Link Adaptive Multiuser MIMO System with MRT Precoding Technique and Limited Feedback

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 8, Issue 1, January 2018)

104

Link Adaptive Multiuser MIMO System with MRT Precoding

Technique and Limited Feedback

Manish Korde

1

, Rajesh Bodade

2

1

Phd Scholar, Pacific Academy of Higher Education and Research University, Udaipur, India

2_{Faculty of Communication Engineering, Military College of Telecommunication Engineering, Mhow, Dist: Indore, India}

Abstract—Many papers have been written to increase the performance of Multiuser MIMO system with full feedback which consumes valuable uplink resource; in contrast, if we use limited feedback in the system, it reduces consumption of uplink resources, but at the same time the sum rate capacity of the multiuser MIMO system reduces. Therefore, it is necessary to maximize sum rate capacity by using limited feedback for satisfactory system performance. This paper compares sum rate capacities of link adaptive multiuser MIMO system with full feedback and with limited feedback. Graph is plotted for capacities of the system for both cases of feedback. In this paper, MRT precoding is adapted in Multiuser MIMO system. To prove superiority of MRT precoding with limited feedback scheme its comparison with other precoding schemes with full CSIT is done for sum rate capacity.

Keywords— Maximum Ratio transmission (MRT), Multiuser MIMO system, Channel state information at transmitter (CSIT), Limited feedback etc.

I. INTRODUCTION

In today’s real world scenario, link adaptive Multiuser MIMO system is most promising technology to increase data rate as well as serving the data and voice services to many people together. The system is in backbone of many wireless technologies such as LTE, Advanced LTE, and 5G. Link adaptation can be used to deal with a fading channel in order to sustain a reliable communication and to increase throughput of a system. For multiuser MIMO systems, we can utilize precoding to investigate MIMO potentials. In essence, the precoding techniques are used to mitigate the interuser interference and to improve the effective received SNR. In this, channel state information at the transmitter (CSIT) is very important component for trying to maximize multiuser MIMO performance via precoding. In time division duplexing (TDD) system, Pilot training in the uplink is done by utilizing the channel reciprocity to acquire the complete CSIT, but imperfect channel estimation and pilot impairment would lead to inaccuracy of the CSIT. In frequency division duplexing (FDD) system, the feedback channel is utilized to acquire CSIT, which is usually consumes uplink resource.

Hence, a finite set of precoding matrices, named codebook, known to both the receiver and the transmitter should be predesigned. The receiver selects the optimal precoding matrix from the codebook according to the channel state information (CSI) and reports the precoding matrix indicator (PMI) to the transmitter via the limited feedback channel [1]. The paper [2] discussed the precoding algorithm such as BD-LRL and compared it with other precoding to compare its performance with other algorithm such as DPC and BD-ZF for sum rate capacity. The paper [3] and [4] discuss about quantization of signal at the receiver with the help of ADC device which leads to quantization error in the received signal.

The aim of this paper is to build a link adaptive multiuser MIMO system with limited feedback which with our proposed precoding technique and limited feedback performs better than the system with other precoding techniques having full CSIT. For the purpose, MRT precoding has been developed for multiuser system and compared its capacity with DPC and BD-ZF precoding [2]. Precoded signal is detected at the each antenna of the each user and quantizes [3, 4] to digital signals. Then digitalized signals are compared with RQV codebook to find out indexes of the feedbacks. These indexes of feedback are represented by B bit to send them to transmitter back. According to these codebook indexes transmitter generates precoding matrix. The precoding matrix is applied to signal in next time interval of symbols to provide beam forming.

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International Journal of Emerging Technology and Advanced Engineering

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II. LINK ADAPTIVE MULTIUSER MIMOSYSTEM

We are interested in modeling of the Link adaptive MIMO system with SVD precoding and full feedback. As given in paper [6] fig 1 shows a multiuser System, Let us assume that a base station has N numbers of antennas and sends signal to K number of users U U₁, ₂...U_k each of

the receiver equipped with M M₁, ₂...M_k

.antennas.

