Interplay of SNR with Diversity for Minimum Mean Squared Error Receiver
Centre for Advanced Studies, APJ Abdul Kalam Technical University, Lucknow
Dr. Vijay Tiwari,“Interplay of SNR with Diversity for Minimum Mean Squared Error Receiver”.
American Research Journal of Electrical Engineering; 1(1): 1-9
Abstract
Poor performance in wireless channel arises due to the Deep Fade and probability of deep fade
in the system is just the reciprocal of the SNR (1/SNR). Solution to this problem lies in use of diversity i.e.
using more links. That could be achieved by the use of multiple transmit and receive antennas. At the receiver
multiple received signals are available as a linear combination of individual signals. These are used at the input
of detection in the form of Beam forming vector. Beam forming vector is a vector combination of the receive
signals. Noise component at the receiver is a random quantity that depends on the Norm of the vector of the
noise at each receive antenna. To maximize the SNR, we may choose appropriate Beam forming vector. The
combiner that provides maximum SNR under such conditions is referred as Maximal Ratio Combiner. This is a
scaled version of fading channel vector (spatial matched filter). Receiver diversity is successfully employed in
WCDMA. HSDPA, LTE and WiMAX technologies. BER performance of the multiple antenna system follows the
Chi square distribution. As receive antennas increase, the probability of deep fade and hence BER also decreases
at a much faster pace. MIMO systems evolve in finding the minimum error vector amongst all possible transmit
vectors. There are attempts to provide a solution that minimizes the least square error as implemented in
Zero Forcing Receivers (ZFR). It uses pseudo inverse to arrive at the ZFR diversity orders in terms of number
of receive and transmit antenna. On the other hand we analyze the Minimum Mean Squared Error (MMSE)
receiver which calculates the mean square of the error following Bayesian approach which is different from
earlier case of ZFR where we considered the deterministic error. In this paper we look in to the conditions as to
how these two receivers operate and conditions under which these converge. Also what could be reason for the
noise enhancement in ZFR and how MMSE improves on this drawback, has been discussed. The requirement
of SNR for various channels and its shortfall has been analytically presented. Impact of diversity over the SNR
requirement has been modeled and same was simulated to verify the SNR shortfall in case of various MIMO
channels.
