Ef ficient Quantization for Feedback in MIMO Broadcasting Systems Charles Swannack, Gregory W. Wornell Dept. EECS, MIT Cambridge MA 02139 Email: {swannack,gww}@mit.edu Elif Uysal-Biyikoglu Dept. ECE, Ohio State University Columbus, OH 43210 Email: elif@ece.osu.edu Abstract— We consider the problem of joint multiplexer-scheduler design for transmitting independent data streams over a Gaussian multiple-antenna broadcast channel in which feedback is used to convey channel state information from receivers to the transmit- ter. It is known that various low complexity strategies can achieve the optimal rate scaling as a function of receiver population size. In this work we develop a simple and efficient quantization strategy for use on the feedback link of such architectures. I. I NTRODUCTION AND BACKGROUND There is growing interest in the development of efficient wireless broadcast systems for distributing independent data streams to different users over some geographical area. It is now widely appreciated that the use of a multiple-element antenna array at the transmitter can, in principle, greatly increase the capacity of such systems. When the number of users is no larger than the array size, the system design issues are rather well-understood. Moreover, when it is desirable for complexity or other reasons to restrict one’s attention to case of linear multiplexing, the literature characterizing the associated performance tradeoffs is particularly extensive. Recent approaches to this scheduling problem have exam- ined the scaling behavior of the multiple-antenna broadcast channel in the large user limit with perfect channel channel state information [1]–[4] using various interference cancelling multiplexers and complexity constraints [2], [3], [5]. Here, we provide a simple architecture for scheduling over the Gaussian MIMO broadcast channel with quantized feedback. We have shown [6] the achieved rate of this architecture asymptotically equals that of the best multiplexer and scheduler. This was done by showing that there exists a group of users equal of size equal to the transmit dimension in which the mutual interference is negligible. In this paper we present a simple quantization scheme and show that good performance can be achieved when the number of users is only a small multiple of the user population. The single user version of the problem was discussed in [7]. We examine the effects of choosing groups of various sizes for a large user pool. II. CHANNEL AND SYSTEM MODEL The system of interest consists of an m-element transmitter antenna array and a pool of n destinations (users). The transmitter has n collections of messages, each such collection destined for one of the n users. The collections are infinite in size, corresponding to an infinite backlog. This work was supported in part by NSF under Grant No. CNS-0434974, Mitre Corporation, and by HP through the MIT/HP Alliance. Our discrete-time channel model is a narrowband block fading one. Specifically, in any particular block, the signal y j (k) received by user j at time k in response to a signal x(k) transmitted from the array is of the form y j (k)= h † j x(k)+ z j (k) (1) where z j (k) is independent identically distributed (i.i.d.) CN(0, 1) noise, and where the (normalized) channel gain vectors h j have i.i.d. CN(0, 1/2m) elements. The noises and channel gains are independent from receiver to receiver, and from block to block. Any message scheduled for delivery is transmitted within one block, and the blocks are long so that messages can be reliably received. Thus each block corresponds to a new signaling (and hence scheduling) interval. Within each sig- naling interval, the transmitter sends from its array a group of messages, one for each of a subset of the user pool. The transmitter is subject to an average total power constraint of P , i.e., E  ‖x‖ 2  ≤ P within each signaling interval. We will let R(H A ) be the achievable rate for the user set A under this power constraint. In our model, channel gains in each signaling interval are known perfectly (i.e., measured to arbitrary accuracy) at the respective receivers at the beginning of each such interval. Moreover, a feedback link exists by which individual users can inform the transmitter of their channel gains (or more generally quantized versions thereof), also at the beginning of each associated signaling interval. The users do not know each other’s channel gains, nor are they able to more generally share information between each other. Finally, the performance criterion of interest in this work is average throughput (i.e., expected sum-rate), and our focus is on the small n regime (with m fixed). III. SYSTEM AND PROTOCOL ARCHITECTURE The architecture of interest is as illustrated in Fig. 1. The protocol is identical in each signaling interval, so we restrict our attention to a single arbitrary one. In such an interval, a subset R of users from the full population U sends a quantized representation of their respective channel gain vectors to the transmitter over the feedback link. The associated quantization codebook C is fixed and the same for all users. Its structure is such that the codewords c ∈ C all lie on the unit sphere in m (complex) dimensions, and the quantization rule corresponds to ˆ h j = arg max c∈C   c † h j   , (2) 784 1424407850/06/$20.00