Efficient Beamforming Algorithm for Mimo Multicast With Application Layer

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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 6464(Print), ISSN 0976 6472(Online) Volume 4, Issue 2, March April (2013), IAEME

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EFFICIENT BEAMFORMING ALGORITHM FOR MIMOMULTICAST WITH APPLICATION LAYER CODING

Dr. H.V. Kumaraswamy

, Vijay B.T

Professor and Head, Department of Telecommunication Engineering, Member, IETE, ISTEM.Tech Student Digital Communication Engineering Student Member, IETE

R.V.College of Engineering RV Vidyaneketan post 8 th mile Mysore Road Bengaluru-59India

ABSTRACT

Communication over a fast fading channel has poor performance due to significantprobability that channel is in deep fading. This motivates the investigate various diversity

techniques. Reliability is increased by providing more signal paths that fading independently.Diversity can be providing across time, frequency and space but the basic idea is the same.Multicast Beamforming was recently proposed as a means of exploiting the broadcast natureof the wireless medium to boost spectral efficiency and meet quality of service (QoS)requirements. The improvement in term of channel capacity provided by using a MIMOantenna system in personal area networks is investigated. Also, adopting Waterfilling powerallocation scheme is provides a higher capacity in the low SNR range while yielding the sameachievable capacity in high SNR.

Index Terms: Beamforming, Channel Capacity, Diversity, MIMO, Multicast, Waterfillingpower allocation, SNR

1. INTRODUCTION

Over the last decade the demand for service provision by wireless communicationshas risen beyond all expectations. As a result, new improved systems emerged in order tocope with this situation. Global system mobile, (GSM) evolved to general packet radioservice (GPRS) and enhanced data rates for GSM evolution (EDGE) and narrowbandCDMA to wideband code division multiple accesses (CDMA). Each new system now facesdifferent challenges: (1) GPRS consumes GSM user capacity as slots are used to supporthigher bit rates. (2) EDGE faces a similar challenge with GPRS in addition to this it requires

INTERNATIONAL JOURNAL OF ELECTRONICS ANDCOMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)

ISSN 0976 6464(Print)ISSN 0976 6472(Online) Volume 4, Issue 2, March April, 2013, pp. 116-128 IAEME : www.iaeme.com/ijecet.asp Journal Impact Factor (2013): 5.8896 (Calculated by GISI)www.jifactor.com

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higher SINR to support higher coding schemes i.e., it also has range problems. (3) WCDMAperformance depends on interference and hence coverage and capacity are interrelated. Highcapacity leads to lower range and vice versa. Each circuit to be considered accepts an inputsignal at a set of input terminals and produces an output signal at a set of output terminals.This process is called signal processing. The circuit processes the input signal and producesan output signal that is a different shape or a different function compared to the input signal.In order to overcome with such system-specific problems but also provide the means for amore general solution to the spectral efficiency problem, spatial filtering has emerged as apromising idea. Spatial filtering can be achieved through adaptive or smart antennas and as aresult the area has seriously attracted the interest of both academia and industry over the lastdecade. [14]- [19]As the number of users and the demand for wireless services increases at an exponential rate,the need for wider coverage area and higher transmission quality rises. Smart-antennasystems provide a solution to this problem. Multiple Antennas can be arranged in space, invarious geometrical configurations, to yield highly directive patterns. These antenna

configurations are called arrays. In an array antenna, the fields from the individualelements add constructively in some directions and destructively (cancel) in others. Forpurpose of analysis, arrays are assumed to consist of identical elements, although it ispossible to create an array with elements such that each has a different radiation pattern [1][3] [5].In a multicast scenario, the performance is usually determined, and therefore limited, by theweakest link present in the system. With multiple co-channel multicast groups, the problem isfurther exacerbated due to interference from other transmissions [5]-[7]. In this work weinvestigate an alternative communicate-on scheme, in which additional coding at theapplication layer is used, spanning over a number of channel realizations. Aiming atmaximization of the weighted sum of rates achieved in each group, we show that the optimaltransmission strategy depends only on the current channel realization, which, assuming

