Performance Analysis of Maximal Spectral Efficiency for...

* Associate Professor, Department of Electronics and Communication Engineering, SR Engineering College, Warangal, Telangana,India, Email: [email protected]

** Professor, Department of Electronics and Communication Engineering, MVSR Engineering College, Hyderabad, Telangana, India,Email: [email protected]

*** Professor, Department of Electronics and Communication Engineering, TRR College of Engineering, Hyderabad, Telangana, India,Email: [email protected]

Performance Analysis of MaximalSpectral Efficiency for Multi-CellMassive MIMO SystemsM. Sampath Reddy*, T. Anil Kumar** and K. Srinivasa Rao***

ABSTRACT

Cellular and wireless communication spectral efficiency (SE) increases massive multiple-input multiple-output(M-MIMO) is play vital role, by accommodate hundreds or thousands of antennas at base station (BS) and performed.A common fundamental procedure of M-MIMO systems should have more number of BS antennas M than scheduledusers (K), because when M/K>10 the all user equipments (UEs) channel vectors suitable to be orthogonal. In thispaper, we studied and evaluate the how depends on M and other system parameters on the number of optimalscheduled UEs (k*). A new SE expression is obtained and to allow the system performance is efficient under powercontrol, random allocation of pilot reuse factor and UE positions. Simulation results shows that the M-MIMOsystem how many number of UEs should be scheduled and obtain the maximum SE per cell with various pilot reusefactors and preprocessing techniques at finite BS antennas.

Keywords: Massive MIMO (M-MIM)), Multi-cell, pilot contamination, SE

1. INTRODUCTION

To increases the demands of wireless data services and throughputs in wireless and cellular communicationnetworks continuously and has been achieved with the help of three major factors [1] such as higher frequencyspectrum, cell density and higher spectral efficiency (SE). Massive multiple-input multiple-output (M-MIMO) system technique has been used to increase the SE of contemporary systems [2]-[5].

M-MIMO system provides the base station (BS) with hundreds or thousands of antennas are operatedin systematic way, this can be provides the unpredictable antennas array again and a spatial resolution. Themultiuser MIMO scheme BS simultaneously communicates with user equipments (UEs) consists of numberof antennas and which allocates the different spatial layers in same time-frequency resources [3]-[4]. M-MIMO system provides robustness to inter-user interference and involves on how BS and active UE antennasand select corresponding transmit power in order to obtain the maximum SE and energy efficiency (EE).

M-MIMO systems researcher and academician has been focused on establishing the fundamental physicallayer, particularly obtaining the limited channel state information (CSI) by channel coherence block, howthis effects the SE and the ability to mitigate effect of inter-user interference.[6]- [7]. In competitive M-MIMO system has been provides improvements of overall EE while maintaining the hardware impairmentsof transceivers have lesser effect than conventional systems. In contrast, researchers and academicians hasbeen mainly focused on the allocation of resources i, e, user scheduling and achievable SEs [8]-[10].

ISSN: 0974-5572I J C T A, 10(8), 2017, pp. 329-341© International Science Press

330 M. Sampath Reddy, T. Anil Kumar and K. Srinivasa Rao

In this paper, we consider a how many number of UEs should be scheduled per cell to achieve maximumSE in multi-cell. We studied that the how coherence block symbol B length, number of BS antennas M,allocation of pilot signals and other system parameter impact on SE of M-MIMO system. We derive newSE equations for M-MIMO system uplink (UL) and downlink (DL) with power control which yield UEperformance is uniform. The maximum ratio (MR) combining, zero-forcing (ZF) and pilot zero-forcing(P-ZF) three liner processing techniques has been used to minimizes or suppresses the effects of inter-cellinterferences in coordinated beamforming fashion.

Organization of this paper as follows, in Section-I explains about introduction, system model is describedin Section-II, Calculations of Average Spectral efficiencies (ASE) per each cell has been discussed inSection-III, in Section-IV numerical results and conclusions in Section-V.