The transmitted signal matrix

x

N M _k is expressed as the

sum of signals intended to usersU U₁, ₂...U_k:

,

1 1

k M K

k l

k l

x X

 





(1)

The channel matrix between userU_k ; k1, 2,...K

and the base station is denoted by

k

M N

H  . At each user,

received signal vector of dimension, k1...K is given by:

.

k k

Y H x nk  ; k1, 2,...K (2)

k

n , k1, 2,...Kis an additive noise signal of sizeM_k1_.

eq.2 can also be written as:

1,

; 1, 2... K

k k k k i k

i i k

Y H X H X n k K

 

[image:2.612.50.287.313.627.2]

  



  (3)

Fig 1: 8×8 multiuser MIMO system with 2 users each having 4 antennas

The second term of the sum in equation (3) represents the multiuser interference (MUI) coming from multiple users.

K

k i

i k

MUI H X







(4)

Block diagonalization using SVD removes the second term of the equations but it cannot remove interference among the antennas of the user itself. With help of Maximum ration transmission technique this interference also removes. Means MRT supports perfect beam forming which need perfect CSI information at transmitter. SVD is applied second time to remove inter antennas interference of the user itself.

A. MRT precoding technique with multiuser MIMO:

Let us define H_k( )j to be the interference channel matrix

of the jth antenna at the kth user:

,

( )

1 1 k j

j

k k

k

K

h





 

 

  

 

 

1 H

H H

H

(5)

Where H( )_kj is thekth channel matrix that removed the

th

i line of

( )i

k

H _{can be expressed through SVD and}

described by:

( )j ( )j ( )j j j

k  k  k  

( )(1) ( )(0) k k

H U V V (6)

Where V_k( )(0)j Þ is the right-singular matrix with zero

singular value and V_k( )(1)j is the right-singular matrix with

non-zero singular value. Therefore, Vk( )(0)j is the zero space

ofH( )_kj . For the kthuser, Maximum ratio transmission

precoding is given by:

( )

(1) (2)

[ , , Mk ]

k k k k

F  F F F ₍₇₎

The total number of the receiver antennas isM_k, the

new precoding matrix of the jthreceiver antenna at the kth

user (M dimension column) denotes ( )j ( )(0)j ( )

k k k

F V M ,

and F_k is the precoding matrix for the th

k user



MkN) dimension.

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International Journal of Emerging Technology and Advanced Engineering

106

Further, the receiver vector at userk is written as:

( ) _{( )}

, _1, , _1,

M _K

M_k k _j

y h F x h F x H F x_i n k k M_k k _j _{j M} k M_k k _{i i k} k k k

k

     

    (8)

_{k k}x n_k₍₉₎

In equations (14) and (15) the first part is the coefficient

of the receiver antenna at userk, _, ( k)

k M

k hk M F



 (M_kis

the dimension column of precoder matrix F), the second part is interference from other antennas of user k which

becomes zero, as _, ( j)

k M

k M k

h F x is zero if jM_k . The third

part is MUI, and H F_k _kis zero obviously for ik.

The received symbol at each antenna at user k is written as:

( )i k( )i



k( )i



 

' k

y y ₍₁₀₎

III. QUANTIZATION OF RECEIVED SIGNAL

Equation (10) can be rewritten after quantization by uniform quantizer as

( _, _, _, )

k

k k k

y Q_{k M} x_{k M} n_{k M}

(11)

(1 ) (1 )

, , ,

b b Q

k

k k k

y x n n

k M k M k M

  

    

₍₁₂₎

Where real and quadrature component of signal are separately quantized and

2

4 ADC precision[3].

k k

b

k

E y y

for b bit E y               (13)

The normalized mean squared error and n_Q

is the quantization noise with variance

(14)

2

, ,

(1 ) _k t _k

b b k M n M

k

P KM

    

  _  _

  (15)

