In the CDMA multiuser communications system introduced in Problem 11.3.8, each user I transmits an independent data bit Xi such that the vector X = [X1 ∙ ∙ ∙ Xn] ʹ has iid components with PXi(1) = PXi (-1) = 1/2. The received signal is

Where N is a Gaussian (0,σ²I) noise.

(a) Based on the observation Y, find the LMSE estimate X_i(Y) of X_i.

(b) Let X = [X₁ ... X_k]' denote the vector of LMSE estimates of bits transmitted by user 1, . . ., k. Show that X = P^1/2S' (SPS' + σ²I)^-1 Y.

Y =X:VPIS, +N, i=1