Three-transmit-antenna space-time codes based on SU(3)

Fully diverse constellations, i.e., a set of unitary matrices whose pairwise differences are nonsingular, are useful in multiantenna communications especially in multiantenna differential modulation, since they have good pairwise error properties. Recently, group theoretic ideas, especially fixed-point-free (fpf) groups, have been used to design fully diverse constellations of unitary matrices. Here, we give systematic design methods of space-time codes which are appropriate for three-transmit-antenna differential modulation. The structures of the codes are motivated by the special unitary Lie group SU(3). One of the codes, which is called the AB code, has a fast maximum-likelihood (ML) decoding algorithm using complex sphere decoding. Diversity products of the codes can be easily calculated, and simulated performance shows that they are better than group-based codes, especially at high rates and as good as the elaborately designed nongroup code

Design of fully diverse multiple-antenna codes based on Sp(2)

Fully diverse constellations, i.e., sets of unitary matrices whose pairwise differences are nonsingular, are useful in multiple-antenna communications, especially in multiple-antenna differential modulation, since they have good pairwise error properties. Recently, group theoretic ideas, especially fixed-point-free (fpf) groups, have been used to design fully diverse constellations of unitary matrices. Here we construct four-transmit-antenna constellations appropriate for differential modulation based on the symplectic group Sp(2). They can be regarded as extensions of Alamouti's celebrated two-transmit-antenna orthogonal design which can be constructed from the group Sp(1). We further show that the structure of Sp(2) codes lends itself to efficient maximum-likelihood (ML) decoding via the sphere decoding algorithm. Finally, the performance of Sp(2) codes is compared with that of other existing codes including Alamouti's orthogonal design, a 4/spl times/4 complex orthogonal design, Cayley differential unitary space-time codes and group-based codes

Unitary space-time modulation via Cayley transform

A prevoiusly proposed method for communicating with multiple antennas over block fading channels is unitary space-time modulation (USTM). In this method, the signals transmitted from the antennas, viewed as a matrix with spatial and temporal dimensions, form a unitary matrix, i.e., one with orthonormal columns. Since channel knowledge is not required at the receiver, USTM schemes are suitable 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. Previous results have shown that if suitably designed, USTM schemes can achieve full channel capacity at high SNR and, moreover, that all this can be done over a single coherence interval, provided the coherence interval and number of transmit antennas are sufficiently large, which is a phenomenon referred to as autocoding. While all this is well recognized, what is not clear is how to generate good performing constellations of (nonsquare) unitary matrices that lend themselves to efficient encoding/decoding. The schemes proposed so far either exhibit poor performance, especially at high rates, or have no efficient decoding algorithms. We propose to use the Cayley transform to design USTM constellations. This work can be viewed as a generalization, to the nonsquare case, of the Cayley codes that have been proposed for differential USTM. The codes are designed based on an information-theoretic criterion and lend themselves to polynomial-time (often cubic) near-maximum-likelihood decoding using a sphere decoding algorithm. Simulations suggest that the resulting codes allow for effective high-rate data transmission in multiantenna communication systems without knowing the channel. However, our preliminary results do not show a substantial advantage over training-based schemes

Interference Cancellation at the Relay for Multi-User Wireless Cooperative Networks

We study multi-user transmission and detection schemes for a multi-access relay network (MARN) with linear constraints at all nodes. In a $(J, J_a, R_a, M)$ MARN, $J$ sources, each equipped with $J_a$ antennas, communicate to one $M$-antenna destination through one $R_a$-antenna relay. A new protocol called IC-Relay-TDMA is proposed which takes two phases. During the first phase, symbols of different sources are transmitted concurrently to the relay. At the relay, interference cancellation (IC) techniques, previously proposed for systems with direct transmission, are applied to decouple the information of different sources without decoding. During the second phase, symbols of different sources are forwarded to the destination in a time division multi-access (TDMA) fashion. At the destination, the maximum-likelihood (ML) decoding is performed source-by-source. The protocol of IC-Relay-TDMA requires the number of relay antennas no less than the number of sources, i.e., $R_a\ge J$. Through outage analysis, the achievable diversity gain of the proposed scheme is shown to be $\min\{J_a(R_a-J+1),R_aM\}$. When {\small$M\le J_a\left(1-\frac{J-1}{R_a}\right)$}, the proposed scheme achieves the maximum interference-free (int-free) diversity gain $R_aM$. Since concurrent transmission is allowed during the first phase, compared to full TDMA transmission, the proposed scheme achieves the same diversity, but with a higher symbol rate.Comment: submitted to IEEE Transaction on Wireless Communicatio

