Abstract — This paper investigates the joint design and optimization of the power control and beamforming codebooks for the single-user multiple-input single-output (MISO) wireless systems with a rate-limited feedback link. The problem is cast in the form of minimizing the outage probability subject to the transmit power constraint and cardinality constraints on the beamforming and power codebooks. We show that by appropriately choosing and fixing the beamforming codebook and optimizing the power codebook for that beamforming codebook, it is possible to achieve a performance very close to the optimal joint optimization. Further, this paper investigates the optimal tradeoffs between beamforming and power codebook sizes for different number of feedback bits and transmit antennas. Given a target outage probability, our results provide the optimal codebook sizes independent of the target rate. As the outage probability decreases, we show that the optimal joint design should use fewer feedback bits for beamforming and more feedback bits for power control. The jointly optimized beamforming and power control modules combine the power gain of beamforming and diversity gain of power control, which enable it to approach the performance of the system with perfect channel state information as the feedback link capacity increases to infinity — something that is not possible with beamforming or power control alone. I.

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 — This paper addresses the performance of bitinterleaved coded multiple beamforming (BICMB) with imperfect knowledge of beamforming vectors. Various wireless standards become equivalent to BICMB when they are operated in beamforming mode. In BICMB, the invariance of the precoding matrix under an arbitrary unitary transform widely studied in the literature is not applicable. On the other hand, the optimum precoder and detector are not unique because of invariance under a diagonal unitary transform. We propose an optimal Euclidean distortion measure and a new linear detector. In addition, a new codebook design is proposed via the generalized Lloyd algorithm based on the new distortion measure. We provide simulation results demonstrating the performance improvement achieved with the proposed distortion measure and the linear detector. I.

Abstract—A point-to-point multiantenna wireless channel is considered. Based on channel information, a receiver selects a transmit beamforming vector, which contains transmit antenna gains, from a vector set or codebook. The codebook index for the selected beamforming vector that maximizes channel capacity is relayed to the transmitter via a rate-limited feedback channel. Previously, we have proposed a Random Vector Quantization (RVQ) codebook, which consists of independent isotropically distributed vectors and showed that it performs close to the optimal codebook. However, RVQ requires exhaustive search to locate the desired beamformer. To lessen the search complexity, we propose a tree-structured (TS) RVQ. Numerical results show that number of computations required for TS-RVQ search can be orders of magnitude fewer than that required for RVQ search for given performance. I.

Abstract-It is well-known that perfect channel state information (CSI) at the transmitter and the receiver (CSIT/CSIR) can be used to decompose a multi-antenna channel into a bank of parallel channels. While perfect CSIR maybe a reasonable assumption for practical systems, perfect CSIT is generally difficult to achieve. Recent attention in communication systems design has thus shifted towards limited feedback schemes where partial CSI is fed back from the receiver to the transmitter. In this work, we consider a precoding scheme which excites a subset of the transmit dimensions with independent data. The main focus is on systematic quantized precoder designs that bridge the gap between statistical precoding and perfect CSIT precoding in spatially correlated channels. In this work, we propose an asymptotic perturbation theory-inspired codebook design obtained from a quantization of the local neighborhood around the statistically dominant precoding direction(s). This design is implemented in practice by maps that can rotate and shrink sets on the Grassmannian manifold. Numerical results show substantial gains can be achieved with the proposed design over statistical precoding. Index Terms-Diversity, limited feedback, MIMO systems, multiplexing, precoding I.

In multiuser wireless radio systems, it may be possible to increase throughput by reducing the feedback-rate of channel quality data while meeting quality of service requirements. By Thomas Eriksson and Tony Ottosson ABSTRACT | For wireless systems with adaptive modulation and/or scheduling, feedback of channel quality information is often necessary. It has been questioned whether the increased system performance is worth the additional feedback rate and the increased algorithm complexity. In this paper, we study how the feedback rate can be minimized, without losing the gains due to adaptive modulation and multiuser diversity. We present an in-depth study of the literature in the area, and evaluate the performance of several state-of-the-art channel quality feedback schemes. By illustrating the compromise between system throughput and feedback channel rate for various schemes, we are able to give valuable insight in choice of method for feedback rate reduction. A major conclusion is that for multicarrier systems, a lossy compression scheme is the best choice, while for single-carrier systems, schemes limiting feedback to only high-SNR users show good performance. Another conclusion is that there are still many issues to study before the schemes can be used in practice.

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Abstract—Signature quantization for reverse-link Direct Sequence (DS)- Code Division Multiple Access (CDMA) is considered. A receiver assumed to have perfect estimates of channel and interference covariance, 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 relayed to the user with finite number of bits via a feedback channel. Previously, it was shown 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. Here we derive exact expressions for a large system SINR for the user whose signature is selected from RVQ codebook. We assume that the receiver is linear minimum mean squared error (MMSE) and consider both ideal and multipath fading channels. I.

For a point-to-point multi-input multi-output (MIMO) wireless channel, we propose a feedback scheme, which consists of transmit-antenna selection algorithm and beamforming quantization. A feedback, which is relayed from a receiver to a transmitter via a feedback channel, specifies a set of active transmit antennas and associated beamforming vector, which contains transmit antenna coefficients. Assuming perfect channel knowledge, the receiver selects the set of transmit antennas that maximizes the largest eigenvalue of a channel covariance matrix and then, chooses the beamforming vector that maximizes the capacity, from a random vector quantization (RVQ) codebook. Entries in the RVQ codebook are independent isotropically distributed and was previously shown to perform close to the optimum. We derive

Abstract—We propose a quantization scheme based on a Kd (K dimensional)-tree algorithm for signature sequence in a reverselink direct sequence (DS)- code division multiple access (CDMA). With a few feedback bits, a receiver quantizes the optimal signature that minimizes interference for a desired user, and relays it to the user via an error-free feedback channel. A user performance depends on the quantization codebook and a number of feedback bits. We show the performance of the proposed Kd-tree codebook with a nearest neighbor criterion and derive the performance approximation. Also we modify the Kd-tree scheme to search for the entry in the codebook, which gives the least interference. Numerical examples show that the Kd-tree codebook performs close to the optimal codebook with only fraction of computational complexity. I.