Suboptimum Receivers

A binary communication system employs the following signals to communicate two equally likely messages over an additive white Gaussian noise channel with spectral height $\frac{N_0}{2}$:

$$\begin{array}{l} s_0(t) = \left\{ \begin{array}{cl} \frac{2At... ...leq t < T$ }\\ 0 & \mbox{else} \end{array}\right. \end{array}$$

1.

Draw a block diagram of the optimum receiver.

2.

Compute the probability of error achieved by your receiver from part (a).

3.

Consider now the following suboptimum receiver:

Find the distribution of R for both cases, s₀(t) was transmitted and s₁(t) was transmitted.

4.

Find the probability of error of the suboptimum receiver.

5.

Assume that the transmitted signal is amplified with a gain $\alpha$ when the receiver in part (c) is used. How must $\alpha$ be chosen so that the performance of the receiver in part (c) equals the performance of the optimum receiver without amplification.

6.

Bonus: Express the result in part (e) in terms of a loss of SNR measured in dB.