multiple antennas at the base station, allows for formulation of an interesting transmitbeamforming problem. In order to find the solution of the problem, we show that the utility-based power control framework, developed for a network consisting of a number of point-to-point wireless links, can be generalized to the case of multigroup multicast. Building uponthis framework, we propose iterative beamforming algorithms which can be applied inscenarios both with and without additional coding at the application layer. Numericalexperiments are included in the paper to demonstrate the performance of the proposedalgorithms.

2. SYSTEM MODEL AND PROBLEM FORMULATION

We consider a slowly fading, quasi-static channel in which the transmitter is equippedwith n antennas and each of the m receivers has a single antenna. The received signal at the i-th receiver, is the transmitted signal, and is unit variance, circularly symmetriccomplex Gaussian additive noise. The transmitter is subjected to an average powerconstraint .The channel is assumed to be quasi-static and thus fixed for a block of transmission. Weassume the channel is known perfectly at the transmitter and the receivers, which allows foroptimization of the input in response to the current channel conditions. Though we assumeperfect CSI, we also study the performance of a simpler channel independent transmission


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strategy. Each of the m channels are assumed to be drawn independently from the Rayleighdistribution, i.e., each element of is i.i.d complex Gaussian. Though the channelrealizations differ from block to block, we only consider the rate achievable within eachblock; this rate is relevant in the slow fading scenario where delay constraint are of the sameorder as the block sizeThe model under study is a downlink multicast MIMO wireless communications network with users. The set of all users is denoted as 1,2, . . . ,. The transmitter (basestation, BS) is equipped with antennas and each receiver (user) with antennas.Denoting the scalar transmit signal as x, the received signal vector at the -th receiver is givenby:

, (1)Where: v is the transmit beamforming vector (transmit beamforming) satisfying

1, is the additive Gaussian noise vector whose entries arei.i.d. circular symmetric complex Gaussian random variables with unit variance, and

is the channel matrix from the transmitter to the -th receiver. We assume block fading channel model, so that channel matrices are constant for the entire duration of transmission block and change from block to block in an i.i.d. manner. The channel matrix is known to the transmitter and to the -th receiver. Each channel is subject to Rayleighfading so that for each is matrix containing i.i.d. circular symmetric Gaussian randomvariables with unit variance 0,1. For notational convenience, all channels are collectedin the matrix . . Furthermore, we assume constant transmit power P andreceive beamformers 1for each , so that the signal-to-noise ratio(SNR) for user k yields:

(2)

At times, when considering the MISO case (single receive antenna), or when consideringxed receive beamformers , we make use of the notation: denoting theeffective channel of the -th user. Now, the SNR determines the maximum rate achievable by user :

, log1 log 1 (3)

The dependence of the maximum instantaneous rate on the receive beamformer isintentionally omitted as the optimal receive beamforming vector in the considered scenario isuniquely determined by the channel matrix and the transmit beamformer so that

, 3. MIMO MULTICAST CHANNEL CAPACITY Receiver beamforming Single input multiple output (SIMO) channel:

Consider a SIMO channel with one transmit antenna and L receive antennas

1,.., ,(4)


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where is the fixed complex channel gain from the transmit antenna to the th receiveantenna, and is 0, is additive Gaussian noise independent across antennas. Asufficient statistic for detecting from ,.., is

(5)

Where ,.,and ,.., . This is an AWGN channel withreceived if P is the average energy per transmit symbol. The capacity of thischannel is therefore

log1 / / (6)Multiple receive antennas increase the effective SNR and provide a power gain . For example,for =2 and | | | | 1, dual receive antennas provide a 3 dB power gain over a singleantenna system. The linear combining (4) maximizes the output SNR and is sometimes calledreceive beamforming .

