Novel Scheme of CSI Feedback Compression for Multi-User MIMO-OFDM System

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Procedia Engineering 29 (2012) 3631 – 3635

Available online at www.sciencedirect.com Available online at www.sciencedirect.com

Procedia Engineering 00 (2011) 000–000

Procedia

Engineering

www.elsevier.com/locate/procedia

2012 International Workshop on Information and Electronics Engineering (IWIEE)

Novel Scheme of CSI Feedback Compression for Multi-User

MIMO-OFDM System

Yongjie Li

a

, Rongfang Song

a

*

,b,

a_{Nanjing University of Posts & Telecommunications, Nanjing 210003, China;}

b_{National Mobile Communication Research Laboratory, Southeast University, Nanjing 210096, China}

Abstract

Downlink multi-user transmission has been recognized as a promising technique to increase system capacity. However, they require accurate channel state information (CSI) at the base station such that appropriate signal processing can be performed to separate multiple users in the space domain. It will lead to overwhelming large feedback overhead in multi-user MIMO-OFDM system. In this paper, a novel CSI feedback compression scheme based on the recently proposed compressive sensing (CS) theory to be used in multi-user MIMO-OFDM system is proposed. Simulation results show that our proposed scheme has the potential of reducing the CSI feedback overhead and providing more accurate CSI at the transmitter than the codebook-based method to suppress multi-user interference under multipath channel conditions.

Keywords: feedback compression, compressive sensing, OFDM, multi-user interference, CSI.

1. Introduction

Multi-user multiple-input multiple-output (MU-MIMO) technique is being considered for the downlink of next generation mobile cellular systems to improve spectral efficiency [1]. In order to achieve full MU multiplexing gain and obtain a high system throughput, MU-MIMO techniques require perfect channel state information at the transmitter. Imperfect CSIT causes residual inter-user interference, which degrades the performance of MIMO broadcast channel [2]. Limited feedback of CSI is a very active area of research. The limited feedback schemes based on codebook are mainstream technologies [3-4]. The

* Corresponding author. Tel.: 025-83492441.

E-mail address: songrf@ njupt.edu.cn.

Open access under CC BY-NC-ND license.

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problem of CSI feedback is especially challenging in case of multi-user MIMO-OFDM transmission over frequency selective channels where the number of complex channel gains is directly proportional to the number of subcarriers. If the channel changes often and there are many users in the system, the feedback burden quickly becomes unmanageable. By exploiting the fact that many natural signals are sparse or compressible, the recently introduced principle and methodology of compressive sensing (CS) provides a new framework to jointly measure and compress signals that allows less sampling and storage resources than traditional approaches based on Nyquist sampling [5]. In this paper, CS is proposed to apply to compression of CSI feedback for multi-user MIMO OFDM systems so as to reduce feedback overhead and provide accurate CSIT to obtain high system throughput. It is verified by simulations that the proposed methods have the potential of reducing the CSI feedback overhead and providing more accurate CSI at the transmitter than the codebook based methods to suppress multi-user interference under multipath channel conditions.

2. System Model

n S

Fig.1. Block diagram of Multi-user MIMO OFDMA downlink system

As system model, we consider the downlink of a cellular OFDM system with Nc subcarriers. The

transmitter has M transmit antennas and U users have one antenna each. Block diagram of multi-user MIMO OFDMA downlink system is shown in Fig.1. Let _{ (1)_{, ,} (Sn)_}

n n n

S = s L s be the set of scheduled users receiving data on subcarrier n and x( )n the 1 M× transmitted symbol vector on subcarrier

0,...., c 1

n= N − , which is related to the information symbols { ( )}d nj for user j S∈ n via linear

beamforming, i.e. ( ) ( ) ( ) n j j j S n n d n ∈ =

∑

x F (1) with { ( )}F_j n 1 M× beamforming vectors. The signal received by user k S∈ _n on subcarrier n can be written as ( ) ( ) T( ) ( ) k k k y n =h n x n +w n ( ), [ ( ) T( )] ( ) [ ( ) T( )] ( ) ( ) k k k k j j k j S n j k n n d n n n d n w n ∈ ≠ = h F +

∑

h F + (2)

where w n_k( ) is the additive complex Gaussian noise with zero mean and unit variance and the summation term in the second line of (2) accounts for multi-user interference on user k .We assumed equal power allocation across all subcarriers, hence the power allocated on subcarrier n is P P= _tol/N_c, where P_tolis the sum power. We have _{( )}2

E⎡_⎣x n ⎤ ≤_⎦ P.

