Optimal STBC over PSK signal sets from cyclotomic field extensions

An n×l (l≥n) space time block code (STBC) C over a complex signal set S consists of a finite number of n×l matrices with elements from S. For quasi-static, flat fading channels, a primary performance index of C is the minimum of the rank of the difference of any two matrices, called the rank of the code. C is of full rank if its rank is n and is of minimum delay if l=n. The rate R, in bits per second per Hertz, of a full rank minimum delay code over S is upper bounded by log₂|S| and those meeting this bound are referred to as full rate codes. A full rank, full rate, minimum delay, space time block code over S is said to be rate-optimal. We present some general techniques for constructing rate-optimal codes from field extensions embedded in matrix rings. Working mostly with cyclotomic fields, we construct rate-optimal n×n STBCs over m-PSK signal sets for arbitrary values of m and a large set of values of n.