Consider a communication system where binary orthogonal signals are employed for

ID: 1810509 • Letter: C

Question

Consider a communication system where binary orthogonal signals are employed for transmission.

The signal space representations for the transmitted signals are given as follows:

s1 = (?Eb; 0) and s2 = (0; ?Eb):

The transmitted signals go through an AWGN channel. Hence, the received signal is either

r = (r1; r2) = (?Eb + n1; n2) if s1 is transmitted

r = (r1; r2) = (n1; ?Eb + n2) if s2 is transmitted

where n1 and n2 are Gaussian random variables with variance No / 2 .

Assume that the bit energy Eb = 1, and consider three cases in which the noise standard deviation

values are = 0.1; = 0.3, and = 0.5. Using Matlab, generate 300 samples of the received vector

r = (r1; r2) for both cases of s1 and s2 being transmitted and for each case of standard deviation . Plot these vectors

for each value of noise standard deviation as separate two dimensional plots with coordinates

(r1; r2), and discuss the eect of noise and its variance on the transmitted signal.

Hint: To generate the Gaussian noise samples of n1 and n2, use the built-in Matlab function

randn(m; n) which generates an m-by-n matrix with random zero mean unit variance = 1.

Gaussian components. For instance you can write

n1 = 0.1*randn(1,300)

to generate 300 zero mean Gaussian noise samples with standard deviation = 0.1

this will help you so please rate me got to sleep its 4 in morning here

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