The signal to quantization noise ratio is given by

2

2 2

, _,

2 2 2 2

,

(1 ) ₍₁ ₎

(1 ) ₁

k

k k

k

k k

t

b k M _b _{k M} _M

k

b n M Q

b k M M

P KM SQNR   _ _ _    _{ } _   _ _  _ _ _            

 _ _ ₍₁₆₎

IV. SUM RATE CAPACITY FOR MRTPRECODING WITH

FULL CSIT

Assuming that the noise nQ follows the worst-case

Gaussian distribution, the average achievable rate with

perfect CSIT and conjugate beam forming is for Mk

antenna of a user k is

2 ,

, , 2 ₂

,

(1 )

( , ) log 1

1

k k

b k M M

MU MIMO M k M

b k M M

h

R b E

h        _     _ _          _ _ _       

 ₍₁₇₎

According to the paper [4]



2



, k

k M t

h N

 

Hence,

, 2

(1 )

( , ) log 1

1

k k

k

b t M

MU MIMO M

b t M

N R b N              _  _   _ _  

if channel

is IID Rayleigh fading channel. (18)

The average achievable rate with perfect CSIT is approximately,





2 , ,

,

2 ,

log 1 (1 ) f low SNR

( , ) ₁

log for large SNR

k k

k

b k M t k M

MU MIMO M

k M b N or R b        _{ }             

(19)

For K users having M k antennas sum rate capacity with

perfect CSIT is given by





2 , ,

1 1

( , ) log 1 (1 ) f low

k

k M

K

MU MIMO b k l t k M

k l

R  b   N or 

   



  (20) 2 , , , 1 1 1

( , ) log f large

k

k M

K

MU MIMO k M

b k l

k l

R b or 

        _ _  



(21) 2 2 (1 )

Q b b yk

   _{ } _

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International Journal of Emerging Technology and Advanced Engineering

107

V. SUM RATE CAPACITY FOR MRT PRECODING WITH

LIMITED FEEDBACK

Averaging over the RVQ codebooks, the achievable rate under B bit (limited) feedback for antenna Mk of user k is

2 ,

, 2 ₂

,

(1 )

log 1

1

k k

k

k k

b k M M

MU MIMO M

b k M M

R

  



 _  

 _ _

   

 

  

 __ __ 

 

22)

1

2

1

(1 ) 1 2

log 1

1 1 2

t k

B N

b t M

B N

b M t

N

 

 

   

     

 

 _ _ __

 

 

 

   

     

 

 _ _ 

 

(23)

In the low and high SNR regimes, the average achievable rate with limited feedback for antenna Mk of

user k is

1

2 , ,

,

2 ,

log 1 (1 ) 1 2 f low

( , )

1

log for large

t

k k

k

k B

N

b k M t k M

MU MIMO M

k M b

N or

R b B

  

 

 



   

    _  _

  

 _ _ __

 

  

  

  

 ₍₂₄₎

For K user having Mk antennas sum rate capacity (bps/Hz) for multiuser MIMO with B bit feedback is given by

,

1 ( , ) log 1 (1 ) 1 2

2 ,

1 1 f low k

MU MIMO k M

B M

K k _Nt

R b B _Nt

b k l

k l   or 



 _

     

 

  

  

 _ _

 _ _

 

(25)

2 ,

, ,

1 1

1

( , ) log f large

k

k M

K

MU MIMO k M

b k l

k l

R b B or 





 

 

 _ _

 



(26)

Theoretical description of limited feedback:

In this paper, we consider MU-MIMO system. The transmitter is equipped with Nt antennas and the receiver is

equipped with Mk antennas. Before quantization of signal,

SVD is applied to signal received form each antenna of each receiver.

First SVD operation removes multiuser interference from the signal, while second SVD operation removes the interantenna interference of the user itself. Now, the system becomes simple SISO system for each of the antenna of each user. After that, there are two, b bit ADC that separately quantize the real and imaginary part of received signal for each antennas of the each user. Uniform quantization is applied to the signal [7]. As analysis given in paper [4] for MISO case, the same case is applicable to all antennas of MU-MIMO system user separately. The random vector quantization (RVQ) is used to quantize direction of channel h. Out of B bit B1 bits are used to

convey direction information. The code book



0

,

1

,

2, ₂B1 1



w



v

v v

v



Where each of the quantization vector is independently chosen from the isotropic distribution of Grassmannian manifold as in [8]. Besides the channel direction information, the remaining bits B2 =B-B1 are used to

quantize the phase of the equivalent channel. If

, _k

h

k M is representing channel matrix of Mk antenna

of user k. Finding out optimum choice of

k M

v

_{for that}

antenna should be

2

,

, ₂

: 1

,

(1 )

arg max 1

k k

k

k k

b k M M

k M v v

b k M M

v







 