2. SYSTEM MODEL

2.1. Uplink (UL) System

The received signal at BS is given as

1

Ky p h x nuj jjlk lkkLl

� ��

�(1)

Where UE kth transmitted symbol is xlk � in cell l, the normalized signal is defined as � �21E xlk � and

UL transmitted signal power is 1lkp � . The additive white gaussian noise is Mn j � with mean zero and the

noise variance 2� .

2.2. Downlink (DL) System

The DL received signal is z jk � at UE kth is given as

1

K Tz h w sjk ljk lm lm jkml L��

��

�(2)

Where (.)T represents transpose of the matrix, the received symbol for UE m in cell l is slm

, the precoding

vector is defined as Mwlm � and DL allocated transmits power is

2wlm .

To estimate the CSI at BS with assumptions of power control in the DL process and select the transmitpower to achieve the same SEs.

3. AVERAGE SPECTRAL EFFICIENCY (ASE) PER CELL

The SE for multi-cell M-MIMO system with random locations of UE was derived in this section.

3.1. Pilot Based Channel Estimation (PBCE)

The M-MIMO system BS uses the M antennas for coherent transmission/receive and combining during theUL and DL process, which is desirable for amplify and suppressing interfered signals. This requires

knowledge of the UEs channel state information (CSI) p hlk jlk in the UL for all cell l and k. This CSI used

to acquire pilot signals where the UEs transmit the known signals in predefined process. One of thechallenging tasks in multi-cell M-MIMO system is accurate CSI, where transmission of allocated pilot

Performance Analysis of Maximal Spectral Efficiency for Multi-Cell Massive MIMO Systems 331

signals reused entire cells in multicell systems because, pilot signals are interfered by other cell interferenceautomatically this is known as pilot contamination. This pilot contamination is maximizes the acquiredCSI quality and capability to avoid the inter-cell interference [11-12]. This pilot signals are used to studyand analysis of pilot contamination in each other cells in M-MIMO system. Arbitrary pilot reuse in eachcell, where each cell may be use only same set of the pilot signals this is the property of M-MIMO systemswith power control. Furthermore, this assumed same pilot signals cover bandwidth B of symbols of eachframe in M-MIMO system where 1 B S� � .

So every pilot signal is deterministic vector vB� and transmitted symbol power is fixed and it’s has

magnitude vector is unit i.e., � � 1v s � denoting the sth element for � �1, ...., Bs � .

All fixed pilot book V is defined as � �, ......,1V v vB�

Where

, 1 20,1 2 1 2

B b bHv vb b b b

��

�

��

(3)

Where (.)H represents complex conjugate transpose. Hence the symbol bandwidth of sequences of pilotsis orthogonal i.e., the columns of a discrete Fourier transform (DFT) matrix [12]. The kth UE in cell l thepilot signal can be transmitted which is defined as v

ilk where i

lk � {1, ...., B}is the index of pilot book. The

transmission of sequences of pilot over coherent bandwidth of symbol sequences, therefore the receivedsignals at BS uplink is given as

1

K TY p h v Nj jlk jlkL k ilkl� �

�� (4)

The additive noise at the receiver during pilot signal is N jM B�� .

Lemma 1: The effective power controlled UL minimum mean-squared error (MMSE) estimate at BS is

� �� 1 *ˆ

d zjeff lk Th Y vj jjlk ilkd zl lk

�� (5)

Where the complex conjugate is represents (.)* and the covariance matrix signal is defined as

� ��

2

1

d zK j lm Hv v Ij Bilm ilmml d zl lm

L

�

��

�� (6)

The covariance matrix estimation error is given by

� � � �ˆ ˆHeff eff eff eff

C E h h h hjlk jlk jlk jlk jlk� � � ��

� ��

� ��

� ��

12

1

d zj lkB

d z d zj lk l lk IMd z d zK jl lk lm Hv vilk ilmml d zl

Llm

��

�

� �

��

��

� ��

(7)


and the mean-squared error (MSE) is � �MSE tr Cjlk jlk� .

