10.1

A signal source generates signals as shown in Figure P10.1. The signals are expressed as s ₁( t) = cos(2 ? t) rect( t), s ₂( t) = cos[2 ? t + (2 ?/3)] rect( t), and s ₃( t) = cos[2 ? t ? (2 ?/3)]rect( t).

Figure P10.1: Signal set.

1. Describe a correlation receiver for these signals.

2. Draw the corresponding decision regions on a signal space.

10.2

A rectangular pulse of known amplitude A is transmitted starting at time instant t ₀ with probability 1/2. The duration T of the pulse is a random variable uniformly distributed over the interval [ T ₁, T ₂]. The additive noise to the pulse is white Gaussian with mean zero and variance N ₀/2.

1. Determine the likelihood ratio.

2. Describe the likelihood ratio receiver.

10.3

Consider the general binary detection problem

where s ₁( t) and s ₀( t) are as shown in Figure P10.3, and W( t) is a white Gaussian noise with mean zero and power spectral density N ₀ /2.

1. Determine the probability of error, assuming minimum probability of error criterion and P( H ₀) = P( H ₁) = 1/2.

2. Draw a block diagram of the optimum receiver

Figure P10.3: Signal set.

10.4

In a binary detection problem, the transmitted signal under...