In this paper, zero-forcing beamforming is employed. The user k feeds back two information for each subcarrier: 1) the channel direction information (CDI) given by a quantized version of the normalized channel matrix $ ( )hk n =h_k( ) /n h_k( )n and an analog channel quality information (CQI). Let

�( ) $ (1)( ) ,...,$ (Sn)( ) n n T T T S S n _{= ⎣}⎡ n n ⎤_⎦

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3633 Yongjie Li and Rongfang Song / Procedia Engineering 29 (2012) 3631 – 3635Yongjie Li.et.al / Procedia Engineering 00 (2011) 000–000 3

users Sn on subcarrier n . By denoting with ( )G n = ⎣⎡gTn(0),...,gnT(Sn)⎦⎤ the right pseudo-inverse of the

quantized channel, the ZF beamforming matrix is given by ( ) T(0),..., T( )

n n n

n _{= ⎣}⎡ S ⎤_⎦

F f f =G( )n diag( ( ))P n 12 =H�_{( ) ( ( ) ( ) )}_n H H� _n �H _n H −1_diag_{( ( ))}P _n 21 (3) where ( )P n is the vector of power normalization coefficients with entries 2

( ) / ( )

k n =P S g nn k

P .

The signal to interference plus noise ratio (SINR) at user k on subcarrier n is 2 2 ( ), ( ) ( ) ( ) 1 ( ) ( ) n n T P k k S k _T P k j S j S n j k n n n n n γ ∈ ≠ = +

∑

h f h f (4) The average achievable throughput of our systems is calculated as

1 1 2 0 0 1 1 ( ) log (1 ( )) c c n N N k n n k S c c C R n n N N γ − − = = ∈ =

∑

=

∑ ∑

+ (5)

3. CSI Feedback Compression Based on Compressive Sensing

CS is a new sampling and reconstruction method for signals that are known to be sparse or compressible in some basis. We assume an N-dimensional signal x to be D -sparse in a sparsity-inducing basis {bi}, that is, there are at most D non-zero coefficients {α } in the basis expansion i x=

∑

_iαi ib

denoted asBα. The signal is sampled using Mcmeasurements with the measurement vectorsφi( 1, , )i= LMc ,

that is,y =_i x,φ_i . The compact representation isy Φx ΦBα= = , where y is called vector of measurements

and α is the N-dimensional vector of coefficients which includes at most D non-zero coefficients. Φ is

the measurement matrix which models the measurement system and is sufficiently incoherent with the sparsity basis. The signal is then recovered with high probability by solving an optimization that ensures the recovered signal is both consistent with the measurements and sparse.

To make the feedback transmission as efficient as possible, spatial, time and frequency correlation should be exploited. Here, our scheme is to use the CS for exploiting correlation in frequency, due to its efficiency. In multi-user MIMO OFDM systems, both scheduling and MIMO precoding need the frequency domain channel coefficients. The channel coefficients are not sparse in frequency domain. However, numerous past and recent channel measurement campaigns have shown that propagation paths in many physical channels tend to be distributed as clusters within their respective channel spreads [6]. Hence, most wireless channels of wideband mobile communication systems are sparse in time domain.

Assuming channel coefficients of all subcarriers has been known at user by employing perfect channel estimation algorithm. In order to reflect effective compression of compressive sensing, we design a permutation of channel coefficients on all subcarriers. The estimated channel frequency response of user

k is denoted by (1), ..., ( ), ..., ( ) T T T k = ⎣⎡ k k n k Nc ⎤⎦ H h h h 1 1 1 2 2 2 (1) (2) ( ) (1) (2) ( ) ( ) (1) (2) ( ) k k k c k k k c m k M M M k k k c h h h N h h h N h n h h h N ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ =_⎢ _⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ L L M M M L 1 2 ˆ ˆ ˆ k k M k ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ M h h h (6) where m( ) k

h n denotes the channel coefficient corresponding to the m -th transmit antenna on n -th subcarrier of user k and ˆm

k

h denotes the m -th row of Hk. At each terminal, ˆ m k

h are compressed separately and transmitted to the transmitter. At the transmitter, base station performs beamforming design based on the reconstructed channel state information. Block diagrams of the encoding and decoding process of feedback information with CS are given in Fig. 2. At a given time instant ˆm

k

h is encoded using CS, quantized by a kind of appropriate design of scalar quantizer and then be transmitted to base station through an error-free feedback link. At base station, the inverse process is applied and the

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compressive sensing reconstruction algorithm is exploited to reconstruct the channel coefficients of all users. In this paper, we exploit orthogonal matching pursuit (OMP) to reconstruct feedback information.

