Re: Unitary Matrix Generation Question

Wei:

I had the same problem as you in extending a code-length-based
algorithm (CLUE) to complex-valued data. Here's the way I
solved the 2x2 unitary matrix generation task:

1) Define a candidate unitary matrix as

U = [cos(th) exp(j alpha) sin(th) exp(j beta)
    -sin(th) exp(j gamma) cos(th) exp(j delta)]

2) Multiply U by U^H to determine the constraints on
alpha, beta, gamma, and delta such that this matrix is an
identity matrix. If you do this calculation, you come up
with one constraint:

delta - beta = gamma - alpha

(ignoring, of course, the modulo-2 pi wraparound). Thus,
a 2x2 unitary matrix is defined by four parameters, because
of the one above constraint on the five parameters.

Hope this helps,

Scott.
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Scott C. Douglas Phone: (214) 768-4595
Associate Professor Dept: (214) 768-3113
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Southern Methodist University email: douglas@seas.smu.edu
Dallas, TX 75275 http://www.seas.smu.edu/ee
Received on Thu Nov 30 18:06:17 2000