On the maximal rate of (n+1) x n and (n+2) x n complex orthogonal designs

Das, Smarajit and Rajan, Sundar B (2006) On the maximal rate of (n+1) x n and (n+2) x n complex orthogonal designs. In: IEEE International Symposium on Information Theory, Jul 09-14, 2006, Seattle, WA, pp. 381-385.

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Abstract

For p x n complex orthogonal designs in k variables, where p is the number of channels uses and n is the number of transmit antennas, the maximal rate L of the design is asymptotically half as n increases. But, for such maximal rate codes, the decoding delay p increases exponentially. To control the delay, if we put the restriction that p = n, i.e., consider only the square designs, then, the rate decreases exponentially as n increases. This necessitates the study of the maximal rate of the designs with restrictions of the form p = n+1, p = n+2, p = n+3 etc. In this paper, we study the maximal rate of complex orthogonal designs with the restrictions p = n+1 and p = n+2. We derive upper and lower bounds for the maximal rate for p = n+1 and p = n+2. Also for the case of p = n+1, we show that if the orthogonal design admit only the variables, their negatives and multiples of these by root-1 and zeros as the entries of the matrix (other complex linear combinations are not allowed), then the maximal rate always equals the lower bound.

Item Type:	Conference Paper
Publisher:	IEEE
Additional Information:	Copyright 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	31 Aug 2010 09:28
Last Modified:	19 Sep 2010 06:12
URI:	http://eprints.iisc.ac.in/id/eprint/30487

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