Abstract — We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into � streams that are simultaneously transmitted using � transmit antennas. The received signal at each receive antenna is a linear superposition of the � transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2–3 dB of the outage capacity for these channels using only 64 state encoders.

Abstract — This paper presents a simple two-branch transmit diversity scheme. Using two transmit antennas and one receive antenna the scheme provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit antenna, and two receive antennas. It is also shown that the scheme may easily be generalized to two transmit antennas and M receive antennas to provide a diversity order of 2M. The new scheme does not require any bandwidth expansion any feedback from the receiver to the transmitter and its computation complexity is similar to MRRC. Index Terms—Antenna array processing, baseband processing, diversity, estimation and detection, fade mitigation, maximalratio combining, Rayleigh fading, smart antennas, space block coding, space–time coding, transmit diversity, wireless communications. I.

Abstract — We introduce space–time block coding, a new paradigm for communication over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space–time block code and the encoded data is split into � streams which are simultaneously transmitted using � transmit antennas. The received signal at each receive antenna is a linear superposition of the � transmitted signals perturbed by noise. Maximumlikelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space–time block code and gives a maximum-likelihood decoding algorithm which is based only on linear processing at the receiver. Space–time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm. The classical mathematical framework of orthogonal designs is applied to construct space–time block codes. It is shown that space–time block codes constructed in this way only exist for few sporadic values of �. Subsequently, a generalization of orthogonal designs is shown to provide space–time block codes for both real and complex constellations for any number of transmit antennas. These codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For an arbitrary complex constellation such as PSK and QAM, space–time block codes are designed that achieve IaP of the maximum possible transmission rate for any number of transmit antennas. For the specific cases of two, three, and four transmit antennas, space–time block codes are designed that achieve, respectively, all, QaR, and QaR of maximum possible transmission rate using arbitrary complex constellations. The best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well. Index Terms — Codes, diversity, multipath channels, multiple antennas, wireless communication.

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Multiple-antenna systems that operate at high rates require simple yet effective space-time transmission schemes to handle the large traffic volume in real time. At rates of tens of bits/sec/Hz, V-BLAST, where every antenna transmits its own independent substream of data, has been shown to have good performance and simple encoding and decoding. Yet V-BLAST suffers from its inability to work with fewer receive antennas than transmit antennas---this deficiency is especially important for modern cellular systems where a basestation typically has more antennas than the mobile handsets. Furthermore, because V-BLAST transmits independent data streams on its antennas there is no built-in spatial coding to guard against deep fades from any given transmit antenna. On the other hand, there are many previously-proposed space-time codes that have good fading resistance and simple decoding, but these codes generally have poor performance at high data rates or with many antennas. We propose a high-rate coding scheme that can handle any...

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

Motivated by information-theoretic considerations, we propose a signalling scheme, unitary space-time modulation, for multiple-antenna communication links. This modulation is ideally suited for Rayleigh fast-fading environments, since it does not require the receiver to know or learn the propagation coefficients. Unitary space-time modulation uses constellations of T \cross M space-time signals {\Phi_l, l= 1,...L},where T represents the coherence interval during which the fading is approximately constant, and M > M . We design some multiple-antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding. We demonstrate that two antennas have a 6-dB diversity gain over one antenna at 15-db SNR.

We derive performance limits for two closely related communication scenarios involving a wireless system with multiple-element transmitter antenna arrays: a point-to-point system with partial side information at the transmitter, and a broadcast system with multiple receivers. In both cases, ideal beamforming is impossible, leading to an inherently lower achievable performance as the quality of the side information degrades or as the number of receivers increases. Expected signal-tonoise ratio (SNR) and mutual information are both considered as performance measures. In the point-to-point case, we determine when the transmission strategy should use some form of beamforming and when it should not. We also show that, when properly chosen, even a small amount of side information can be quite valuable. For the broadcast scenario with an SNR criterion, we find the efficient frontier of operating points and show that even when the number of receivers is larger than the number of antenna array ...

Several aspects of the design and optimization of coded multiple-antenna transmission diversity methods for slowly time-varying channels are explored from an information-theoretic perspective. Both optimized vector-coded systems, which can achieve the maximum possible performance, and suboptimal scalar-coded systems, which reduce complexity by exploiting suitably designed linear precoding, are investigated. The achievable rates and associated outage characteristics of these spatial diversity schemes are evaluated and compared, both for the case when temporal diversity is being jointly exploited and for the case when it is not. Complexity and implementation issues more generally are also discussed.

Abstract—This paper treats multiple-input multiple-output (MIMO) antenna subset selection employing space-time coding. We consider two cases differentiated based on the type of channel knowledge used in the selection process. We address both the selection algorithms and the performance analysis. We first consider the case when the antenna subsets are selected based on exact channel knowledge (ECK). Our results assume the transmission of orthogonal space-time block codes (with emphasis on the Alamouti code). Next, we treat the case of antenna subset selection when statistical channel knowledge (SCK) is employed by the selection algorithm. This analysis is applicable to general space-time coding schemes. When ECK is available, we show that the selection algorithm chooses the antenna set that maximizes the channel Frobenius norm leading to both coding and diversity gain. When SCK is available, the selection algorithm chooses the antenna set that maximizes the determinant of the covariance of the vectorized channel leading mostly to a coding gain. In case of ECK-based selection, we provide analytical expressions for average SNR and outage probability improvement. For the case when SCK-based selection is used, we derive expressions for coding gain. We also present extensive simulation studies, validating our results. Index Terms—Antenna subset selection, MIMO, space-time coding.