Novel Constructions of Complex Orthogonal Designs for Space-time Block Codes

Complex orthogonal designs (CODs) are used to construct space-time block codes in wireless transmission. COD O-z with parameter [p, n, k] is a p x n matrix, where nonzero entries are filled by +/- z(i) or +/- z(i)*, i = 1, 2, ... , k, such that (OzOz)-O-H = (vertical bar z(1)vertical bar(2) + vertical bar z(2)vertical bar(2) + ... + vertical bar z(k)vertical bar(2))I-n x n. In practice, n is the number of antennas, k/p the code rate, and p the decoding delay. One fundamental problem is to construct COD to maximize k/p and minimize p when n is given. Recently, this problem is completely solved by Liang and Adams et al. It's proved that when n = 2m or 2m - 1 the maximal possible rate is (m + 1)/(2m) and the minimum delay ((2m)(m-1)) (with the only exception n equivalent to 2 (mod 4) where it is 2 ((2m)(m-1))). However, when the number of antennas increase, the minimum delay grows fast and eats the otherwise fast decoding. For example, when n = 1 4 the minimal delay for a code with maximal rate is 6006! Therefore, it is very important to study whether it is possible, by lowering the rate slightly, to shorten the decoding delay considerably. In this paper, we demonstrate this possibility by constructing a series of CODs with parameter [p, n, k] = [((n)(w - 1)) + ((n)(w + 1)), n, ((n)(w))]; where 0 <= w <= n. Besides that, all optimal CODs, which achieve the maximal rate and minimal delay, are contained in our explicit-form constructions. And this is the first explicit-form construction, while the previous are recursive or algorithmic.