Figure 3.1 Receive diversity

Transmit beamforming Multiple input single output (MISO) channel:Consider a MISO channel with L transmits antennas and a single receive antenna:

(7)

Where ,, and is the (fixed) channel gain from transmit antenna to thereceive antenna. There is a total power constraint of P across the transmit antennas. In theSIMO channel above, the sufficient statistic is the projection of the L-dimensional receivedsignal onto h : the projections in orthogonal directions contain noise that is not helpful to thedetection of the transmit signal. A natural reciprocal transmission strategy for the MISOchannel would send information only in the direction of the channel vector h ; informationsent in any orthogonal direction will be nulled out by the channel anyway. Therefore, by

setting the MISO channel is reduced to the scalar AWGN channel:

(8)

with a power constraint P on the scalar input. The capacity of this scalar channel is

log1 / / (9)


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Figure 3.2 Transmit diversity

Intuitively, the transmission strategy maximizes the received SNR by having the receivedsignals from the various transmit antennas add up in-phase (coherently) and by allocatingmore power to the transmit antenna with the better gain. This strategy, aligning the transmitsignal in the direction of the transmit antenna array pattern, is called transmit beamforming .Through beamforming, the MISO channel is converted into a scalar AWGN channel and thusany code which is optimal for the AWGN channel can be used directly. In both the SIMO andthe MISO examples the benefit from having multiple antennas is a power gain. To get a gainin degrees of freedom, one has to use both multiple transmit and multiple receive antennas(MIMO).

4. ALGORITHMS FOR APPLICATION LAYER CODING

As previously statistically optimum weight vectors for adaptive beamforming can becalculated by the Wiener solution. However, knowledge of the asymptotic second-orderstatistics of the signal and the interference-plus-noise was assumed. These statistics areusually not known but with the assumption of ergodicity, where the time average equals theensemble average, they can be estimated from the available data [2] [8] [11] [12].For time-varying signal environments, such as wireless cellular communication systems,statistics change with time as the target mobile and interferers move around the cell. For thetime-varying signal propagation environment, a recursive update of the weight vector is

needed to track a moving mobile so that the spatial ltering beam will adaptively steer to thetarget mobiles time-varying DOA, thus resulting in optimal transmission/reception of thedesired signal. To solve the problem of time-varying statistics, weight vectors are typicallydetermined by adaptive algorithms which adapt to the changing environment.

Figure 4.1 Functional diagram of an N-element adaptive array


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Figure 4.1 shows a generic adaptive antenna array system consisting of an N-element antennaarray with a real time adaptive array signal processor containing an update control algorithm.The data samples collected by the antenna array are fed into the signal processing unit whichcomputes the weight vector according to a specic control algorithm.Steady-state and transient-state are the two classications of the requirement of an adaptiveantenna array. These two classications depend on whether the array weights have reachedtheir steady-state values in a stationary environment or are being adjusted in response toalterations in the signal environment. If we consider that the reference signal for the adaptivealgorithm is obtained by temporal reference, a priori known at the receiver during the actualdata transmission, we can either continue to update the weights adaptively via a decisiondirected feedback or use those obtained at the end of the training period. Several adaptivealgorithms can be used such that the weight vector adapts to the time-varying environment ateach sample; some of them are now reviewed.

4.1 The Least Mean-Square (LMS) Algorithm

The LMS algorithm is probably the most widely used adaptive ltering algorithm,being employed in several communication systems. It has gained popularity due to its lowcomputational complexity and proven robustness. It incorporates new observations anditeratively minimizes linearly the mean-square error. The LMS algorithm changes the weightvector w along the direction of the estimated gradient based on the negative steepest descentmethod. By the quadratic characteristics of the mean square-error function | | that hasonly one minimum, the steepest descent is guaranteed to converge. At adaptation index ,given a mean-square-error (MSE) function | | | | , the LMSalgorithm updates the weight vector according to weighted vector 1.LMS Algorithm:

