Unitary Space Time Constellation Analysis: An Upper Bound for the Diversity

The diversity product and the diversity sum are two very important parameters for a good-performing unitary space time constellation. A basic question is what the maximal diversity product (or sum) is. In this paper we are going to derive general upper bounds on the diversity sum and the diversity product for unitary constellations of any dimension $n$ and any size $m$ using packing techniques on the compact Lie group U(n).Comment: 15 pages, 3 figures, submitted to IEEE trans. inf

Maximum Rate of Unitary-Weight, Single-Symbol Decodable STBCs

It is well known that the Space-time Block Codes (STBCs) from Complex orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol decodable (SSD). The weight matrices of the square CODs are all unitary and obtainable from the unitary matrix representations of Clifford Algebras when the number of transmit antennas $n$ is a power of 2. The rate of the square CODs for $n = 2^a$ has been shown to be $\frac{a+1}{2^a}$ complex symbols per channel use. However, SSD codes having unitary-weight matrices need not be CODs, an example being the Minimum-Decoding-Complexity STBCs from Quasi-Orthogonal Designs. In this paper, an achievable upper bound on the rate of any unitary-weight SSD code is derived to be $\frac{a}{2^{a-1}}$ complex symbols per channel use for $2^a$ antennas, and this upper bound is larger than that of the CODs. By way of code construction, the interrelationship between the weight matrices of unitary-weight SSD codes is studied. Also, the coding gain of all unitary-weight SSD codes is proved to be the same for QAM constellations and conditions that are necessary for unitary-weight SSD codes to achieve full transmit diversity and optimum coding gain are presented.Comment: accepted for publication in the IEEE Transactions on Information Theory, 9 pages, 1 figure, 1 Tabl

Generalized PSK in Space Time Coding

A wireless communication system using multiple antennas promises reliable transmission under Rayleigh flat fading assumptions. Design criteria and practical schemes have been presented for both coherent and non-coherent communication channels. In this paper we generalize one dimensional phase shift keying (PSK) signals and introduce space time constellations from generalized phase shift keying (GPSK) signals based on the complex and real orthogonal designs. The resulting space time constellations reallocate the energy for each transmitting antenna and feature good diversity products, consequently their performances are better than some of the existing comparable codes. Moreover since the maximum likelihood (ML) decoding of our proposed codes can be decomposed to one dimensional PSK signal demodulation, the ML decoding of our codes can be implemented in a very efficient way.Comment: 22 pages, 3 figures, submitted to IEEE transactions on communicaton

A Numerical Approach for Designing Unitary Space Time Codes with Large Diversity

A numerical approach to design unitary constellation for any dimension and any transmission rate under non-coherent Rayleigh flat fading channel.Comment: 32 pages, 6 figure

Precoding for Outage Probability Minimization on Block Fading Channels

The outage probability limit is a fundamental and achievable lower bound on the word error rate of coded communication systems affected by fading. This limit is mainly determined by two parameters: the diversity order and the coding gain. With linear precoding, full diversity on a block fading channel can be achieved without error-correcting code. However, the effect of precoding on the coding gain is not well known, mainly due to the complicated expression of the outage probability. Using a geometric approach, this paper establishes simple upper bounds on the outage probability, the minimization of which yields to precoding matrices that achieve very good performance. For discrete alphabets, it is shown that the combination of constellation expansion and precoding is sufficient to closely approach the minimum possible outage achieved by an i.i.d. Gaussian input distribution, thus essentially maximizing the coding gain.Comment: Submitted to Transactions on Information Theory on March 23, 201

Full Diversity Unitary Precoded Integer-Forcing

We consider a point-to-point flat-fading MIMO channel with channel state information known both at transmitter and receiver. At the transmitter side, a lattice coding scheme is employed at each antenna to map information symbols to independent lattice codewords drawn from the same codebook. Each lattice codeword is then multiplied by a unitary precoding matrix ${\bf P}$ and sent through the channel. At the receiver side, an integer-forcing (IF) linear receiver is employed. We denote this scheme as unitary precoded integer-forcing (UPIF). We show that UPIF can achieve full-diversity under a constraint based on the shortest vector of a lattice generated by the precoding matrix ${\bf P}$. This constraint and a simpler version of that provide design criteria for two types of full-diversity UPIF. Type I uses a unitary precoder that adapts at each channel realization. Type II uses a unitary precoder, which remains fixed for all channel realizations. We then verify our results by computer simulations in $2\times2$, and $4\times 4$ MIMO using different QAM constellations. We finally show that the proposed Type II UPIF outperform the MIMO precoding X-codes at high data rates.Comment: 12 pages, 8 figures, to appear in IEEE-TW

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