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.

Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. In this paper, we propose the point of view that both types of gains can be simultaneously obtained for a given multiple antenna channel, but there is a fundamental tradeo# between how much of each any coding scheme can get. For the richly scattered Rayleigh fading channel, we give a simple characterization of the optimal tradeo# curve and use it to evaluate the performance of existing multiple antenna schemes.

Multiuser diversity is a form of diversity inherent in a wireless network, provided by independent time-varying channels across the different users. The diversity benefit is exploited by tracking the channel fluctuations of the users and scheduling transmissions to users when their instantaneous channel quality is near the peak. The diversity gain increases with the dynamic range of the fluctuations and is thus limited in environments with little scattering and/or slow fading. In such environments, we propose the use of multiple transmit antennas to induce large and fast channel fluctuations so that multiuser diversity can still be exploited. The scheme can be interpreted as opportunistic beamforming and we show that true beamforming gains can be achieved when there are sufficient users, even though very limited channel feedback is needed. Furthermore, in a cellular system, the scheme plays an additional role of opportunistic nulling of the interference created on users of adjacent cells. We discuss the design implications of implementing this scheme in a complete wireless system.

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...

It has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space–time block code is not possible for more than two antennas. Previous attempts have been concentrated in generalizing orthogonal designs which provide space–time block codes with full diversity and a high transmission rate. In this work, we design rate one codes which are quasi-orthogonal and provide partial diversity. The decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols.

Cooperative diversity has been recently proposed as a way to form virtual antenna arrays that provide dramatic gains in slow fading wireless environments. However, most of the proposed solutions require distributed space–time coding algorithms, the careful design of which is left for future investigation if there is more than one cooperative relay. We propose a novel scheme that alleviates these problems and provides diversity gains on the order of the number of relays in the network. Our scheme first selects the best relay from a set of available relays and then uses this “best ” relay for cooperation between the source and the destination. We develop and analyze a distributed method to select the best relay that requires no topology information and is based on local measurements of the instantaneous channel conditions. This method also requires no explicit communication among the relays. The success (or failure) to select the best available path depends on the statistics of the wireless channel, and a methodology to evaluate performance for any kind of wireless channel statistics, is provided. Information theoretic analysis of outage probability shows that our scheme achieves the same diversity-multiplexing tradeoff as achieved by more complex protocols, where coordination and distributed space–time coding for relay nodes is required, such as those proposed by Laneman and Wornell (2003). The simplicity of the technique allows for immediate implementation in existing radio hardware and its adoption could provide for improved flexibility, reliability, and efficiency in future 4G wireless systems.

The design of space--time codes to achieve full spatial diversity over fading channels has largely been addressed by handcrafting example codes using computer search methods and only for small numbers of antennas. The lack of more general designs is in part due to the fact that the diversity advantage of a code is the minimum rank among the complex baseband differences between modulated codewords, which is difficult to relate to traditional code designs over finite fields and rings. In this paper, we present general binary design criteria for PSK-modulated space--time codes. For linear BPSK/QPSK codes, the rank of (binary projections of) the unmodulated codewords, as binary matrices over the binary field, is a sufficient design criterion: full binary rank guarantees full spatial diversity. This criterion accounts for much of what is currently known about PSK-modulated space-time codes. We develop new fundamental code constructions for both quasi-static and time-varying channels. These are perhaps the first general constructions---other than delay diversity schemes---that guarantee full spatial diversity for an arbitrary number of transmit antennas.

One method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter, and to decode differentially without knowing the channel coefficients at the receiver. Since channel knowledge is not required at the receiver, differential schemes are ideal for use on wireless links where channel tracking is undesirable or infeasible, either because of rapid changes in the channel characteristics or because of limited system resources. Although this basic principle is well understood, it is not known how to generate good-performing constellations of unitary matrices, for any number of transmit and receive antennas and for any rate. This is especially true at high rates where the constellations must be rapidly encoded and decoded. We propose a class of Cayley codes that works with any number of antennas, and has efficient encoding and decoding at any rate. The codes are named for their use of the Cayley transform, which maps the highly nonlinear Stiefel manifold of unitary matrices to the linear space of skew-Hermitian matrices. This transformation leads to a simple linear constellation structure in the Cayley transform domain and to an information-theoretic design criterion based on emulating a Cauchy random matrix. Moreover, the resulting Cayley codes allow polynomial-time near-maximum-likelihood decoding based on either successive nulling/cancelling or sphere decoding. Simulations show that the Cayley codes allow efficient and effective high-rate data transmission in multi-antenna communication systems without knowing the channel.

Space-time block codes are a remarkable modulation scheme discovered recently for the multiple antenna wireless channel. They have an elegant mathematical solution for providing full diversity over the coherent, at-fading channel. In addition, they require extremely simple encoding and decoding. Although these codes provide full diversity at low computational costs, we show that they incur a loss in capacity because they convert the matrix channel into a scalar AWGN channel whose capacity is smaller than the true channel capacity. In this letter the loss in capacity is quantied as a function of channel rank, code rate, and number of receive antennas.

In this paper, noncoherent receivers for differential space-time modulation (DSTM) are investigated. It is shown that the performance of the previously proposed conventional differential detection (DD) receiver is satisfactory only for very slow flat fading channels. However, conventional DD suffers from a considerable loss in performance even for moderately fast fading. In order to overcome this problem, multiple-symbol detection (MSD) and low-complexity decision-feedback differential detection (DF-DD) receivers are derived.