In M-MIMO system literature two important differences between Lemma1 and conventional channelestimators (CEs). The effective channels estimation with controlling of UL power and MMSE allows anarbitrary pilot signal allocation. Hence each BS can only resolve B with different spatial dimensions sincethere are only B orthogonal pilot signals uses. For simplicity, we define the M � B matrix

� � 1 * *ˆ , ....,, 1TH Y v vv j j j B

��

� � (8)

The kth UE in cell l, channel estimate in (6), pilot sequences vilk

are uses to column of ˆ,Hv j further it

is defined as

� ��

ˆ ˆ,

d zjeff lkh H ev jjlk ilkd zl lk

� (9)

Where the ei represents the ith column of the identity matrix.

3.2. The Achievable UL Spectral Efficiencies

The BS coherently or semi coherently detects the transmitted UEs data signals during channel estimation

(CE) process. For simplicity we assume that pilot reuse factor is B

K� � , in each L number of cell is divided

into � � 1 disjoint subsets. Hence same subsets of cell uses same pilot and different sets of cell uses thedifferent pilots this is known as non universal reuse the pilot.

Lemma 2: The uplink kth UE per cell j achievable SE is defined as

� ��

� �� 1 log 12ul ulB

E SNRz jkS� � �

� � � ��

[bit/s/Hz] (10)

Where the effective signal to interference and noise ratio (SINR) of the UL is given as

� � � � � �

� � � � � � � �

2

22 22

1

Hp E g hjk jk jjkhulSNR jk K H H

p E g h p E g h E glm jk jlk jk jk jjk jkh hmL hl�

�

� ��

��

(11)

Where the expectations of UE location is � � ��.E z and the expectation of channel realizations � � ��.Eh

respectively.

Any UE in cell j the achievable SE derived in Lemma 2 which is a channel capacity lower limit unknownfor multicell networks. To compute expectation of UE locations and channels we need to uses combiningtechniques. The M-MIMO system combining techniques use to study impact of passive or active interferencein system performance. The passive interference rejection of maximum ratio (MR) combining is defined as

ˆˆ,

effMRg H e hv jjk ijk jjk� � (12)


Therefore this passive rejection is maximizes the gain of the desired signals and removed it’s

automatically since the intra-cell interference channel are quasi orthogonal to ˆeffh jjk if BS antennas M is

large.

In contrast, zero-forcing (ZF) combining scheme is used remove the active interference, where theorthogonal to selected channels in K intra-cell channels and it is defined as

� � 1ˆ ˆ ˆ

, , ,ZF H Hg H E E H H E ev j j j v j v j jjk ijk

�� (13)

Where .....1E e ej ijK

iB

Kj� �� and different pilot sequences are required in all the UEs in cell j.

Now we defined the closed form in per cell SEs expressions of MR and ZF schemes in the next section.

Theorem 1: Now consider Lj(�)�L the subsets of each cells in multicell networks uses the same pilots.

Therefore the uplink achievable SE per cell is given as

� � � � 11 log 12

ul ul BSE Kj schemeS I j

��

(14)

Where the interference term can be defined as

� ��

2(2) (1)(2) jl jlscheme

I j jl schemel GL jj �

� ��

��

�

� ��

� � � �2 21 1schemeZjl jl jll l B

schemeG

L L

� ��

� ��

� ��

�

� �� (15)

In above equation (15) pilot contamination and user interferences describes in first term and secondterm respectively. The basic contrast between the MR and ZF is that the some interference cancels through

schemeZ jl by minimizing the antennas gain scheme

G from M to M-K.

The MR combining is obtained by substituting MRG M� and MR

Z Kjl � and ZF combining is obtained

by substituting MRG M K� � and therefore

� �

� ��

� �

� �

1

1 21

jlK if lZF

Z jljl Bl

L j

L j

ifl LK j

�

�

�

�

��

�

�

�

�

��

��

� � ��

� ��

(16)


For simplification the following notation is used

� � � ��

d zlmjEjl zlm d zlml

��

� ��

for 1, 2� � (17)

The ZF combining techniques is uses active suppresses in intra- cell interference, while the using MRcombining inter-cell interference is passive suppressed. Furthermore coordinating the ZF and MR combiningtechniques across cell interference rejection can be easily achieved. Therefore with use of both combiningtechniques such as ZF and MR techniques are actively suppressed intra-cell and inter-cell interferences.

