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How to do exhaustive search in case of Maximum Likelihood detector in MATLAB ?

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Hello all, I came across the following Maximum Likelihood detector expression:
----(1)
where is received signal of dimension , is channel between transmitter to receiver of dimension and is transmitted signal of dimension such that , L denotes time slots. is a set that consists of N column vectors of dimension .
Also each , i ranging from 1 to L, is chosen randomly from set .
My query is how to do exhaustive search over .
Any help in this regard will be highly appreciated.

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