A linear processing complex orthogonal design (LPCOD) is a ptimesn matrix epsiv, (pgesn) in k complex indeterminates x 1 ,x 2 ,...,x k  such that (i) the entries of epsiv are complex linear combinations of 0, plusmnx i , i=1,...,k and their conjugates, (ii) epsiv H epsiv=D, where epsiv H  is the Hermitian (conjugate transpose) of epsiv and D is a diagonal matrix with the (i,i)-th diagonal element of the form l 1   (i) |x 1 | 2 +l 2   (i) |x 2 | 2 +...+l k   (i) |x k | 2  where l j   (i) ,i=1,2,...,n, j=1,2,...,k are strictly positive real numbers and the condition l 1   (i) =l 2   (i) =...=l k   (i) , called the equal- weights condition, holds for all values of i. For square designs it is known that whenever a LPCOD exists without the equal-weights condition satisfied then there exists another LPCOD with identical parameters with l 1   (i) =l 2   (i) =...=l k   (i) =1. This implies that the maximum possible rate for square LPCODs without the equal-weights condition is the same as that of square LPCODs with equal-weights condition. In this paper, this result is extended to a subclass of non-square LPCODs. It is shown that, a set of sufficient conditions is identified such that whenever a non- square (p>n) LPCOD satisfies these sufficient conditions and do not satisfy the equal-weights condition, then there exists another LPCOD with the same parameters n, k and p in the same complex indeterminates with l 1   (i) =l 2   (i) =...=l k   (i) =1.
['Saif Khan Mohammed', 'B.S. Rajan', 'Ananthanarayanan Chockalingam']
On the Maximal Rate of Non-Square STBCs from Complex Orthogonal Designs