 _  

 _ _

  

 

 _ 

 __ __ 

  (27)

Where , _k ( k)

M

k hk M F



 and precoding

matrix ( k) _,

k M

k M

F v as given in eq. (8) and (9). The

optimization problem is non-convex and very difficult to solve.

For the case of full CSIT, transmitter chooses the best beamforming in the set



w v, _max



form the codebook. In

case of finite feedback the receiver compute the term (27) for the each antenna of the user and match it with

v

in codebook and feedback the index of best one.

The paper [4] also prove that if E || h||2= Nt then it is

possible to maximize sum rate capacity of MISO system with full CSIT and if

1

|| * || (1 2 t )

B N t

E h v N

 

  Then we can maximize the

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International Journal of Emerging Technology and Advanced Engineering

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Both of these conclusions are applicable to multiuser MIMO system also. Because, when proposed MRT technique is applied to MU-MIMO system, it converts each antenna of each user into a separate MISO system.

VI. SIMULATIONS &RESULTS

In simulation, we investigate the performance of proposed scheme of precoding with limited feedback for the case of multiuser MIMO system. The proposed scheme is compared with DPC and BD-ZF precoding schemes [2] with full CSIT multiuser MIMO. A spatially uncorrelated MIMO Rayleigh fading of wireless channel and the noise distributed complex Gaussian variables with zero mean and unit-variance are assumed. The modulation QPSK is applied on signal.

For simplicity, we consider number of antennas for the each user is same; the simulation is performed for three

configurations of antennas 8 × 4, 8 × 6 and 8 × 8. The 8 ×

4 multiuser MIMO system is simulated for two users; each

having two antennas. The 8 × 6 multiuser MIMO system is

simulated for two users; each having three antennas, while

the 8 × 6 multiuser MIMO system is simulated for two

users; each having four antennas. Sum rate capacity Vs SNR are plotted & compared with other precoding schemes to prove superiority of MRT algorithm with limited feedback at lower SNR.

0 5 10 15 20 25

0 10 20 30 40 50 60

S

u

m

r

a

te

ca

p

a

ci

ty

b

p

s/

H

z

SNR dB

[image:5.612.359.532.146.273.2]

MRT with full CSIT MRT with 4 bit feedback MRT with 8 bit feedback MRT with 16 bit feedback MRT with 24 bit feedback MRT with 32 bit feedback MRT with no feedback

Fig 2: Sum rate capacity upper and lower bound for MRT precoding with feedback for 8×8 configuration with two users, each user has

four antennas.

0 5 10 15 20 25

0 5 10 15 20 25 30

SNR dB

S

u

m

R

a

te

C

a

p

a

c

it

y

b

p

s

/H

z

[image:5.612.359.530.323.443.2]

MRT with Full CSIT MRT with 4 feedback MRT with 8 bit feedback MRT with 16 bit feedback MRT with 24 bit feedback MRT with 32 bit feedback MRT with No feeedback

Fig 3: Sum rate capacity upper and lower bound for MRT precoding with feedback for 8×4 configuration with two users, each user has two

antennas.

0 5 10 15 20 25

0 5 10 15 20 25 30 35 40 45

SNR db

S

u

m

R

a

te

C

a

p

a

c

it

y

b

p

s

/H

z

[image:5.612.86.254.453.586.2]

MRT with full CSIT MRT with 4 bit feedback MRT with 8 bit feedback MRT with 16 bit feedback MRT with 24 bit feedback MRT with 32 bit feedback MRT with No feedback

Fig 4: Sum rate capacity upper and lower bound for MRT precoding with feedback for 8×6 configuration with two users, each user has

three antennas.