A new combining technique is pilot zero-forcing (P-ZF) for rejection of active and passive interferencesuppresses which is defined as

� � 1ˆ ˆ ˆ

, , ,P ZF Hg H H H ev j v j v jjk ijk

�� (18)

In contrast conventional ZF is defined in (13) only orthogonalize the K intra-cell channels in ˆ,H Ev j j

where as P-ZF exploits that all the coherent channel bandwidth B estimated channel directions in ˆ,Hv j are

known at BS and orthogonalize all these directions so therefore we mitigate inter-cell interference. Indownlink, the same procedure is used to suppress the intra-cell and inter-cell interferences. The achievableSEs of P-ZF combining scheme is defined in theorem 2 next.

Theorem 2: Let’s consider Lj(�)�L the subset of each cells j in multicell networks uses the same pilots.

The UL achievable SE of P-ZF combing in cell j is given as (14) for substituting P ZFG M B

� � � and it isgiven as

� �

� ��

1

1 21

jlP ZFZ Kjl

jl Bl L j

�

��

��

� �

�

�

��

� ��

(19)

Here assuming the M and K are the same values in all cell SEs can be easily derived.

3.3. The Achievable DL Spectral Efficiencies

The BS coherently or semi coherently detects the transmitted UEs data signals during channel CE process.

The precoding vector is w jkM� and related to kth UE in cell j. Now corresponding precoding vectors is

given as

� �

*ˆ2

ˆ

q jkw gjk jk

E g jkh

��

(20)

Here, we consider the average transmitted signal power should be greater than equal to zero i, e, 0q jk �

and its function of random location of UE, but not consider the instantaneous channels.


Lemma 3: The downlink (DL) SE of an random location of kth UE in cell j is given by

� ��

� �� 1 log 12dl dlB

E SNRz jkS� � �

� � � ��

[bit/s/Hz] (21)

Where the DL effective � �dl

SNR jk is written as

� �

� � � �

� �

� �

� � � ��

ˆ

2ˆ

22ˆ ˆ

22 21

ˆ ˆ

HE g hjk jjkh

q jkE g jkhdl

SNR jkH HE g h E g hlk ljkh jk jjkhK

q qL lm jkml

E g E glk lkh h

��

�

� �

� ��

� ��

(22)

The next section describes theorem 3 shows that the transmit precoding in the DL and receive combiningin the UL

Theorem 3: Let consider � �schemeg jk be the set of UL receive combining vectors and then DL power

control is � �jkq with 1 1

K Kq pjk jkl L l kLk

��

� ��

� for which

� � � �dl ulSINR SINRjk jk� (23)

by using ˆ schemeg gjk jk� for all j and k.

Consequently, an achievable SE in the DL of cell j is given as

� � � � 11 log 12

dl dl BSE Kj schemeS I j

��

[bit/s/Hz/cell] (24)

In the above equation the interference term schemeI j is the same as in the UL (for MR, ZF, or P-ZF).

Theorem 3 concludes that the SINRs of UL and DL with uses proper adjustment of power control coefficients.Therefore, the total transmit power is same in DL and UL but allocated pilot signals different over the UEsin Per-cells.

Three different types of linear precoding algorithms were consider in this paper, MR precoding which

amplifies the targeted signal by chose ˆ MRg gjk jk� , ZF is actively suppressed intra-cell interferences by

substituting ˆ ZFg gjk jk� and P-ZF is rejects both intra-cell and inter-cell interference actively by putting

ˆ P ZFg gjk jk

�� .


3.4. Finite and Asymptotic Analysis of Achievable Spectral Efficiencies

This sub-section describes the sum of achievable SEs in DL and UL per cell following.

Corollary 1: the DL and UL per cell achievable SE is given as

� � � �ul dlSE SE SEj j j� �

11 log 12

BK schemeS I j

� � ��

[bit/s/Hz/cell] (25)

For simplicity and obtained exact results of M-MIMO system that allows analyzing optimize the SEwithout considering separate the UL and DL.

