by the Broadcast group. This is achievedby computing the optimal broadcast beamforming vector andmaintaining orthogonality to the successively scheduled broad-cast groups. This leads to a significant improvement in thevideo quality in broadcast scenarios as compared to the othercompeting techniques based on BD, SO and CTR for broadcastscenarios.

Moreover, as the number of users increases, it becomesprogressively difficult to schedule all the users simultaneously,which necessitates the selection of a subset of users to bescheduled for transmission of the parallel bitstreams. In [11],the authors have proposed various scheduling algorithms toachieve the best possible trade-off between throughput and

fairness without MU-MIMO i.e. for single antenna scenarios.In [12], the author has proposed a scheduling algorithm forMIMO systems with beamforming. However, this scheme issimplistic as it neglects the interference and assumes a singleantenna at each of the users. Subset selection in BD is complexowing to a combinatorial optimization over the user set, whilesuccessive optimization is better suited for such scenarios. Thisease of low-complexity user selection is naturally inheritedby the MS-MRT, BS-MRT schemes. We demonstrate the netenhancement in the video quality by implementing variousscheduling algorithms such as Proportional Fairness (PF),Round Robin (RR), etc. for MU-MIMO systems to select theoptimal set of users for the proposed beamforming technique.

Furthermore, in the context of video transmission, thescalable video coding (SVC) extension of the H.264 videocompression standard has been demonstrated in [13] as beingideal for video transmission over wireless networks. Hence,we employ an H.264 SVC based 4G wireless system forcomparing the video quality provided by the various precodingtechniques. This is subsequently used to compare the videoquality achieved by the usage of various scheduling algorithmssuch as Round Robin, Max-Rate and Proportional Fair inconjunction with the proposed beamforming technique. Thesesimulations in terms of video quality optimization employingpractical H.264 parameters clearly demonstrate directly thevideo quality performance compared to existing works such asBD and SO [6], [10] which focus exclusively on the data rate.This shows the suitability of the proposed schemes specificallyin the context of multimedia content transmission in currentand next generation 3G/ 4G wireless networks.

The organization of the rest of this paper is as follows.Section II describes the system model and the algorithm forthe proposed MS-MRT scheme. Section III provides a glimpseof the competing Block Diagonalization, Successive Optimiza-tion and Coordinated Transmit-Receive Processing for MU-MIMO systems. The proposed BS-MRT scheme for broadcastscenarios has been described in Section IV. Simulation resultshave been presented in Section V followed by conclusions inSection VI.

II. MULTIUSER SUCCESSIVE MAXIMUM RATIOTRANSMISSION FOR MIMO WIRELESS SYSTEMS

We consider a multiuser MIMO system, with one basestation with NT transmit antennas and K users. The number ofreceive antennas for user k is Nk for k = 1, 2, ...,K. Let eachHk ∈ CNk×NT denote the channel matrix between the basestation and user k. Let the distance from the base station andrandom shadowing factor for the kth user be denoted by rk andSk respectively. The quantity P denotes the power transmittedper subchannel per user. The Nk × 1 received signal vectoryk at user k is given as,

yk =

J∑j=1

Hkwjxj + nk, (1)

where xj is the symbol transmitted by the base station forthe user j, wj represents the NT × 1 beamforming vectorfor user j. The quantity nk is the Nk × 1 vector representing



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additive white Gaussian noise with zero mean and covarianceE{nkn

Hk

}= σ2I. Further, J ≤ K is the number of users

scheduled simultaneously per OFDMA subcarrier.Now, we describe the proposed MS-MRT beamforming

algorithm for multi-user MIMO transmission. Similar to SO[5], the selected user at each step experiences interferenceonly from the previous users. By choosing the beamformingvector which maximizes the user SINR, while maintaining nointerference to the previous users, it results in an increase inthe number of users being scheduled simultaneously, leading tohigher video quality. Further, this approach does not involvedecomposition of the aggregate channel matrices as is donein BD, SO, thereby decreasing the computational complexity.It employs successive orthogonal projections to achieve thiscriterion. Consider the initial user set U (0) = {1, 2, . . . ,K}.Let the SVD of H

(0)k = Hk, the channel matrix of the kth

user at stage 0 be given as,

H(0)k = U

(0)k Σ

(0)k

(V

(0)k

)H,

where U(0)k =

[u

(0)k,1,u

(0)k,2, . . . ,u

(0)k,Nk

]∈ CNk×Nk and

V(0)k =

[v

(0)k,1,v

(0)k,2, . . . ,v

(0)k,NT

]∈ CNT×NT are the left

and right singular matrices of H(0)k , while Σ

(0)k ∈ CNk×NT

contains the singular values σ(0)k,1 ≥ σ

(0)k,2 ≥ . . . ≥ σ

(0)k,Nk

alongits principal diagonal. Similar to maximum ratio transmissionone can now choose the first user ξ(0) as,

ξ(0) = arg maxiσ

(0)i,1 ,

with the transmit beamformer w0 = v(0)

ξ(0),1and the corre-

sponding receive beamformer u(0)

ξ(0),1. The user set can be

updated by removing the selected user ξ(0) as U (1) = U (0) \{ξ(0)}

. The channel matrices H(1)k for each k ∈ U (1) are

derived as,

H(1)k = H

(0)k P

((v

(0)

ξ(0),1

)⊥)= H

(0)k V

(0)

ξ(0)

(V

(0)

ξ(0)

)H, (2)

where P(a⊥)

denotes the projection matrix of the subspaceorthogonal to a and V

(0)

ξ(0)denotes the matrix,

V(0)

ξ(0)=[v

(0)

ξ(0),2,v

(0)

ξ(0),3, . . . ,v

(0)

ξ(0),NT

].