0 5 10 15 20 25

0 10 20 30 40 50 60

S

u

m

r

a

te

ca

p

a

ci

ty

b

p

s/

H

z

SNR dB

MRT with full CSIT MRT with 4 bit feedback MRT with 8 bit feedback MRT with 16 bit feedback MRT with 24 bit feedback MRT with 32 bit feedback MRT with no feedback DPC with full CSIT BD-ZF with full CSIT

Fig 5: Sum rate capacity Vs SNR Curve for MU-MIMO system for various precoding and feedback schemes for 8×8 configuration with

[image:5.612.344.541.485.616.2]

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International Journal of Emerging Technology and Advanced Engineering

109

TABLEI

RESULTS OF SIMULATIONS

SN R in

dB

Configuratio n of antennas

Algorith m

User s

No. of antenna s with

each users

Sum Rate Capacity bps/Hz

20

MIN (With no

feedbac k)

MAX (Wit h full CSIT

)

8×4 MRT 2 2 15.9 28.32 8×6 MRT 2 3 22.6 42.48 8×8 MRT 2 4 30.18 56.65 8×8 BD-ZF 2 4 -- 30.18 8×8 DPC 2 4 -- 43.88

Figure 2, 3, 4, 5 and table 1 show the maximum and minimum sum rate capacity can be achieved with MRT precoding with feedback for multiuser MIMO system at different configuration of user and antennas. Maximum Sum rate capacity at 20 dB SNR is 56.65bps/Hz, while minimum sum rate capacity is 30.185bps/Hz with MRT precoding in 8×8 configuration (two users each with four antennas). If transmitter has more antennas then users antennas, the sum rate capacity reduces. For all configurations of system antennas, the sum rate capacity is increases with SNR in db. Also the sum rate capacity of BD-ZF and DPC precoding with full CSIT for 8×8 configuration (two users, each with four antennas) are laid below the sum rate capacity of MRT precoding with 4 bit feedback for 8×8 configuration (two users, each with four antennas) up to 20 db SNR. At higher SNR sum rate capacities of all precoding algorithm converges. Eq. (21) and (26) indicates the behavior of sum rate capacity at higher SNR.

VII. CONCLUSION

As explained in simulation and result, MRT precoding schemes with limited feedback results in a better performance of Multiuser MIMO system at lower SNR. The improved performance is resulted from beam forming of each of transmission stream of each user. Maximum Ratio transmission precoding scheme with limited feedback provide multiple benefits of providing good sum rate capacity while saving of uplink resources at lower SNR. At Higher SNR, it saves valuable uplink resource and gives same capacity as MRT with full CSIT.

REFERENCES

[1] E. Visotsky and U. Madhow, ―Space-time transmit precoding with imperfect feedback,‖ IEEE Transactions on Information Theory, vol. 47, no. 6, pp. 2632–2639, 2001.

[2] Sukriti Garg, Krati Mittal, Divyang Rawal, Dec 2015, ―Improved Signal Detection for Multiuser MIMO System using BD QR-LRL‖, in proceedings of IEEE conference on Computers and Devices for Communication (CODEC),Institute of Radio Physics & Electronics, University of Calcutta.

[3] J. Mo and R. W. Heath Jr., 2015, ―Limited feedback in multiple-antenna systems with one-bit quantization,‖ in proceeding of Asilomar conference on Signals, Systems and Computers, pp. 1432– 1436.

[4] ] J. Mo and R. W. Heath Jr. 2016, ―Limited feedback in MISO systems with finite-bit ADCs,‖ in proceedings of Asilomar Conference on Signals, Systems and Computers, pp. 479–483. [5] J. Mo and Robert W. Heath. 14 April 2017, ―Limited Feedback in

Single and Multi-user MIMO Systems with Finite-Bit ADCs‖, IEEE transition on wireless communication.

[6] Ben Zid Maha, Raoof Kosai, ―Recent Trends in Multi-user MIMO Communications‖, In Tech, Ch. 1, December 04, 2013, pp. 10-13. [7] J. Max, ―Quantizing for minimum distortion,‖ IRE Transactions on

Information Theory, vol. 6, no. 1, pp. 7–12, 1960.

[image:6.612.34.302.153.328.2]