Sorry, but your question makes no sense mathematically.
H is 64x199. Frf is 100x5. So H*Frf is 64x5. No problem there. Both matrices are known.
Similarly, the transpose of those matrices on the other end is 5x64. Still NO problem. You don't tell us what Fbb is expected to be. One presumes it must have 5 rows. Suppose Fbb is a 5xN array. I really don't give a hoot what N is, nor does it seem to matter. Then the product array, I'll call it A,
A = H * Frf * Fbb * Fbb '* Frf' * H '
will be a 64x64 array. This is basic linear algebra and the rules of matrix multiplication. The rank of that array will be at MOST 5, but that is hardly relevant. We are left with the question
7 = log2(1 + A)
where A is actually a function of some unknown array Fbb. We can even unroll that a bit, to be
2^7 - 1 = A
R is a scalar, after all. Therefore, we are asked to find some array Fbb, such that A == 127.
Do you see the problem? A is a 64x64 rray, not a scalar. No matter what size Fbb is, the result will ALWAYS be 64x64.
Are you asking to find Fbb such that the result A is a 64x64 array that contains only the number 127, replicated over the entire array? For general matrices H and Frf that cannot be achieved.
So until you improve the mathematics of what you are asking, what you are asking makes no sense at all.