Let the SVD of H(1)k be given as H

(1)k = U

(1)k Σ

(1)k

(V

(1)k

)Hand σ

(1)k,j be the jth singular value of H

(1)k . Consider now

beamforming along the direction v(1)k,j , which is the right

singular vector associated with the singular value σ(1)k,j . This

is now precoded with the matrix P((

v(0)

ξ(0),1

)⊥)to yield

the beamformer w1 = P((

v(0)

ξ(0),1

)⊥)v

(1)k,j . Consider beam-

forming symbol xk of the user k ∈ U (1) chosen at stage 1. Thecorresponding received signal at user ξ(0) is given as, yξ(0) =

Hξ(0)v(0)

ξ(0),1xξ(0) + Hξ(0)P

((v

(0)

ξ(0),1

)⊥)v

(1)k,jxk︸︷︷︸

yIξ(0)

+nξ(0) .

It can now be readily seen that the interference yIξ(0)

=

Hξ(0)P((

v(0)

ξ(0),1

)⊥)v

(1)k,jxk can be simplified as,

U(0)

ξ(0)Σ

(0)

ξ(0)

(V

(0)

ξ(0)

)Hv

(1)k,jxk,

where the matrices U(0)

ξ(0), Σ

(0)

ξ(0), are defined as,

U(0)

ξ(0)=

[u

(0)

ξ(0),2,u

(0)

ξ(0),3, . . . ,u

(0)

ξ(0),NT

]Σ

(0)

ξ(0)= diag

(σ

(0)

ξ(0),2, . . . , σ

(0)

ξ(0),NT

).

Hence, beamforming in the direction of u(0)

ξ(0),1at user ξ(0) as

described above results in the interference,(u

(0)

ξ(0),1

)HyIξ(0)

=(u

(0)

ξ(0),1

)HU

(0)

ξ(0)Σ

(0)

ξ(0)

(V

(0)

ξ(0)

)Hv

(1)k,jxk = 0.

Thus, the net interference at user ξ(0) is 0. Further, it can bereadily seen that the receive beamformer at the chosen userk ∈ U (1) at stage 1 is u

(1)k,j . Hence, the SINR at user k for

mode j is therefore given as,

SINR(1)k,j =

PSkr2k

(σ

(1)k,j

)2

σ2n + PSk

r2k

∣∣∣∣(u(1)k,j

)HH

(0)k v

(0)ξ(0),1

∣∣∣∣2(3)

Naturally then, the criterion to choose user ξ(1) and its modeζ(1) at stage 1 can be formulated as,(

ξ(1), ζ(1))

= arg max(k,j)

SINR(1)k,j .

Continuing for J stages, selection of J users yields the finalMS-MRT transmitted vector for the selected users ξ(i) withrespective modes ζ(i), 0 ≤ i ≤ J − 1, with each ξ(i) ∈ U (0)

as,J−1∑j=0

j−1∏k=0

P((

v(k)

ξ(k),ζ(k)

)⊥)v

(j)

ξ(j),ζ(j)xξ(j) .

Note that we define∏−1j=0 , 1,

∑−1j=0 , 0 and ζ(0) = 1. The

SINR at user ξ(j) for mode ζ(j) chosen at the lth stage isgiven as, SINR

(l)

ξ(l),ζ(l)=

PSξ(l)

r2ξ(l)

(σ

(l)

ξ(l),ζ(l)

)2

σ2n +

∑l−1k=0

PSξ(l)

r2ξ(l)

∣∣∣∣(u(l)

ξ(l),ζ(l)

)HH

(0)

ξ(l)w

(k)

ξ(k),ζ(k)

∣∣∣∣2, (4)

where w(j)

ξ(j),ζ(j), the beamformer for user ξ(j) and mode ζ(j)

is given as

w(j)

ξ(j),ζ(j)=

j−1∏k=0

P((

v(k)

ξ(k),ζ(k)

)⊥)v

(j)

ξ(j),ζ(j)(5)

and ζ(0) = 1. Thus, successive transmission on a specific modeof each user while simultaneously nulling the interference atthe previously chosen users can be achieved through MS-MRT,thereby enhancing the fairness of the overall data and videoscheduler. This is succinctly summarized in Algorithm 1. Thus,



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the NT × NT interference matrix is lower triangular sincethe interference from the successively scheduled users is zeroalong the dominant receive mode of the previously scheduledusers. The above procedure corresponds to an a opportunisticscheduler which schedules the user with the maximum SINRat each stage. This can be readily adapted for proportionalfairness based PF-MS-MRT scheduling, which maximizes thevideo quality, by choosing the user and corresponding modeat stage u as,

(ξ(u), ζ(u)

)= arg max

(k,j)

log2

(1 + SINR

(u)k,j

)Rtk

, (6)

where Rtk is the average rate experienced by user k at time t.This average rate is updated as,

Rtk = It (k)α log2

(1 + SINR

(u)

k,ζ(u)

)+ (1− α) Rt−1

k ,

where It (k) is the indicator function of user k being sched-uled at time instant k, meaning to say it is equal to 1 if userk is scheduled at time t and zero otherwise. Finally, the naiveround robin (RR) scheduler simply chooses the next user atstage u as ξ(u) =

(ξ(u−1) + 1

)mod K and its mode as

ζ(u) = arg maxj

SINRξ(u),j . (7)

III. ALLIED BEAMFORMING TECHNIQUES

Below, we describe the existing BD, SO and CTR beam-forming schemes for MU-MIMO scheduling for the purposesof comparison with the proposed MS-MRT scheme.

