IEICE TRANS. COMMUN., VOL.E95–B, NO.2 FEBRUARY 2012 655 LETTER Antenna Selection SFN Precoding Scheme for Downlink Cooperative MIMO Systems ∗ Ming DING †,†† a) , Student Member, Jun ZOU † , Zeng YANG †† , and Hanwen LUO † , Nonmembers SUMMARY In this letter, we propose an antenna selection single fre- quency network precoding (AS-SFNP) scheme for downlink cooperative multiple-input multiple-output (MIMO) systems, which efficiently im- proves system capacity with low feedback overhead and low complexity. key words: cooperative MIMO, antenna selection, precoding 1. Introduction Recently, there has been considerable interest in cooperative multiple-input multiple-output (MIMO) systems, where the data intended for a user equipment (UE) is simultaneously transmitted from multiple base stations (BSs). In [1], the authors investigated cooperative MIMO as a means to miti- gate co-channel interference and to exploit macro-diversity for the Wyner’s model and its variants. Moreover, cooper- ative MIMO technologies have been adopted by 4G mobile communication standards [2]. Although the large theoretical gain in spectral effi- ciency promised by cooperative MIMO transmissions can be achieved by performing global precoding (GP) across multiple BSs, this approach significantly increases com- plexity and feedback overhead [3]. This has motivated re- searches into simpler precoding schemes with low feed- back overhead, such as the weighted local precoding (WLP) scheme in which each BS computes its precoder based on the local channel state information [4]. In [5], we proposed a novel antenna selection single frequency network precod- ing scheme (AS-SFNP), in which smart antenna selection (AS) is performed at BSs and identical precoders are em- ployed at all cooperating BSs. In this letter, we investigate the performance of sev- eral precoding schemes. For single-antenna UEs, both an- alytical lower bounds and simulation results are provided to show that the proposed AS-SFNP scheme and the WLP scheme achieve performance close to that of the optimal global precoding (GP) scheme in terms of average signal- to-interference-plus-noise ratio (SINR). For multi-antenna Manuscript received June 28, 2011. Manuscript revised October 8, 2011. † The authors are with School of Electronic, Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. †† The authors are with Sharp Laboratories of China Co., Ltd., China. ∗ This work was sponsored by Sharp Laboratories of China Co., Ltd. a) E-mail: dm2007@sjtu.edu.cn; ming.ding@cn.sharp-world.com DOI: 10.1587/transcom.E95.B.655 UEs, simulation results demonstrate the AS-SFNP scheme with a lower load of feedback overhead can still achieve ca- pacity gain compared with the WLP scheme. Notations:(·) T ,(·) H , det(·), tr(·) and {·} L stand for the transpose, conjugate transpose, determinant, trace and L right singular vectors with respect to the L largest singu- lar values of a matrix, respectively. ε{·} is the expectation operator. χ 2 (n, σ 2 ) represents the probability density func- tion (PDF) of a chi-square-distributed random variable (RV) with n degrees of freedom, and the variance of each degree is σ 2 . |a| and a(i) denote the Euclidean norm and the i-th element of a vector a, respectively. I N stands for an N × N identity matrix. 2. Precoding Schemes and SINR Analysis We consider a uniform downlink cooperative MIMO sce- nario, where there are B cooperative BSs and each BS has N T transmit antennas. The data for the target UE equipped with N R antennas is transmitted simultaneously from all B BSs. The channel between BS b ∈{1, 2,..., B} and the UE is denoted as H b ∈ C N R ×N T . The UE can report its precod- ing matrix information either to each individual cooperative BS or to one primary BS. In the latter case, the primary BS can exchange this information amongst cooperating BSs through the backhaul links. Let W b ∈ C N T ×L be the local precoding matrix at BS b, where L is the number of data streams. The received signal at UE can be described as y = [H 1 , H 2 , ··· , H B ] ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ W 1 W 2 . . . W B ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ x + n, (1) where x ∈ C L×1 is the transmission data with covariance ma- trix I L and n is an additive zero-mean circularly symmetric complex Gaussian (ZMCSCG) noise vector with ε  nn H  = N 0 I N R . To simplify the analysis, we treat the interference from outside of the B BSs as white Gaussian signals, which has been incorporated into n. We denote per-BS power- noise ratio by γ = P/N 0 , where P is the maximum trans- mission power at each BS. 2.1 The GP Scheme The GP scheme can be viewed as a generalization of Copyright c  2012 The Institute of Electronics, Information and Communication Engineers