2X2 MIMO Zero Forcing
2016-08-23
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Script for computing the BER for BPSK modulation in a Rayleigh fading channel with 2 Tx, 2Rx MIMO channel Zero Forcing equalization
y=Hx+n,
where y is received vector, H is Rayleigh channel matrix, x is transmitted symbols and n is white Gaussian noise.
ZF demodulation:
choose a matrix W such that WH=I,
i.e Wy=WHx+Wn
=> Wy=Ix+Wn
by mathematical calculations it can be shown that W=inv(H*H).(H*) i.e making off diagonal terms=0
where * is hermition.
Now, Hard decision is used for recovering symbols and theoretical and practical BER is plotted on semi-log axis.
Disadvantage:
in equation Wy=Ix+Wn , one can see noise is getting amplified. which is the reason behind low BER compared to MMSE and ML decoding.
y=Hx+n,
where y is received vector, H is Rayleigh channel matrix, x is transmitted symbols and n is white Gaussian noise.
ZF demodulation:
choose a matrix W such that WH=I,
i.e Wy=WHx+Wn
=> Wy=Ix+Wn
by mathematical calculations it can be shown that W=inv(H*H).(H*) i.e making off diagonal terms=0
where * is hermition.
Now, Hard decision is used for recovering symbols and theoretical and practical BER is plotted on semi-log axis.
Disadvantage:
in equation Wy=Ix+Wn , one can see noise is getting amplified. which is the reason behind low BER compared to MMSE and ML decoding.
matlab
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