A. Block Diagonalization

BD precodes the transmission of each user to lie in a spaceorthogonal to the rest of the users, thereby zero-forcing theinterference [5]. This is achieved as follows. For each useri ∈ U , define the augmented matrix Hi as,

Hi =[HT

1 ,HT2 , . . . ,H

Ti−1,H

Ti+1, . . . ,H

TK

]T.

Let SVD(Hi

)= UiΣiV

Hi . The zero-forcing precoding

vectors for user i are therefore given by the columns of thematrix Vi associated with zero singular values i.e. the rightsub-matrix of dimension NT ×

(NT − rank

(Hi

)). Denote

this matrix by V⊥i . Further, for optimal power allocation,let Hi = HiV

⊥i be decomposed as UiΣiV

Hi . The power

loading matrix Qi is computed by water-filling on the diagonalelements of Σi with power constraint PSi

r2i. Hence, the precoder

for the ith user is given as, Wi = V⊥i ViQ1/2i . Further, the

covariance of the received output is HiWiWHi HH

i , whichcan be employed to compute the rate. However, observe thatthe key problem with BD is user selection, since knowledge ofthe all the K users is necessary to zero-force the interferencefor each user. As the number of users grows, this problemis combinatorially complex, rendering it impractical in largeuser scenarios. A more practical algorithm, which successivelycancels the interference at each of the previously chosen usersis successive optimization, which is summarized below.

B. Successive Optimization

Consider the users Ξi−1 ,{ξ(0), ξ(1), ..., ξ(i−1)

}chosen

until stage i. The augmented channel matrix for user k ∈U − Ξi−1 can be defined as,

H(i)k =

[HTξ(0) ,H

Tξ(1) , . . . ,H

Tξ(i−1)

]T.

Similar to BD, let SVD(H

(i)k

)= U

(i)k Σ

(i)k

(V

(i)k

)H. Again

denote the right NT ×(NT − rank

(Hk

))sub-matrix of

V(i)k , corresponding to zero singular values by

(V

(i)k

)⊥.

Further, the interference matrix Γi can be defined as Γ(i)k ,

σ2nI +

∑i−1j=0 HkWξ(j)W

Hξ(j)

HHk , where Wξ(j) is the precod-

ing matrix for user ξ(j) [5]. Let

U(i)k Σ

(i)k

(V

(i)k

)H= SVD

(H

(i)k

),

where H(i)k =

(Γ

(i)k

)−1/2

Hk

(V

(i)k

)⊥. The optimal power

loading matrix Q(i)k for user k can then be computed by wa-

terfilling on the diagonal matrix Σ(i)k with the power constraint

PSkr2k

. The transmit precoding matrix for user k is then given as

Wk =(V

(i)k

)⊥V

(i)k

(Q

(i)k

)1/2

. Naturally, the user at stagei can be chosen as

ξ(i) = arg maxk∈U−Ξi−1

log2

∣∣∣∣I + HkWkWHk HH

k

(Γ

(i)k

)−1∣∣∣∣ .

C. Coordinated Transmit Receive Processing

BD and SO algorithms require NT ≥∑Jj=1Nj . CTR

generalizes these precoding techniques while also describinga method for single mode transmission. Let wj be the 1×Nkbeamformer for user j. Let SVD (Hj) = UjΣjV

Hj . As de-

scribed in [5], the reception of the data using a beamformer wj

is equivalent to normal reception using the modified channelmatrices given by, Hj = wH

j Hj . The non-iterative (NI)versions, i.e. CTR-BD-NI and CTR-SO-NI simply suggest wj

to be given by the first column of Uj . The optimal iterativeCTR-BD-I and CTR-SO-I, described in [7] employ thesereceive beamformers wj to compute the transmit beamformerfor each user j using Hj as the effective channel matrix viathe BD and SO algorithms respectively, which in turn areused to iteratively update the respective receive beamformingvectors wj . This process is repeated until convergence. In eachiteration, NT SVD operations are required for the iterativeCTR schemes, compared to MS-MRT, which is a single passalgorithm similar to successive optimization. Hence, in MS-MRT, there is only one iteration with NT SVD operations.Therefore, the complexity of CTR-BD-I and CTR-SO-I is ofthe order of the number of iterations times that of MS-MRT.Further, convergence is also an issue in the iterative CTRalgorithms, since convergence cannot be proved in general tothe optimal beamformers. Thus, they are less robust comparedto MS-MRT.



5

Algorithm 1 Multiuser Successive Maximum Ratio Transmission (MS-MRT)

1: Set user group U (0) = U = {1, 2, ...K}. Let H(0)k = Hk for all users k ∈ U (0), and [U

(0)k ,Σ

(0)k ,V

(0)k ] = SVD(H

(0)k ).

