Hybrid Transform Coding for Channel State Information in MIMO-OFDM Systems Yong-Ping Zhang * , Peng Wang † , Qiang Li * , and Philipp Zhang ‡ * Research Department of Hisilicon, Huawei Technologies Co., Ltd, Beijing, P. R. China, † Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China ‡ Research Department of Hisilicon, Huawei Technologies Co., Ltd, Plano, Texas, USA, Emails: zhangyongping79@huawei.com, pengwang@cityu.edu.hk, johnlee@huawei.com, pzhang@huawei.com Abstract—This paper is concerned with the efficient feedback of the channel state information (CSI) in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. A hybrid transform coding (HTC) scheme is proposed by exploiting the frequency and time correlation of CSI. An upper bound for the overhead-distortion performance of HTC is derived. Numerical results show that, compared with the available alternatives, the HTC scheme can achieve higher compression efficiency. Keywords—feedback, channel state information (CSI), multiple-input multiple-output (MIMO), orthogonal frequency division multiplexing (OFDM), hybrid transform coding (HTC) I. INTRODUCTION Orthogonal frequency division multiplexing (OFDM) [1][2] and multiple-input multiple-output (MIMO) [3][4] are two promising techniques for the high speed transmission in wireless channels. These two techniques can provide fold capacity increase by exploiting, respectively, the frequency diversity and spatial diversity in frequency selective channels. They have been adopted in current and next generation wireless standards such as IEEE 802.16 [5] and Long-Term Evolution (LTE) [6]. The feedback channel state information (CSI) from user equipments (UEs) plays an important role in the downlink of MIMO-OFDM systems operating in frequency-division duplex (FDD) mode. With CSI at the base station (BS), the system performance can be significantly improved by adaptively customizing the transmitted waveforms to the channel, enabling channel-aware scheduling for multiple users, and so on. However, the overhead of the feedback CSI that guarantees an acceptable CSI accuracy at the BS is always a serious concern due to the limited bandwidth of feedback links. Hence feedback schemes with high compression efficiency are in demand. In [7][8], Ericsson and DOCOMO propose a sclar compression technique by directly quantizing each element of the frequency-domain channel matrix at the UE. This technique, though incurs minor quantization errors, can reduce the overhead of CSI. However, it doesnot exploit the correlation of CSI in either the frequency or time domain and so the corresponding compression efficiency is not high. In [8], DOCOMO proposes a vector compression technique, where each row of the channel matrix is quantized by a pre-determined Grassmanian codebook known at both the UE and BS. Only the quantization index is sent to the BS for CSI reconstruction. This method can improve the compression efficiency but involves complicated quantization process. Qualcomm [9] proposes a compression technique based on multiple descriptions coding (MDC). In this technique, the CSI at different time instances is compressed by different codebooks with the same statistical properties. Compared to single codebook compression schemes with the same compression ratio, it can improve the feedback accuracy with a little more implementation cost. This method exploits the time-domain correlation of the channel but doesnot consider the frequency-domain correlation. Currently, how to improve the compression efficiency by exploiting the correlation in both the time and frequency domains at the same time still remains an open problem. In this paper, we propose a novel compression scheme for the CSI of MIMO-OFDM systems. This scheme is referred to as hybrid transform coding (HTC). There are two compression options in HTC, i.e., direct coding and differential coding. The former exploits the correlation of CSI in the frequency domain by quantizing and coding in the time domain. The latter further exploits the correlation of CSI in the time domain by using the reconstructed CSI at one previous OFDM symbol as a reference for the CSI compression of the current OFDM symbol. Only the residual between the reference CSI and the current CSI is quantized and coded in the same way as that in direct coding. Numerical results show that HTC has significantly higher compression efficiency compared with the available alternatives. II. PRELIMINARIES Consider an MIMO-OFDM system with K subcarriers, a BS with N antennas and a UE with M antennas. The overall downlink frequency-domain CSI at the s-th OFDM symbol is a three-dimensional matrix, i.e., ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ = - - - - - - ) ( 1 , 1 ) ( 1 , 1 ) ( 0 , 1 ) ( 1 , 1 ) ( 1 , 1 ) ( 0 , 1 ) ( 1 , 0 ) ( 1 , 0 ) ( 0 , 0 ) ( s N M s M s M s N s s s N s s s H H H H H H H H H H A B D B B A A (1) 978-1-61284-231-8/11/$26.00 ©2011 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings