Abstract — We examine the capacity of beamforming over a block Rayleigh fading Multi-Input/Multi-Output (MIMO) channel with finite training for channel estimation and limited feedback. A fixed-length packet is assumed, which is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error (MMSE) estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2 B i.i.d. random vectors, and relays the corresponding B-bit index back to the transmitter. We derive bounds on the large system capacity, i.e., as the number of transmit antennas Nt → ∞ and receive antennas Nr → ∞ with fixed ratio Nt/Nr. The bounds are used to show that the optimal T, which maximizes the capacity, increases as Nt / log Nt, whereas the optimal B increases as Nt / log 2 Nt. I.

Abstract — We consider a MIMO fading broadcast channel where channel state information is acquired at user terminals via downlink training and explicit analog feedback is used to provide transmitter channel state information (CSIT) to the base station. The feedback channel (the corresponding uplink) is modeled as a MIMO multiple access channel. Under the assumption that data transmission, downlink training, and feedback are performed within the same channel coherence interval of length T symbols, the optimization of a lower bound on the achievable ergodic rate sum yields a non-trivial resource allocation tradeoff. We solve this tradeoff and provide the optimal training and feedback resource allocation for the case of zero-forcing beamforming. When the same power level is used during all stages, it is found that the optimal length of the training + feedback phases increases as O ( √ T) for large T. On the other hand, when different power levels can be used for different stages, for sufficiently large T it is optimal to use the minimum number of symbols for training + feedback but to use power of order O ( √ T). I.

We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over time-frequency blocks that span a coherent time × a coherence bandwidth. In closed-loop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base station and an explicit feedback from each user terminal. In open-loop systems, CSIT is obtained by exploiting uplink training and channel reciprocity. We use a tight closed-form lower bound on the ergodic achievable rate in the presence of CSIT errors in order to optimize the overall system throughput, by taking explicitly into account the overhead due to channel estimation and channel state feedback. Based on three time-frequency block models inspired by actual systems, we provide some useful guidelines for the overall system optimization. In particular, digital (quantized) feedback is found to offer a substantial advantage over analog (unquantized) feedback.

In this paper, we analyze the performance of a signature quantization scheme for reverse-link Direct Sequence (DS)- Code Division Multiple Access (CDMA). Assuming perfect estimates of channel and interference covariance, the receiver selects the signature that maximizes signal-to-interference plus noise ratio (SINR) for a desired user from a signature codebook. The codebook index corresponding to the optimal signature is then relayed to the user with finite number of bits via a feedback channel. Previously, we showed that a Random Vector Quantization (RVQ) codebook, which contains independent isotropically distributed vectors, is optimal (i.e., maximizes SINR) in a large system limit in which number of interfering users, processing gain, and feedback bits tend to infinity with fixed ratios. Dai et al. have analyzed the large system SINR for a matched filter with nonfading channel. Here we extend the results to linear minimum mean squared error (MMSE) receiver and multipath fading channel. Numerical examples show that the derived large system results give a good approximation to the performance of finite-size system. Index Terms Random Vector Quantization, large system limit, signature quantization, limited feedback, multipath