2: for u = 0 to J − 1 do3: for k ∈ U (u) do4: for l = 1 to Nk do5: Set beamformer w

(u)k,l as in (5) and compute SINR

(u)k,l as in (4).

6: end for7: end for8: Choose ξ(u) and mode ζ(u) at stage u as

(ξ(u), ζ(u)

)= arg max(k,l)

SINR(u)k,l

Rk, where SINR

(u)k,l ,

P(u)k,l

I(u)k,l

, Rk is the

average rate for proportional fair scheduling and Rk = 1 for max rate scheduling. For round robin, ζ(u) is simply the nextuser to be scheduled.

9: Update user group U (u+1) = U (u) \{ξ(u)

}and H

(u+1)k as in (2).

10: Let [U(u+1)k ,Σ

(u+1)k ,V

(u+1)k ] = SVD(H

(u+1)k ).

11: end for12: The transmit vector for the chosen users ξ(i), 0 ≤ i ≤ J − 1 is

∑J−1j=0 w

(j)

ξ(j),ζ(j)xξ(j) , where xξ(j) is the symbol intended

for user ξ(j).13: Additionally, for PF-MS-MRT, update the average user rate for each user in U .

IV. BS-MRT FOR BROADCAST SCENARIOS

The beamforming techniques presented thus far are focusedtowards point-to-point unicast communication scenarios. How-ever, frequently, multimedia transmission occurs in multicast/broadcast mode, where the same content is required to betransmitted to a particular set of users. A simplistic simulcastin which similar content is streamed to different users is sub-optimal and leads to inefficiency in bandwidth utilization.Thus, motivated by this requirement, we develop a multiuserMIMO precoding framework for optimal broadcast transmis-sion employing MS-MRT. Consider the initial set of groupsG(0) = {G1,G2, ...,GL} where each Gl =

{l(1), l(2), ..., l(Kl)

}denotes the lth group of broadcast users. Let H

(0)l(k)

= Hl(k)

denote the channel matrix of user k in group Gl at stage 0.Let Ml,j =

{j(1), j(2), ..., j(Kl)

}denote the set of respective

modes of the users in the group Gl. Hence, the broadcast MS-MRT signal meant for group Gl at stage 0 is given as,

s(0)l,j =

(Kl∑k=1

γ(0)l(k)

v(0)l(k),j(k)

)︸︷︷︸

w(0)l,j

x(0)l , (8)

where x(0)l is the symbol corresponding to group Gl, v

(0)l(k),j(k)

denotes the(j(k)

)thright singular vector of the matrix H

(0)l(k)

and the Kl dimensional vector γ(0)l =

[γ

(0)l(1), γ

(0)l(2), ..., γ

(0)l(Kl)

]Tis the precoding vector for group Gl at stage 0. Let the NT×Kl

dimensional beamformer matrix V(0)l,j be defined as,

V(0)l,j = [v

(0)l(1),j(1)

,v(0)l(2),j(2)

, ...,v(0)l(Kl)

,j(Kl)].

Hence, the broadcast beamforming vector w(0)l,j for the lth

broadcast group at stage 0 is given as w(0)l,j = V

(0)l,j γ

(0)l . The

signal received by the kth user l(k) ∈ Gl for mode j(k) at stage0 corresponding to the receive beamformer u

(0)l(k),j(k)

is given

as,(u

(0)l(k),j(k)

)Hy

(0)l(k),j(k)

= r(0)l(k),j(k)

= σ(0)l(k),j(k)

γ(0)l(k)xk +

(u

(0)l(k),j(k)

)Hn

(0)l(k)

+

Kl∑m=0m6=k

σ(0)l(k),j(k)

(v

(0)l(k),j(k)

)Hγ

(0)l(m)

v(0)l(m),j(m)

xk, (9)

where σ(0)l(k),j(k)

denotes the jth(k) singular value of the channel

matrix H(0)l(k)

. Consider the vector of gains σ(0)l(k),j(k)

definedas,

σ(0)l(k),j(k)

=

σ(0)l(k),j(k)

(v

(0)l(1),j(1)

)Hv

(0)l(k),j(k)

,

...σ

(0)l(k),j(k)

,

...

σ(0)l(k),j(k)

(v

(0)l(Kl)

,j(Kl)

)Hv

(0)l(k),j(k)

σ

(0)l(k),j(k)

= σ(0)l(k),j(k)

(V

(0)l,j

)Hv

(0)l(k),j(k)

. (10)

Hence, the relation in (9) for the test statistic r(0)l(k),j(k)

can besimplified as,(

σ(0)l(k),j(k)

)Hγ

(0)l xk +

(u

(0)l(k),j(k)

)Hn

(0)l(k).

Thus, the sum total SINR for all the users in the broadcastgroup Gl with respective modes Ml,j at stage 0 is given as,

SINR(0)l,j =

(γ

(0)l

)HP

(0)l,j γ

(0)l ,

where the matrix P(0)l,j is defined as,

P(0)l,j =

Kl∑k=1

(Sl(k)r2l(k)

)σ

(0)l(k),j(k)

(σ

(0)l(k),j(k)

)Hσ2n

.