(10)1 (11)

Where is a scalar constant which controls the rate of convergence and stability of thealgorithm. It requires about 2N complex multiplications per iteration, where N is the numberof weights (elements) used in the adaptive array

4.2 The Recursive Least-Squares (RLS) Algorithm

Unlike the LMS algorithm which uses the method of steepest descent to update theweight vector, the RLS adaptive algorithm approximates the Wiener solution directly usingthe method of least squares to adjust the weight vector, without imposing the additionalburden of approximating an optimization procedure. In the method of least squares, theweight vector w(k) is chosen so as to minimize a cost function that consists of the sum of error squares over a time window, i.e., the least-square (LS) solution is minimizedrecursively. In the method of steepest-descent, on the other hand, the weight vector is chosento minimize the ensemble average of the error squares. The recursions for the most common


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version of the RLS algorithm, which is presented in its standard form in steps, are a result of the weighted least-squares (WLS) objective functionRLS Algorithm

0 ,

1 (12)

(13) 1 (14)

(15)

1 (16)}

The resulting rate of convergence is therefore typically an order of magnitude faster than thesimple LMS algorithm. This improvement in performance, however, is achieved at theexpense of a large increase in computational complexity. The RLS algorithm requires

4 4 2complex multiplications per iteration, where is the number of weights usedin the adaptive array.

4.3 Modified Lozanos algorithm

A simple iterative algorithm was proposed for computing the transmit beamformingvector in the MISO multicast scenario. Two modes of operation are possible with the

algorithm: (1) maximize the number of users which support a given SNR threshold or (2)maximize the minimum SNR achieved by a subset with a required number of users. Assumethat is the transmit beamforming vector in iteration of the algorithm. Then, thecorresponding values for are computed and sorted. A subset of active usersis now chosen according to selected mode of operation (1) or (2), and the weakest user (i.e.with the smallest SNR among all active users) in the subset is identied. The transmitbeamformer 1is then computed by making a gradient step towards the selected user .Under assumption of unit noise variance, this yields with subsequentnormalization

and with some stepsize 0.Algorithm is motivated by thefollowing observation. Assume again that is the transmit beamforming vector in the iteration. The optimal transmission rate and the optimal subset Si can be determined

efficiently according to Proposition an important property of the multicast with outer codingconsists in the fact that the coded multicast beamforming capacity does not decrease to zeroas number of users grows to innity. Informally speaking, three possibilities are identied forimproving the performance in the sense of increasing | |log1 min : (1)attempt to increase the SNR of the best user among the inactive users so that it becomesactive and | | is incremented, (2) increase the SNR of the weakest user among the activeusers so that min increases, 3) improve the SNR of the second weakest user amongthe active users so that | | is decremented, but this is compensated for by the increase inmin .


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Propositions:

1. As , the multicast beamforming capacity O 2. The optimal transmission strategy for achieving the coded multicast beamformingcapacity is max| | for every .3. For a fixed transmit beamforming vector v and fixed receive beamforming vectors , , let be the sequence of SNRs ordered such that

. Now ,the maximum of | | max , ,.log1 Modified Lozanos algorithm:

0, (17) .3 (18), (19)

min (20)

1, , 1 (21), , , (22) .3 , , , (23)max, , | | (24), 1 (25). (26)5. MAX-MIN MULTICAST BEAMFORMING

The goal of multicast transmit beamforming is to allow for the transmission of thecommon message to all users with the highest possible rate. An adequate Performance metric

is the highest rate achievable over all transmit beamformer vectors and we willrefer to it as the multicast beamforming capacity for a given channel realization :

maxmin , (27)maxmin log1 | | (28)log1 maxmin| | (29)

