Unitary Space-Time Constellation Design Based on the Chernoff Bound of the Pairwise Error Probability

• Published in: IEEE transactions on information theory Vol. 54; no. 8; pp. 3842 - 3850
• Main Authors: Yi Wu, Ruotsalainen, K., Juntti, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antenna theory; Antennas; Antennas and propagation; Applied sciences; Channels; Codes; Coding, codes; Communication channels; Constellation diagram; Constellations; Data transmission; Decoding; Design; Errors; Exact sciences and technology; Fading; Fading channel; Information theory; Information, signal and communications theory; Mathematical models; Matrix; multiple antennas; noncoherent communications; Optimization; Pairwise error probability; Radiocommunications; Receiving antennas; Searching; Signal and communications theory; Telecommunications; Telecommunications and information theory; Theorems; Transmitters; Transmitters. Receivers; Transmitting antennas; unitary constellations; Wireless communication; Fading channels; Performance evaluation; Fading; Singularity; Design criterion; Unitary matrix; unitary constellations; Error probability; Computer simulation; Transmitter; noncoherent communications; Space time; Decoding; Optimization; Descent method; Fading channel; multiple antennas; Antenna array; Gradient method
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2008.926310

Unitary space-time constellation design is considered for noncoherent multiple-antenna communications, where neither the transmitter nor the receiver knows the fading coefficients of the channel. By employing the Clarke's subdifferential theorem of the sum of the kappa largest singular values of a unitary matrix, we present a numerical optimization procedure for finding unitary space-time signal constellations of any dimension. The Chernoff bound of the pairwise error probability is used directly as a design criterion. The constellations are found by performing gradient descent search on a family ldquosurrogaterdquo functions that converge to the maximum pairwise error probability. The complexity of the search procedure increases with the dimension and the size of the constellation, but it can be considered to be acceptable for an off-line design procedure. Since the designed constellations are unstructured, and, thus, require an exhaustive search over all codewords in decoding, their main practical value is to serve as constellation design performance benchmarks. We compare the performance of the new constellations to that of some other well-known constellations. Computer simulation results illustrate typically about 0.4-3.5 dB performance gains.