6

Further, the constraint on the transmitted broadcast signalpower requires,(

γ(0)l

)H (V

(0)l,j

)HV

(0)l,j γ

(0)l ≤ KlP,

where P denotes the power transmitted per subchannel peruser. The optimal broadcast precoding vector γ

(0)l which

maximizes the sum SINR(0)l,j for the above transmit power

constraint is given as,

γ(0)l =

√KlPvm

(A

(0)l,j

)√(

vm

(A

(0)l,j

))H (V

(0)l,j

)HV

(0)l,j vm

(A

(0)l,j

) , (11)

where A(0)l,j =

(P

(0)l,j

)−1 (V

(0)l,j

)HV

(0)l,j and vm

(A

(0)l,j

)de-

notes the principal eigenvector corresponding to the matrixA

(0)l,j . Moreover, the optimal choice of the group Gξ(0) and

the respective modes of the broadcast members Mξ(0),ζ(0) isgiven as, (

Gξ(0) ,Mξ(0),ζ(0))

= arg max(l,j)

SINR(0)l,j .

The set of groups of users is updated by removing the selectedbroadcast group Gξ(0) as G(1) = G(0) \

{Gξ(0)

}. Similar to

MS-MRT for multiuser MIMO scheduling over point-to-pointlinks, it is required to maintain orthogonality of the signalspace of the successively scheduled groups to the previouslyscheduled ones. In this context, let the SVD of V

(0)

ξ(0),ζ(0)be

given as V(0)

ξ(0),ζ(0)= U

(0)

ξ(0),ζ(0)Σ

(0)

ξ(0),ζ(0)

(V

(0)

ξ(0),ζ(0)

)Hwhere

the NT ×NT matrix V(0)

ξ(0),ζ(0) is defined as,

V(0)

ξ(0),ζ(0) =[v

(0)1 ,v

(0)2 , . . . ,v

(0)NT

].

Thus, the channel matrices H(1)l(k)

for each l(k) ∈ G(l) for eachG(l) ∈ G(1) are derived as,

H(1)l(k)

= H(0)l(k)P((

V(0)

ξ(0),ζ(0)

)⊥)= H

(0)l(k)

V(0)

ξ(0),ζ(0)

(V

(0)

ξ(0),ζ(0)

)H, (12)

and P((

V(0)

ξ(0),ζ(0)

)⊥)denotes the projection matrix cor-

responding to the null space of V(0)

ξ(0),ζ(0)and is given as

P((

V(0)

ξ(0),ζ(0)

)⊥)= V

(0)

ξ(0),ζ(0)

(V

(0)

ξ(0),ζ(0)

)H, where the

NT −K(0)ξ ×NT matrix V

(0)

ξ(0)is defined as,

V(0)

ξ(0)=[v

(0)Kξ(0)

+1,v(0)Kξ(0)

+2, . . . ,v(0)

ξ(0),NT

].

Consider now beamforming employing the precoding vectorγ

(1)l for the broadcast group chosen at stage 1 as V

(1)l,j γ

(1)l ,

where V(1)l,j is defined as,

V(1)l,j = [v

(1)l(1),j(1)

,v(1)l(2),j(2)

, ...,v(1)l(Kl)

,j(Kl)],

and v(1)l(k),j(k)

denotes the(j(k)

)thright singular vector of

the matrix H(1)l(k)

at stage 1. Maintaining the successive or-thogonality between the broadcast groups, the beamforming

vector w(1)l,j is given as w

(1)l,j = P

((V

(0)

ξ(0),ζ(0)

)⊥)V

(1)l,j γ

(1)l .

Consider now, beamforming the symbol xl of the broadcastgroup G(l) ∈ G(1) chosen at stage 1.The correspondingreceived signal y

ξ(0)

(k),ζ

(0)

(k)

at user ξ(0)(k) ∈ Gξ(0) is given as,

yξ(0)

(k),ζ

(0)

(k)

= Hξ(0)

(k)

w(0)

ξ(0),ζ(0)xξ(0) + nξ(0)

+ Hξ(0)

(k)

P((

V(0)

ξ(0),ζ(0)

)⊥)w

(1)l,j xl︸︷︷︸

yIξ(0),ζ(0)

.

It can now be readily seen similar to MS-MRT that beamform-ing in the direction of u

(0)

ξ(0)k ,ζ

(0)k

forces the net interference ateach user k of group Gξ(0) to be 0. Further, it can be readilyseen that the receive beamformer at the user l(k) for modej(k) at stage 1 is u

(1)l(k),j(k)

. Hence, the optimal sum total SINRfor all users in the broadcast group Gl with respective modes

Ml,j at stage 1 is given as SINR(1)l,j =

(γ

(1)l

)HP

(1)l,j γ

(1)l ,

where P(1)l,j and γ

(1)l are given as,

P(1)l,j =

Kl∑k=1

Sl(k)r2l(k)

σ(1)l(k),j(k)

(σ

(1)l(k),j(k)

)Hσ2n +

PSl(k)r2l(k)

∣∣∣q(1)l(k),j(k)

∣∣∣2γ

(1)l =

√KlPvm

(A

(1)l,j

)√(

vm

(A

(1)l,j

))H (V

(1)l,j

)HV

(1)l,j vm

(A

(1)l,j

)where q

(1)l(k),j(k)

=(w

(0)l,j

)H (H

(1)l(k)

)Hu

(1)l(k),j(k)

and A(1)l,j =(

P(1)l,j

)−1 (V

(1)l,j

)HV

(1)l,j . Naturally then, the criterion to

choose broadcast group Gξ(1) and the respective modes of itsusers Mξ(1),ζ(1) is given as,

(Gξ(1) ,Mξ(1),ζ(1)

)= arg max

(l,j)SINR

(1)l,j .

