(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The aim of this exercise is to derive and simulate the error rate performance

of binary PSK when the signal is transmitted over a single-path (or frequency

non-selective) slowly fading channel. The frequency-nonselective channel results

in multiplicative distortion of the transmitted signal s(t). In addition, the con-

dition that the channel fades slowly implies that the multiplicative process may

be regarded as a constant during at least one signaling interval. Therefore, the

received equivalent lowpass signal in one signaling interval is

r(t) = [itex]\alpha[/itex] * exp(j * [itex]\phi[/itex]) * s(t) + z(t) 0 [itex]\leq[/itex] t [itex]\leq[/itex] ts

where z(t) represents the complex-valued white Gaussian noise process with

power spectral density [itex]N_0[/itex]/2

Assume that the channel fading is sufficiently slow that the phase shift, [itex]\phi[/itex] can

be estimated from the received signal without error. Then, we can achieve ideal

coherent detection of the received signal. The received signal can be processed

by passing it through a matched filter. Show that for a fixed (time-invariant)

channel, i.e., for a fixed attenuation [itex]\alpha[/itex], the error rate of binary PSK as a function

of the received SNR, [itex]\gamma[/itex] is

[itex]P_b[/itex]([itex]\gamma[/itex]) = Q([itex]\sqrt{}2\gamma[/itex])

where [itex]\gamma[/itex] = [itex]\alpha^2 E_b / N_0[/itex] and [itex]E_b[/itex] is the energy of the transmitted signal per bit.

2. Relevant equations

3. The attempt at a solution

Can someone give me an idea on how to start..

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# BPSK singlepath Rayleigh channel

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