Home /
Expert Answers /
Electrical Engineering /
obtain-bit-error-rate-ber-and-symbol-error-rate-ser-curves-over-additive-white-gaussian-noise-a-pa781
(Solved): Obtain Bit Error Rate (BER) and Symbol Error Rate (SER) curves over additive white Gaussian noise (A ...
Obtain Bit Error Rate (BER) and Symbol Error Rate (SER) curves over additive white Gaussian
noise (AWGN) and Nakagami- m fading channels(m=1,4,10) with the Monte Carlo Simulation for the modulation types of M-PSK( M=2,4,16), M-FSK (M=2,4,16). Verify your simulation results with the analytical results which expressions are given below.
Theorical Expressions of M-PSK:
g_(PSK)=(sin((\pi )/(M)))^(2)
For the AWGN Channel:
P_(b)(e)=Q(\sqrt((2E_(b))/(N_(0)))),P_(s)(e)=2Q(\sqrt((log_(2)ME_(b))/(N_(0)))sin((\pi )/(M)))
For the Nakagami-m Fading Channel:
P_(b)(e)=(1)/(\pi )\int_0^(((M-1)\pi )/(M)) (1+(g_(PSK)\gamma )/(m\times (sin\theta )^(2)))^(2)d\theta
The Theoretical Expressions of M-FSK:
For the AWGN Channel:
P_(s)(e)=1-\int_(-\infty )^(\infty ) (Q(-q-\sqrt((2E_(s))/(N_(0)))))^(M-1)(1)/(\sqrt(2\pi ))e^(-(q^(2))/(2))dq
For the Nakagami-m Fading Channel:
P_(s)(e)=(1)/(\sqrt(2\pi ))\int_(-\infty )^(\infty ) (1-(1-Q(y))^(M-1))\int_0^(\infty ) e^(((y-\sqrt(2\gamma ))^(2))/(2))p_(\gamma )(\gamma )d\gamma dy
p_(\gamma )(\gamma )=(\gamma ^(M-1))/((2\sigma ^(2))^(2)(M-1)!)e^(-(\gamma )/(2\sigma ^(2)))
Do the simulations with MATLAB and solve analytically.