Continuing for J stages, the selection of J groups yields thefinal MS-MRT transmitted vector for the selected groups Gξ(i)with respective modes Mξ(i),ζ(i) , 0 ≤ i ≤ J − 1, with eachGξ(i) ∈ G(0) as,

J−1∑j=0

(j−1∏l=0

P((

V(l)

ξ(l),ζ(l)

)⊥))Kξ(j)∑k=1

γ(j)

ξ(j)

(k)

v(j)

ξ(j)

(k),j(k)

xξ(j) ,

and the SINR at group Gξ(l) and respective modes of its usersMξ(l),ζ(l) chosen at the lth stage is given as SINRξ(l),ζ(l) =(γ

(l)

ξ(l)

)HP

(l)

ξ(l),ζ(l)γ

(l)

ξ(l)where the matrix P

(l)

ξ(l),ζ(l)is defined



7

as,

P(l)

ξ(l),ζ(l)=

Kξ(l)∑k=1

Sξ(l)(k)

r2ξ(l)(k)

σ(l)

ξ(l)

(k),ζ

(l)

(k)

(σ

(l)

ξ(l)

(k),ξ

(l)

(k)

)Hσ2n +

Sξ(l)(k)

r2ξ(l)(k)

∣∣∣∣q(l)

ξ(l)

(k),ζ

(l)

(k)

∣∣∣∣2. (13)

The quantity q(l)

ξ(l)

(k),ζ

(l)

(k)

is given as

q(l)

ξ(l)

(k),ζ

(l)

(k)

=

(l−1∑m=0

(w

(m)

ξ(m),ζ(m)

)H)H

(l)

ξ(l)

(k)

Hu

(l)

ξ(l)

(k),ζ

(l)

(k)

,

and the optimal broadcast precoding vector γ(l)

ξ(l)=√

Kξ(l)Pvm

(A

(l)

ξ(l),ζ(l)

)√(

vm

(A

(l)

ξ(l),ζ(l)

))H (V

(l)

ξ(l),ζ(l)

)HV

(1)

ξ(l),ζ(l)vm

(A

(l)l,j

) ,(14)

with the matrix A(l)

ξ(l),ζ(l)defined as

A(l)

ξ(l),ζ(l)=

((P

(l)

ξ(l),ζ(l)

)−1 (V

(l)

ξ(l),ζ(l)

)HV

(l)

ξ(l),ζ(l)

).

The beamforming vector w(l)

ξ(l),ζ(l)for the broadcast group

Gξ(l) chosen at stage l is given as,

w(l)

ξ(l),ζ(l)=

(l−1∏m=0

P((

V(m)

ξ(m),ζ(m)

)⊥))Kξ(l)∑k=1

γ(l)

ξ(l)

(k)

v(l)

ξ(l)

(l),j(k)

.

(15)

This technique is succinctly summarized in Algorithm 2. As inthe case of MS-MRT for unicast scenarios, this can be readilyadapted to PF-MS-MRT and RR-MS-MRT for proportionallyfair and round robin broadcast group scheduling scenariosrespectively. Simulation results to validate the performance ofthe MS-MRT, BS-MRT beamforming schemes for unicast andbroadcast multimedia transmission under various schedulingalgorithms are given below.

V. SIMULATION RESULTS

To simulate the performance of the proposed algorithm,we consider a typical WiMAX scenario with a cell of radius10 Km, number of subchannels Ns = 30, with 24 OFDMsubcarriers per subchannel, [14] resulting in a bandwidth persubchannel of Bw = 262.56 KHz. In [15], the authors havedescribed various parametric models which can be employedto model the video rate and quality for an H.264 SVC based4G wireless system. In [16] the overall video rate as a functionof the frame rate t and quantization parameter q of the videosequence has been modeled as,

R (q, t) = Rmax

(1− e−ct/tmax

1− e−c

)ed(1−q/qmin),

where Rmax refers to rate of the video of highest qualitycorresponding to the highest frame rate tmax = 30 framesper second and finest quantization parameter qmin = 15. Themaximum quantization parameter qmax is set to 40 as valuesof q beyond 40 lead to poor video quality. Similarly, the video

Algorithm 2 Broadcast MS-MRT

1: Consider initial set G(0) = {G1,G2, ...,GL}. Let H(0)l(k)

= Hl(k) and [U(0)l(k),Σ

(0)l(k),V

(0)l(k)

] = SVD(H(0)l(k)

) for each userl(k) ∈ G(l) for all G(l) ∈ G(0). Let Ml,j =

{j(1), j(2), ..., j(Kl)

}for all Gl and all possible sets of respective modes of the

users.2: for u = 0 to J − 1 do3: for Gl ∈ G(u) do4: for all Ml,j do5: for k ∈ Gl do6: Set V

(u)l,j =

[v

(u)l(1),j(1)

,v(u)l(2),j(2)

, ...,v(u)l(Kl)

,j(Kl)

].

7: Set σ(u)l(k),j(k)

= σ(u)l(k),j(k)

(V

(u)l,j

)Hv

(u)l(k),j(k)

.

8: Compute q(u)l(k),j(k)

=(u

(u)l(k),j(k)

)HH

(u)l(k)

∑u−1m=0 w

(m)

ξ(m),ζ(m) . Note∑−1m=0 , 0.