Corollary 2: Consider the subset of each cell Lj(�)�L same pilots uses in each cell j. The MR, ZF and

P-ZF precoding has to meet effective SINRs when M �� (with K; B � S < �)

� ��

1 1 1 1, ,

2MR ZF P ZFI I Ij j j

jjjlLl �

��

�� (26)

In above equation (26) very clearly confirmed the effected pilot contamination only per each cells.

Corollary 3: the subset of each cells j in multicell networks uses the same pilot’s sequences hence theper cell SE is given as

� ��

11 log 12 2

KSE Kj S

jll L jj

�

��

� � � ��

�

� ��

� � � ��

(27)

When the number of scheduled UEs is *

2

SK

��

or *

2

SK

��

which gives SE is maximized for all cells.

The corollary 3 concludes that the when BS antennas M large then scheduled UEs is directly proportional

to the length of the frame S. For example let assumed that *

2

SK � if � is equal to one and

*

6

SK � if � is

equal to three, the UE mobility and propagation channel environment values depending on coherent symbolis (S) 200 and 10000and block lengths.

In order to obtain the optimal performance of multi-cell M-MIMO system should scheduled the tens or

several thousands of UEs. If scheduled UEs *

2

SK

�� where � is an integer and optimal SE asymptotic

limit is given as

� ��

11 log 12 24

S K

L

S

j lj

E j Sjl �

�

� �

� � � ��

�

� ��

� � � ��

(28)


Interestingly, the asymptotically optimal SE achieved scheduled UEs pilot allocation transmission is

half the frame 2

SB � .

4. NUMERICAL AND SIMULATION RESULTS

The optimize the SE of M-MIMO system we considered reasonable integer values of the number of BSantennas (M), UEs(K) and pilot reuse factor � (B = �K). We consider the length of coherence block is S =

400), SNR values to 52�

�� dB and path loss exponent � = 3.7. For example 2 ms coherence duration and

coherence frame B is 200 kHz.

The following assumptions are the three different propagation environment of inter-cell interference

i. Average Case: all UEs averaging in all cells

ii. Best Case: in other cells UEs has further defined most from BS

iii. Worst case: all other cells in UEs very near to the BS.

The best case is excessively optimistic because the UE position is interfering cell with other differentcells. The worst case is excessively suspicious therefore UEs cannot find with respect to all other cells. Inpractice, average case is most applicable where averaging of UEs mobility, scheduling and random changesof pilot signal between the different UEs in each cell.

The optimized SE simulation results as a function of number of BS antennas M ith averaging all cellsinter-cell interference is shown in Figure 1, the best SE optimized case in Figure 2 and the worst case inter-

(a) Optimized SE per each cell


(b) Optimal number of Scheduled UE K*

Figure 1: The optimized SE for average inter-cell interference.

Figure 2: The optimized SE for best-case inter-cell interference.


Figure 3: The optimized SE for worst-case inter-cell interference.

cell interference in Figure 3. The corresponding scheduled UEs K* optimized SE are shown in figures 1(a),1 (b) 2(a), 2 (b) and 3(a), 3(b) respectively.

The achievable SEs of the best case interference very different than other two cases so hence single cellM-MIMO system is not appropriate to multi-cell M-MIMO system and vice versa.

Under the best case inter- cell interference ZF gives better SEs than MR so therefore intra- cell interferenceis very high. In the best case the inter-cell interference of P-ZF is identical to ZF performance but not samein worst case. In practical scenarios average case SEs are similar for MR, ZF and P-ZF if BS antennasshould be 10 � M � 200. In all cases huge difference appears when the BS antennas are very high.

Figures 1 to3 shows that optimum SE of MR, ZF and P-ZF but SE can achieve only number of scheduledUE and pilot reused factor reuse factor â are used approximately.

4.1. System Parameters Impact on SEs

We consider the inter-cell interference in average case for practical applications, how system parameteraffects the performance M-MIMO system. Also consider the BS M antennas range 10 � M � 1000. Figure4 describe that the interference from the various cells in the average case and UEs (K) = 10 and Monte-Carlo simulations used.

