Let's say I am simulating as simple as BFSK, it has two symbols one entirely on the real plane while other on the complex plane for representing let's say zero and one, that is how the constellation of BFSK looks like. s=data + j*(~data); %Baseband BFSK modulation
Now let's say we added AWGN (N) and Rayleigh fading (h) as well. Rx= h*x + N; Now when I tried to detect it on the receiving side I will have to divide this entire Rx by an h, well that makes sense. My entire graphs for the BER curve match non-coherent detection for FSK. It exactly matched the theory, Eb/N0 vs. BER for BFSK over Rayleigh Channel. Now how to do the same for Non-coherent detection? If I do not divide Rx by h Rx/h, I get a few very very bad results and that doesn't match anything. Theory tells us that In non-coherent detection, prior knowledge of the channel impulse response is not known at the receiver.
In Coherent systems, the receiver needs phase information of the transmitter (the carrier phase) to recover the transmitted data at the receiver side. I haven't used any such thing but still simulation results for BER matched with that of theory for Coherent FSK.
Can someone here help me with this? By not diving by h, will I get better results for Non coherent FSK ? Whether BPSK or BFSK every time we need to divide h*x + N by an h for getting results that match theory.
"BFSK is done by selecting between two frequencies for each symbol (Binary Frequency Shift Keying). What the OP is showing is samples from M-PSK (Phase Shift Keying); selecting between M phases for each symbol (which would result in two distinct dots on the IQ constellation). Here the two symbols selected are phases 0° and 90°, so these could be 2 of the 4 symbols for QPSK.
To do any form of FSK, the phase must transition over the course of the symbol, given that frequency is by definition the derivative of phase. Thus if one symbol is at a fixed frequency, the phase would vary linearly with time over the duration of that symbol. On an IQ constellation, we would see the phasor rotate at a constant rate from one dot to the next (rotating counter-clockwise to represent a positive frequency and clock-wise to represent a negative frequency).
MSK (Minimum Shift Keying) is the case of the phase rotating ±90° over the symbol duration, as this would be the minimum frequency offset between symbols where the symbols would still be orthogonal. Out of band emissions can be reduced by smoothing the phase from one symbol to the next (generally abrupt transitions in phase or magnitude have high spectral content), which is the intention for GMSK (Gaussian Minimum Shift Keying) where instead of linear phase ramps going up and down according to the symbol used, the phase trajectory is filtered with a Gaussian filter such that the transitions are continuous in the first derivative, meaning the frequency transitions smoothly from one symbol to the next. " Dann Boschen Marcuus Müller
Code --
%This program simulates BER of BFSK in AWGN channel%
clear all; close all; clc;
num_bit=100000; %Signal length
max_run=20; %Maximum number of iterations for a single SNR
Eb=1; %Bit energy
SNRdB=0:1:50; %Signal to Noise Ratio (in dB)
SNR=10.^(SNRdB/10);
hand=waitbar(0,'Please Wait....');
for count=1:length(SNR) %Beginning of loop for different SNR
avgError=0;
avgError_awgn=0;
No=Eb/SNR(count); %Calculate noise power from SNR
for run_time=1:max_run %Beginning of loop for different runs
waitbar((((count-1)*max_run)+run_time-1)/(length(SNRdB)*max_run));
Error=0;
Error_awgn=0;
data= round(rand(1,num_bit)); %Generate binary data source
s=data+j*(~data); %Baseband BFSK modulation
NI=sqrt(No/2)*randn(1,num_bit);
NQ=sqrt(No/2)*randn(1,num_bit);
N=NI+j*NQ; %Generate complex AWGN
h = 1/sqrt(2).* (randn(1,num_bit) + j*randn(1,num_bit)); % Rayleigh channel coefficent
Y_with_AWGN = s +N; %Receievd signal with AWGN only
Y=s.*h +N; %Received Signal with both Rayleigh and AWGN
Y= Y./h; %Channel equalization
%---------------------------------------------------------------
%---------------------------------------------------------------
for k=1:num_bit %Decision device taking hard decision and deciding error
Z(k)=real(Y(k))-imag(Y(k)); %Y(k) is actual trasmited signal signal
Z_1(k)=real(Y_with_AWGN(k))-imag(Y_with_AWGN(k));
% if real that mean we chose 1 and if imaginary we chose zero
if ((Z(k)>0 && data(k)==0)||(Z(k)0 && data(k)==0)||(Z_1(k)
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