9: end for10: Compute P

(u)l,j as in (13) and γ

(u)l as in (14).

11: Set beamformer w(u)l,j as in (15).

12: Compute SINR(u)l,j =

(γ

(u)l

)TP

(u)l,j γ

(u)l .

13: end for14: end for15: Choose group Gξ(u) and modes Mξ(u),ζ(u) given as

(Gξ(u) ,Mξ(u),ζ(u)

)= arg max(l,j) (SINR)

(u)l,j .

16: Update set G(u+1) = G(u) \{Gξ(u)

}and H

(u+1)l(k)

as in (12).17: end for18: The transmit vector for the chosen groups Gξ(i) with respective modes Mξ(i),ζ(i) , 0 ≤ i ≤ J − 1 is

∑J−1j=0 w

(j)

ξ(j),ζ(j)xξ(j) ,

where xξ(j) is the symbol intended for group Gξ(j) .19: Additionally, for PF-MS-MRT, update the average group rate for each group in G(0).



8

16 18 20 22 24 26 28 30 32 34

50

55

60

65

70

75

80

85

90

95

Power transmitted per subchannel per user (dB)

Vid

eo Q

ualit

yVideo Quality Vs Power transmitted per subchannel per user

SOMS−MRTBDCTR−BD−ICTR−BD−NICTR−SO−ICTR−SO−NI

Fig. 1: Video Quality vs Power for various competing MU-MIMOtransmission techniques SO, MS-MRT, BD, CTR-BD, CTR-SO (I,NIi.e. iterative and non-iterative versions).

quality can be expressed as,

Q(q, t) = Qmax

(1− e−at/tmax

1− e−a

)(βq + γ),

where Qmax refers to the video quality when it is coded att = tmax and q = qmin. In this work, we have normalizedQmax to have a value of 100. The JSVM reference codecparameters a, c, d, β, γ for various video sequences allotted tothe users are given in Table I. These H.264 video rate andquality parameters are derived from the work in [16] basedon the theory in [15]. For this study, we set the frame ratet = tmax and consider exclusively the variation of the videoquality with the quantization parameter. Hence, given the rateof the user, the corresponding video quantization parameter qand the associated video quality can be derived from the aboveframework.

Fig.1 and Fig.2 show the plot of the video quality andthroughput respectively vs. power for the proposed MS-MRTbeamforming scheme and several other existing techniquesdescribed in Section III. Fig.3 gives the cumulative distributionfunction of the video quality for these techniques. For BlockDiagonalization (BD), an optimal subset of users is chosen byiterating through all the possible user subsets and selecting theone with the maximum SINR. For the other techniques such asSuccessive Optimization (SO), successive users in the subsetwere chosen based on the MaxSINR criterion. In the figure,CTR-BD and CTR-SO refer to the Coordinated Transmit Re-

16 18 20 22 24 26 28 30 32 34

2

4

6

8

10

12


Ave

rage

Thr

ough

put (

Mbp

s)

Average Throughput Vs Power transmitted per subchannel per user

SOMS−MRTBDCTR−BD−ICTR−BD−NICTR−SO−ICTR−SO−NI

Fig. 2: Average Throughput vs Power for various competing MU-MIMO transmission techniques SO, MS-MRT, BD, CTR-BD, CTR-SO(I,NI i.e. iterative and non-iterative versions).

65 70 75 80 85 90 95 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Video Quality

CD

F

CDF of Video Quality for various MU−MIMO techniques at P = 32 dB

MS−MRTCTR−BD−ICTR−BD−NIBDCTR−SO−ICTR−SO−NISO

Fig. 3: CDF of Video Quality for various competing MU-MIMOtransmission techniques SO, MS-MRT, BD, CTR-BD, CTR-SO (I,NIi.e. iterative and non-iterative versions) at P=32 dB.

TABLE I: Model Parameters for Various Video Sequences

Video Sequence Rmax(Kbps) a c d β γ

City 2775.5 7.3500 2.0440 2.3260 -0.0346 1.5196Crew 4358.2 7.3400 1.6270 1.8540 -0.0393 1.5898City 4CIF 20900 8.4000 1.0960 2.3670 -0.0346 1.5196Crew 4CIF 18021 7.3400 1.1530 2.4050 -0.0393 1.5898



9

16 18 20 22 24 26 28 30 32 34

40

50

60

70

80

90


Vid

eo Q

ualit

yVideo Quality Vs Power transmitted per subchannel per user

BS−MRTSO (S)MS−MRT (S)BD (S)CTR−BD−I (S)CTR−BD−NI (S)CTR−SO−I (S)CTR−SO−NI (S)

Fig. 4: Video Quality vs Power for various competing MU-MIMOtransmission techniques BS-MRT and simulcast versions of SO, MS-MRT, BD, CTR-BD, CTR-SO (I,NI i.e. iterative and non-iterativeversions).

ceive Beamforming scheme described in Section III, while I,NI refer to their respective iterative and non-iterative versions.