Distributed space-time codes in wireless relay networks

We apply the idea of space-time coding devised for multiple antenna systems to the communication over a wireless relay network. We use a two stage protocol, where in one stage the transmitter sends information and in the other, the relay nodes encode their received signals into a "distributed" linear dispersion code, and then transmit the coded signals to the receiver. We show that for high SNR the pairwise error probability (PEP) behaves as (log P/P)^(min{T,R}) with T the coherence interval, R the number of relay nodes and P the total transmit power. Thus, apart from the log P factor and assuming T≥R, the system has the same diversity as a multi-antenna system with R transmit antennas, which is the same as assuming that the R relay nodes can fully cooperate and have full knowledge of the transmitted signal. We further show that for a fixed total transmit power across the entire network, the optimal power allocation is for the transmitter to expend half the power and for the relays to collectively expend the other half. We also show that at low and high SNR, the coding gain is the same as that of a multi-antenna system with R antennas. At intermediate SNR, it can be quite different, which has implications for the design of distributed space-time codes

Cooperative diversity in wireless relay networks with multiple-antenna nodes

In [1], the idea of distributed space-time coding was proposed to achieve a degree of cooperative diversity in a wireless relay network. In particular, for a relay network with a single-antenna transmitter and receiver and R single-antenna relays, it was shown that the pairwise error probability (PEP) decays as ((log P)/P)^R, where P is the total transmit power. In this paper, we extend the results to wireless relay networks where the transmitter, receiver, and/or relays may have multiple antennas. Assuming that the transmitter has M antennas, the receiver has N antennas, the sum of all the antennas at the relay nodes is R, and the coherence interval is long enough, we show that the PEP behaves as (1/P)^(min{M,N}R), if M ≠ N, and ((log^(1/M)P)/p)^(MR), if M=N. Therefore, for the case of M ≠ N, distributed space-time coding has the same PEP performance as a multiple-antenna system with min{M, N}R transmit and a single receive antenna. For the case of M = N, the penalty on the PEP compared to a multiple-antenna system is a log^(1/M) P factor, which is negligible at high SNR. We also show that for a fixed total transmit power across the entire network, the optimal power allocation is for the transmitter to expend half the power and for the relays to share the other half with the power used by each relay being proportional to the number of antennas it has

Design of fully-diverse multi-antenna codes based on Sp(2)

Fully-diverse constellations, i.e., a set of unitary matrices whose pairwise differences are nonsingular, are useful in multi-antenna communications, especially in multi-antenna differential modulation, since they have good pairwise error properties. Recently, group theoretic ideas, especially fixed-point-free (FPF) groups, have been used to design fully-diverse constellations of unitary matrices. Here we construct four-transmit-antenna constellations appropriate for differential modulation based on the symplectic group Sp(2) These can be regarded as extensions of S.M. Alamouti's celebrated two-transmit-antenna orthogonal design which can be constructed from the group Sp(1) (see IEEE J. Sel. Area Commun., p.1451-8, 1998). We further show that the structure of the code lends itself to efficient maximum likelihood (ML) decoding via the sphere decoding algorithm. Finally, the performance of the code is compared with existing methods including Alamouti's scheme, Cayley differential unitary space-time codes and group based codes

High-rate space-time codes motivated by SU(3)

Fully-diverse constellations, i.e., a set of unitary matrices whose pairwise differences are nonsingular, are useful in multi-antenna communications especially in multi-antenna differential modulation, since they have good pairwise error properties. Recently,group theoretic ideas, especially fixed-point-free (fpf) groups, have been used to design fully-diverse constellations of unitary matrices. Here we give systematic methods to design space-time codes which are appropriate for three-transmit- antenna differential modulation. The structures of the codes are motivated by the Lie group SU(3). One of the codes, called the AB code, has a fast decoding algorithm using the complex sphere decoder. The diversity products of the codes can be easily calculated and simulated performances show that the codes are better than the group-based codes [1] especially at high rates and as good as the elaborately-designed non-group codes[1]