This formulation gives rise to the so-called max-min transmit beamforming problem. Theoptimal beamforming vector is given by:

maxmin| | (30)The problem defined above can be shown to be NP-hard [4]. For the MISO case, a convexrelaxation [9] was proposed, which leads to semi definite program and thus can be efficientlysolved by appropriate solvers. Based on this approach, algorithms for the MIMO case wereproposed in [13].The multicast beamforming capacity decreases to zero when the number of users K grows toinfinity. In [3], scaling laws for several transmission strategies in the MISO case wereprovided. The capacity in the case of multimode transmit beamforming, which is lessrestrictive than solving (4), was shown to scale as , providing thus the upper bound for


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the multicast beamforming capacity. As for the multicast beamforming in the sense of (3), a

lower bound was proposed in [1] to be . This lower bound can be improved byobserving that the multicast beamforming performance is at least as good as the performance in

the SISO/SIMO case, where a single transmit antenna is used.

6. SIMULATION RESULTS

We consider a highly scattered environment is considered. The capacity of a MIMOchannel with transmit antenna and receiver antenna is analyzed. The power in parallelchannel (after decomposition) is distributed as water-filling algorithm. The pdf of the matrixlamda elements is depicted too in figure 6.1. By considering 2 2MIMO, =0.5, 0.5 andSNR in dB 20 we get Average_ C=10.9959, Empirical CDF shown in figure 6.2 and alsobeamforming graph shown in figure 6.3 We simulate the operation of Butler matrix usingHamming window, general Antenna Array specifications, it used in Switched beamformingAlgorithms shown in figure 6.4. Here we consider LMS algorithm for Application layer coding,

Angle of Arrival (AOA) desired users: 0 and arrival (AOA) interferences: 45and elementspacing .75 . Simulated graphs are shown in the figure 6.5.

Figure 6.1 (a) MIMO capacity vs. SNR in Db

Figure 6.1 (b) Probability density functions


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Figure 6.2 Cumulative distribution function

Figure 6.3 operating frequency f = 900MHz

Figure 6.4 Beam pattern 8 8 Butler Matrix

Figure 6.5 (a) Normalized weighted Array factor


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Figure 6.5 (b) Beam pattern

Figure 6.5 (c) Array factor plot of 8 elements

Figure 6.5 (d) mean square error functions

7. CONCLUSION

Opportunistic communication techniques primarily provide a power gain this powergain is very significant in the low SNR regime where systems are power-limited but less so inthe high SNR regime where they are bandwidth-limited. As we know that, MIMO techniquescan provide both a power gain and a degree-of-freedom gain Thus, MIMO techniquesbecome the primary tool to increase capacity significantly in the high SNR regime. DOF gainis most useful in the high SNR regime. The capacity of such a MIMO channel with n transmitand receive antennas is proportional to n. MIMO channel provides spatial degrees of freedom (Beamforming). Well-conditioned channel matrices facilitate communication in thehigh SNR regime.


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ACKNOWLEDGEMENT

The authors would like to thank Dr.B.S.Satyanarana Principal R.V.College EngineeringBengaluru.

REFERENCES

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[20] Sharon. P. S, M.Vanithalakshmi, Arun.S and G. Dharini, Spectrum Managementand Power Control in MIMO Cognitive Radio Network and Reduction of PowerOptimization Problem Using Water-Filling Method, International journal of Electronicsand Communication Engineering & Technology (IJECET), Volume 3, Issue 1, 2012,

pp. 160 - 170, ISSN Print: 0976- 6464, ISSN Online: 0976 6472. [21] Bharti Rani and Mrs Garima Saini, Cooperative Partial Transmit Sequence for PAPRReduction in Space Frequency Block Code MIMO-OFDM Signal, International journalof Electronics and Communication Engineering & Technology (IJECET), Volume 3,Issue 2, 2012, pp. 321 - 327, ISSN Print: 0976- 6464, ISSN Online: 0976 6472.

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Efficient Beamforming Algorithm for Mimo Multicast With Application Layer