DEPARTMENT OF ELECTRONICS & ELECTRICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI

October 2015

ANALYTICAL PERFORMANCE OF ZERO-FORCING RECEIVERS IN CORRELATED RAYLEIGH FADING ENVIRONMENTS

Preliminary Project Report

By

Mukesh Chaudhary 120102038

Gopi Sai Teja 120102024

1. IntroductionCorrelation between the antennas significantly increases the symbol error rate of MIMO receivers. In order to improve the performance we need to estimate the correlation at the transmitter as well as receiver and model the channel properly in the analysis.

Though ML gives better performance than Zero Forcing Equalizer in SISO case but as the number of receiver and transmitter antennas increases, complexity of decoding increases exponentially.

2.Signal and Channel ModelNT and NR are the number of transmitting and receiving antennas respectively. Channel is a flat fading Rayleigh channel modelled by channel matrix H and S is the transmitted signal and n is the additive complex white Gaussian noise.

Y=HS+n

Y is the received signal at the receiver antennas.

3.Correlated MIMO Channel ModelAny correlated MIMO channel can be represented by channel matrix

H=AH HW B

Where Hw is NrX NT matrix of complex iid Gaussian channel matrix and AAH =RRX BBH=RTX

where RRX and RTX are correlation matrices at the receiver and transmitter respectively.

Using the properties of kronecker operators and results on complex matrix variate normal distribution, statistics of H are given by

H NNR,NT(0 , RRX⊗RTX¿ )

4. Zero Forcing Equalizer

Zero forcing matrix filter is given the pseudo-inverse

G=(H HH )−1H H

With GH=I.We can calculate the signal to noise ratio on subchannel 1 can be expressed as

Typeequationhere .