Naresh Sharma

A study of opportunism for multiple-antenna systems

Recently proposed opportunistic beamforming exploits the multiuser diversity to reduce the feedback by not requiring the precoding information used for closed-loop schemes to be known at the transmitter. Opportunism could also be beneficially employed for other multiple-antenna transmission techniques like cophasing and antenna selection. For opportunistic beamforming and antenna selection, we give closed-form expressions for throughput that closely approximate the performance of these schemes with a Proportionally Fair scheduler (PFS) at low signal-to-noise ratios (SNRs). For large number of transmit antennas, opportunistic cophasing has similar performance as opportunistic beamforming. Asymptotic dependence of the required number of users to achieve the gains of opportunism on the number of transmit antennas is exponential for opportunistic beamforming (and cophasing for large numbers of transmit antennas), and at best linear for opportunistic antenna selection. For multiple-antenna receivers, we additionally examine an opportunistic multiple-input multiple-output (MIMO) scheme that transmits multiple data streams simultaneously to the same user.

Full-rate full-diversity linear quasi-orthogonal space-time codes for any number of transmit antennas

We construct a class of linear quasi-orthogonal space-time block codes that achieve full diversity over quasistatic fading channels for any transmit antennas. These codes achieve a normalized rate of one symbol per channel use. Constellation rotation is shown to be necessary for the full-diversity feature of these codes. When the number of transmit antennas is a power of 2, these codes are also delay optimal. The quasi-orthogonal property of the code makes one half of the symbols orthogonal to the other half, and we show that this allows each half to be decoded separately without any loss of performance. We give an iterative construction of these codes with a practical decoding algorithm. Numerical simulations are presented to evaluate the performance of these codes in terms of capacity as well as probability of error versus SNR curves. For some special cases, we compute the pairwise probability of error averaged over all the channel states as a single integral that shows the diversity and coding gain more clearly.

Improved quasi-orthogonal codes

Orthogonal codes are a class of space-time block codes that achieve full diversity, though at a loss of code rate. Such codes have simple single-symbol decoders. The code rate can be made higher by constructing quasi-orthogonal codes, which trade a small loss of performance for full rate coding. Typically, quasi-orthogonal codes perform the best when joint maximum likelihood (ML) decoding is used within subsets of the space-time codewords that are mutually orthogonal. We show that for a particular class of quasi-orthogonal codes, the interference which the subset of the symbols to be jointly decoded sees from other symbols is such that the signal to interference ratio remains constant for all channel realizations. Using the same constellation for all symbols in the subset reduces the minimum distance for such codes and results in a loss of performance. As a remedy to this problem, we introduce a rotation-based method that aims at maximizing the minimum distance in the space-time constellation. Numerical simulations show that significant improvements to previously reported results without rotation can be attained.

Improved quasi-orthogonal codes through constellation rotation

Orthogonal codes are a class of space-time block codes that achieve full diversity gain, though typically at a loss of code rate. Such codes have simple single-symbol decoders. The code rate can be made higher by constructing quasi-orthogonal codes (such as those proposed last year in [1], [2]) which trade a small loss of performance for full rate coding. In this paper, which builds on previous work in [1], we propose a novel rotation technique for improving the performance of quasi-orthogonal codes in terms of bit-error rate (BER). Numerical simulations show that significant improvements to previously reported results without rotation can be attained.

Reduced-complexity ML decoding of rate 6/8 and rate 1 linear complex space-time codes for up to eight transmit antennas with phase feedback

It is shown that single symbol maximum-likelihood (ML) decoding for chosen rate 6/8 linear complex space-time codes for up to eight transmit antennas is possible in the presence of a phase feedback. The performance of the code is the same as that of an ideal code, for which the sufficient statistic of the channel is its Frobenius norm. For rate 1 codes for up to eight antennas, a two-phase feedback enables a symbol to see the interference from only one symbol instead of three, thereby reducing the complexity of ML decoding. Quantization of the feedback is also considered.

MIMO channel statistics in the presence of non-uniform angle spread

We give analytical expressions for correlation, spectrum, level crossing rate, and average fade duration for the multiple-antenna fading channel in the presence of nonuniform power azimuth spectrum (PAS). Classical expressions for uniform PAS are a special case of these expressions. The expressions are valid for any antenna patterns and for any PAS.

Per antenna/stream union bound as a channel quality indicator for MIMO systems

We address the issue of rate allocation for layered coded MIMO (multiple input multiple output) systems for a given flat fading channel with APP (a posteriori probability) decoding. Transmission parameters for a given MIMO channel are found using per antenna/stream union bound that enables one to find the SNR (signal to noise ratio) of an equivalent AWGN (additive white Gaussian noise) channel for each transmit antenna/stream. Comparison with the ergodic Shannon capacity is made for some example rate controlled systems.