The plots clearly demonstrate the superior performance interms of video quality provided by the proposed MS-MRTtechnique compared to other non-iterative techniques as wellas the iterative version of Coordinated Tx-Rx SO technique.However, the optimal iterative CTR-BD scheme provides amarginal improvement in the video quality compared to MS-MRT at the cost of significantly high computational complex-ity due to the multiple rounds of optimization. This superiorvideo quality performance of CTR-BD-NI arises because ofits fair interference distribution properties compared to MS-

16 18 20 22 24 26 28 30 32 34

0.8

1.6

2.4

3.2

4.0

4.8

5.6

6.4

7.2

8.0


Ave

rage

Thr

ough

put (

Mbp

s)

Average Throughput Vs Power transmitted per subchannel per user

BS−MRTSO (S)MS−MRT (S)BD (S)CTR−BD−I (S)CTR−BD−NI (S)CTR−SO−I (S)CTR−SO−NI (S)

Fig. 5: Average Throughput vs Power for various competing MU-MIMO transmission techniques BS-MRT and simulcast versions ofSO, MS-MRT, BD, CTR-BD, CTR-SO (I,NI i.e. iterative and non-iterative versions).

16 18 20 22 24 26 28 30 32 34

60

65

70

75

80

85

90

95

100


Vid

eo Q

ualit

y

Video Quality Vs Power transmitted per subchannel per user

PF−BS−MRTRR−BS−MRTMR−BS−MRTPF−MS−MRTRR−MS−MRTMR−MS−MRT

Fig. 6: Video Quality vs Power for the proposed MS-MRT andBS-MRT MU-MIMO transmission schemes in conjunction with thestandard PF, RR and MR scheduling algorithms

MRT, which nulls the interference to the previously scheduledusers, thereby resulting in a higher interference level at thesuccessively scheduled users. They also depict the ability ofthe MS-MRT scheme to provide the highest average through-put as compared to the other beamforming techniques. Thus,MS-MRT is a practical scheme to achieve performance close tothe optimal joint transmit receive beamforming scheme whilelimiting the computational complexity.

Fig.4 and Fig.5 demonstrate the performance of the pro-posed BS-MRT scheme described in section IV in comparisonto the simulcast extensions of other competing schemes suchas BD, SO, CTR-BD, CTR-SO and MS-MRT, where (S)indicates the simulcast version. Clearly, BS-MRT attains ahigher video quality and system throughput because of itsability to reinforce the net broadcast signal of all the users inthe broadcast group leading to a substantial enhancement in theoverall signal power at the receiver. BS-MRT is specificallyoptimized for broadcast scenarios, and computes the jointlyoptimal broadcast beamforming vector as described in sectionV, which enhances the net video quality and rate of the entirebroadcast group. Thus, it results in a significant performanceimprovement compared to the CTR schemes which focus onlyon the individual users.

Fig.6 and Fig.7 show the plot of video quality and through-put respectively vs. power for the various scheduling algo-rithms used in conjunction with MS-MRT, such as proportionalfairness (PF) based PF-MS-MRT and round robin (RR) basedRR-MS-MRT described in Section II. MR-MS-MRT denotesthe conventional Max-Rate scheduling algorithm for MS-MRT.Further, Fig.6 and Fig.7 also demonstrate the video qualityand throughput performance of the BS-MRT in conjunctionwith the PF, RR and MR scheduling algorithms. These figuresdemonstrate the ability of the PF-MS-MRT, PF-BS-MRT, i.eMS-MRT, BS-MRT employed in conjunction with the PFscheduling algorithm to deliver the highest video qualityin MU-MIMO wireless networks, while maintaining a high



10

16 18 20 22 24 26 28 30 32 34

2

4

6

8

10

12


Ave

rage

Thr

ough

put (

Mbp

s)Average Throughput Vs Power transmitted per subchannel per user

PF−BS−MRTRR−BS−MRTMR−BS−MRTPF−MS−MRTRR−MS−MRTMR−MS−MRT

Fig. 7: Average Throughput vs Power for the proposed MS-MRT andBS-MRT MU-MIMO transmission schemes in conjunction with thestandard PF, RR and MR scheduling algorithms

system throughput.

VI. CONCLUSION

In this work, we presented a novel MS-MRT beamformingtechnique for video quality and system throughput maximiza-tion in high rate MU-MIMO wireless networks for unicastand broadcast scenarios. The proposed scheme computes theoptimal beamformer for Maximal Ratio Transmission whilemaintaining orthogonality of a successively scheduled userto each of the previously scheduled users. For unicast sce-narios, we compare the performance of this algorithm interms of system throughput and video quality with the twopopular precoding techniques namely Block Diagonalization(BD) and Successive Optimization (SO). We also compare itsperformance with the single mode beamforming versions ofthese two algorithms termed Coordinated Transmit-ReceiveProcessing (CTR)-BD and CTR-SO algorithms respectively.We derived a framework to employ various scheduling algo-rithms namely Max-Rate, PF and RR in conjunction with theproposed technique for H.264 SVC based video schedulingscenarios. Further, the extension of the MS-MRT to BroadcastMU-MIMO video transmission scenarios, BS-MRT, is seento substantially enhance the net video quality performanceof various broadcast groups while simultaneously maintainingzero interference at each of the previously scheduled groups.As demonstrated by the simulation results, PF-MS-MRT, PF-BS-MRT are ideally suited for video quality maximizationin unicast and broadcast 4G MU-MIMO video streamingscenarios.

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Documents

Multiuser Successive Maximum Ratio Transmission (MS-MRT) for Video Quality Maximization in Unicast and Broadcast MIMO OFDMA-Based 4G Wireless Networks