5. CONCLUSIONS

This paper we investigated to maximize per cell SE of M-MIMO system with fixed the BS antennas howmany UEs should be scheduled where as standard SE expression is depends on UE position which formulateto optimize active UEs. We defined a new SE equations are derived, which are independent of UE position


with assumptions of power control and positions of UE averaging. The simulation and analytical resultsshows that MR, ZF and P-ZF has suppresses inter-cell interference with considering pilot signal transmission

from neighboring cells. The SE optimal selection of scheduled UEs K* reaches 2

S

� if M � � , regardless

of the processing techniques. When M is large *

2

SB K�� therefore half of the half frame can be used to

pilot signal transmission. The limit of SE does not reached when M-MIMO system BS antennas M arelarge but unfortunately maximum frame should be used to pilot signal transmission such as 5% to 40%.Normally high SEs per cell is achieved scheduling each UE position, while the SE per UE can only be 1-4bit/s/Hz. The P-ZF technique obtains better SE per UE as compare with MR technique, where as the P-ZFschedule the small number of UE than MR scheduled UE. Therefore to obtain SE per cell ZF is the best andoptimum choice, thus in particular cases only P-ZF is need to inter-cell interference suppression.

REFERENCES[1] Nokia Siemens Networks, “2020: Beyond 4G radio evolution for the Gigabit experience,” White Paper, Tech. Rep.,

2011.

[2] T. L. Marzetta, “Non cooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Trans. WirelessCommun., vol. 9, no. 11, pp. 3590–3600, Nov. 2010.

[3] Patteti Krishna, Kalitkar Kishan Rao and Tipparti Anil Kumar, “Multiuser MIMO Transmission Modes for TransmitDiversity and Spatial Multiplexing in Long Term Evolutions,” ARPN Journal Engineering and Applied Sciences, Vol 10,No-10,pp.2198-2202, March 2015.

[4] F. Boccardi, R. Heath, A. Lozano, T. Marzetta, and P. Popovski, “Five disruptive technology directions for 5G,” IEEECommun. Mag., vol. 52, no. 2, pp. 74–80, Feb. 2014.

[5] E. G. Larsson, F. Tufvesson, O. Edfors, and T. L. Marzetta, “Massive MIMO for next generation wireless systems,” IEEECommun. Mag., vol. 52, no. 2, pp. 186–195, Feb. 2014.

Figure 4: The SE of Per-cell for K = 10.


[6] J. Jose, A. Ashikhmin, T. L. Marzetta, and S. Vishwanath, “Pilot contamination and precoding in multi-cell TDD systems,”IEEE Trans. Commun., vol. 10, no. 8, pp. 2640–2651, Aug. 2011.

[7] J. Hoydis, S. ten Brink, and M. Debbah, “Massive MIMO in the UL/DL of cellular networks: How many antennas do weneed?” IEEE J. Sel. Areas Commun., vol. 31, no. 2, pp. 160–171, Feb. 2013.

[8] Björnson, J. Hoydis, M. Kountouris, and M. Debbah, “Massive MIMO systems with non-ideal hardware: Energy efficiency,estimation, and capacity limits,” IEEE Trans. Inf. Theory, vol. 60, no. 11, pp. 7112– 7139, Nov. 2014.

[9] E. Björnson, M. Matthaiou, and M. Debbah, “Massive MIMO with arbitrary non-ideal arrays: Hardware scaling lawsand circuit-aware design,” IEEE Trans. Wireless Commun., vol. 14, no. 8, pp. 4353–4368,Aug. 2015.

[10] A. Pitarokoilis, S. K. Mohammed, and E. G. Larsson, “Uplink performance of time-reversal MRC in massive MIMOsystems subject to phase noise,” IEEE Trans. Wireless Commun., vol. 14, no. 2, pp. 711–723, Feb. 2015.

[11] R. Müller, M. Vehkaperä, and L. Cottatellucci, “Blind pilot decontamination,” in Proc. WSA, 2013.

[12] M. Biguesh and A. B. Gershman, “Downlink channel estimation in cellular systems with antenna arrays at base stationsusing channel probing with feedback,” EURASIP J. Appl. Signal Process., vol. 2004, no. 9, pp. 1330–1339, 2004.

Performance Analysis of Maximal Spectral Efficiency for...

Documents

Transcript of Performance Analysis of Maximal Spectral Efficiency for...