ˆm k

h

Fig. 2. Diagram of the encoding and decoding of feedback information with CS

4. Simulation

In this section, simulation results are provided to investigate the performance of channel state information feedback compression method based on CS. For comparison purposes, the performance of conventional codebook based method with different size of cluster which is widely employed is also illustrated. The downlink of a cellular OFDM system with 1024 subcarriers is considered. The transmitter has M =4 transmit antennas. We assumed P is 10 dB. Here, the frequency selective channel with six paths which is widely used is employed. For compressive sensing, the IDFT basis and the i.i.d. random Gaussian measurement matrix are adopted. To reduce the performance loss, an optimal bit allocation method called Lloyd-max method [7] is employed. If the dimension of measurement matrix is denoted by

c

M and every real value is quantized to B_lloyd bits, the feedback rate with CS method is calculated as

( 2 ) /

CS c lloyd c

R = M × ×B ×M N bits/subcarrier. Here, B_lloyd = bits. Also, random vector quantization 5 (RVQ) codebook is used because it is very amenable to analyze and also performs measurably close to optimal quantization [8]. What’s more, clustering is a simple and effective method to reduce the feedback overhead. In this work, we also exploit the performance of CSI feedback compression based on CS with different sizes of cluster. The feedback rate of codebook method with clustering is calculated as

(( / ) ) /

codebook c cluster c

R = N D ×B N bits/subcarrier, where D_cluster denotes the size of cluster.

0 2 4 6 8 10 12 14 16 1 2 3 4 5 6 7 8

Feedback Rate [bits/subcarrier]

T hr oug hput [bi ts /s /H z] Codebook with K=1 CS with K=1 Ideal with K=1 Codebook with K=2 Ideal with K=2 CS with K=2 Codebook with K=4 Ideal with K=4 CS with K=4 0 0.5 1 1.5 2 2.5 3 3.5 4 1 2 3 4 5 6 7 8

Feedback Rate [bits/subcarrier]

T hr oug hpu t [bi ts /s /Hz ] Codebook with K=4 CS with K=4 Ideal with K=4 (without clustering) Ideal with K=4 Codebook with K=2 CS with K=2 Ideal with K=2 (without clustering) Ideal with K=2 Codebook with K=1 CS with K=1 Ideal with K=1 (without clustering) Ideal with K=1

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3635 Yongjie Li and Rongfang Song / Procedia Engineering 29 (2012) 3631 – 3635Yongjie Li.et.al / Procedia Engineering 00 (2011) 000–000 5

In (a) of Fig. 3, we plot the throughput with different transmit modes as a function of feedback rate without clustering. Here, the transmit mode can be explained as the number of active users which communicate with base station. The number of active users K can be assumed 1, 2 or 4. From (a), we can see that the throughput that can be achieved with the maximum mode K =4 is the best under ideal CSI and the throughput with K =2 is following. The throughput with single user mode is the worst. With alternate CSI available at the transmitter, it is not true that one transmission strategy always dominates the other. The throughput performance of codebook based method with different transmit modes in (a) provides the powerful evidence. From (a), we also can see that the throughputs of CS method outperform codebook-based method with the same feedback rate under the same transmit mode. (b) shows the feedback rate of CSI feedback and the corresponding achievable throughput with cluster size 4. From (b), we can see that the gap between the ideal CSIT without clustering and cluster=4 is bigger with the increase of transmit mode. We can also see that one transmission strategy always dominates the other is not true with CS method when feedback rate is smaller than 1 bits/subcarrier. But CS method is superior to codebook method with the same transmit mode.

5. Conclusions

In this work, CS is proposed to apply to compression of CSI feedback for multi-user MIMO OFDM systems so as to reduce feedback overhead and provide accurate CSIT to obtain high system throughput. It exploits the fact that the channel coefficient at a certain frequency is highly correlated with the channel coefficient at a neighboring frequency. Simulation results show the effectiveness of the proposed method. With the same feedback rate, the throughputs with CS method outperform the codebook based method which is usually employed in most situations.

Acknowledgements

This work was supported by National Natural Science Foundation of China (60972041); Open Research Foundation of National Mobile Communications Research Laboratory, Southeast University(N200809); Natural Science Fundamental Research Program of Jiangsu Universities (08KJD510001); PH.D. Program Foundation of Ministry of Education (200802930004); National Special Project (2009ZX03003-006); National Basic Research Program of China (2007CB310607) and Graduate Innovation Program (CX10B_186Z).

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