A receiver in a multiuser communication system accepts k binary signals from k independent transmitters:

Y=(Y1; Y2; : : : ; Yk), where Yk is the received signal from the Kth transmitter. In an ideal

system the received vector is given by

Y = Ab +N;

where A = [k] is a diagonal matrix of positive channels gains 1; : : : ; k forming the diagonal, b =

(b1; b2; : : : ; bk) is the vector of bits from each of the transmitters where bi = 1, and N is a vector of

k independent zero-mean unit-variance Gaussian random variables. Assume the transmitted bits bk are

independent and equally likely +1 or -1.

Find the minimum mean square linear estimator for b given the observation Y. How can this

estimator be used in deciding what where the transmitted bits?

\f