Krishna Kiran Mukkavilli

On beamforming with finite rate feedback in multiple-antenna systems

We study a multiple-antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t-1)2/sup -B/t-1/, where B is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook, and is equivalent to the problem of designing unitary space-time codes under certain conditions. Finally, we show that good beamformers are good packings of two-dimensional subspaces in a 2t-dimensional real Grassmannian manifold with chordal distance as the metric.

Improved 8- and 16-state space-time codes for 4PSK with two transmit antennas

New space-time codes for 4PSK constellations, designed via a modified determinant criterion, send 2 b/s/Hz and show improved performance in quasi-static flat fading.

Design of multiple antenna coding schemes with channel feedback

We derive multiple antenna transmission strategies in the presence of limited channel information at the transmitter and the receiver. In, particular, we look at the cases of complete channel information, channel phase information and channel amplitude information at the transmitter. We highlight that transmission along the eigenvector of the channel corresponding to the maximum eigenvalue minimizes error probability, when complete channel information is available at the transmitter. In the case where only the channel phase information is available at the transmitter, we derive the beamformer which minimizes the error probability. We also show that, in the presence of channel amplitude information at the transmitter without any phase information, selection diversity at the transmitter is the best beamforming strategy. We evaluate the penalty in SNR incurred by the transmission schemes in the case of limited channel information compared to the case of complete channel information at the transmitter.

Generalized beamforming for MIMO systems with limited transmitter information

In this work, we investigate the outage performance of beamforming schemes in wireless systems equipped with multiple transmit and receive antennas. In particular, we analyze the outage performance of unit rank beamforming in the presence of finite rate channel feedback at the transmitter. Further, we present finite size beamformer codebook constructions which result in near-optimal outage performance for unit rank beamforming. The constructions obtained for the unit rank beamforming scheme are then extended to higher rank beamforming schemes with quantized channel information. We show that significant performance improvements as well as reduction in decoding complexity can result from a small number of feedback bits.

Performance limits on beamforming with finite rate feedback for multiple antenna systems

In this work, we address the problem of evaluating the outage performance of beamformers designed for multiple transmit and single receive antenna systems when quantized channel state information is available at the transmitter. We present a tight universal lower bound for the outage probability of an arbitrary beamformer codebook consisting of a finite number of beamforming vectors. We also characterized the loss in outage performance due to the quantized nature of the channel information available at the transmitter. In particular, we show that the outage probability of beamforming based on quantized channel information approaches the performance of perfect information beamforming as (t-1)2/sup -B/(t-1)/, where B is the number of bits used to quantize the vector channel and t is the number of transmit antennas.

Design of space-time codes with optimal coding gain

Space time codes have been proposed in the literature as an efficient means for improving the data rates over fading channels with multiple transmit antennas. In particular, the rank and the determinant of code difference matrices have been shown to be important in the design of space time codes for fading channels. In the present work, we investigate the problem of maximizing the coding gain of space-time codes, given by the minimum of the determinants of all the code difference matrices. We rely on equality of the singular values of the code difference matrices as a necessary and sufficient condition for obtaining the optimal coding gain. Finally, we discuss the construction of trellis codes and present simulation results.

Beamformer design with feedback rate constraints: criteria and constructions

This paper describes the design of beamformers when finite rate channel feedback is available in a multiple transmit antenna system. This paper also discusses a geometrical framework for the analysis and design criterion of beamformer codebooks construction with finite number of beam-former vectors to minimize the outage probability.

On the outage probability of a class of signaling schemes for multiple antennas

The concept of outage probability is appropriate for delay-constrained transmission over quasi-static channels since it serves as a useful lower bound for the frame error probability. In this work, we characterize a rich class of schemes, each member of which exhibits an identical asymptotic (in SNR) outage probability decay, given by maximum spatial diversity available in the system. The class includes several commonly used spatial power allocation and beamforming schemes, derived for varying amount of channel information at the transmitter and the receiver.