In order to have accurate reception of high-speed digital signals at relatively low signal to noise ratios (SNR), we used array processing.  Transmission of the radio signal also undergoes distortions due to InterSymbol Interference (ISI) caused by the nature of the multi-path channel.  Our receiver combined Blind Equalizers (BEs) with array antennas to compensate for both ISI and noise.  Our blind equalizer consist of an adaptive 33-tap filters, which adaptation process is controlled by the Least Mean Square (LMS) algorithm.  Since blind equalization does not provide us with a training or a desired sequence, we use a non-linear function called Sato algorithm to estimate for the desired signal. 

Presently, we are investigating the LMS/Sato algorithms  to four difference systems.  These systems which have different configurations for the adaptive filters and the Sato algorithm are as follows:  1) The Single Channel;  2) One BE After the Summer;  3) The Independent BEs in each Channel;  4) BEs in each Channel based on Sato on Sum Signal. 

Our goal is to measure the performance of the blind equalizers for each system, particularly with respect to the convergence time and recovery of the original signal.  (This is strongly dependent on signal to noise ratio).                     
This is done through a number of different parameters used, which are based on case sensors close together as well as sensors widely separated.  Also, we will evaluate performance under varying multipath models; performance as a function of varying the signal to interference ratio; bit error probability as a function of the number of receivers in the array; bit error probability as a function of the signal of noise ratio; and of course convergence rate as a function of SNR and the number of receivers in the array.   

We begin with a single array antenna, which is modeled by a multipath channel block as our baseline system.  We use a digital signal modulation scheme called Quadrature Amplitude Modulation (QAM), and add Additive White Gaussian Noise (AWGN) to our signal. The signal is distorted by the nature of the multipath channel, which consists of a direct path and one reflection. This reflected signal is delayed by the arm delay and scaled by the arm gain.  The resultant signal is then passed through an adaptive filter. The filter includes an input for setting step size.  After the filter, the signal is passed through Sato. The result is then fed back to the filter to aid for convergence, by attempting to adjust to cancel the channel distortion effects. The result of the signal is then compared with the original clean QAM signal for performance evaluation.

The signal to noise ratio of this signal is three times that of the single detector system.  Since the signal adds coherently, the signal power increases by a factor of 9.  If the three noise sources are independent, the noise powers would add, therefore, the noise power increases by a factor of 3.  This requires that the three receivers by separated enough so the noise is independent.  The model above assumes that the multipath channel is identical for each of the three receivers.  This is a reasonable assumption for most outdoor channels.  Therefore, this is not appropriate for indoor channels where a movement of several meters is enough to significantly change the multipath.

In this approach, outputs of three individual adaptive filters are summed up and fed into a single sato which adjust the average weights and feed the results back to the three filters. The final output is produced by taking the average of the three output of the adaptive filters.

In this scheme, three separate adaptive filters (receivers) feed their received signals to the Sato algorithm. Since each filter outputs directly to the Sato block to improve error rates, the adjustment of it's weights are independent of the other filters. The final output of the receiver, an average output of the independently adjusted adaptive filter signals, is expected to achieve the actual information sent by the transmitter (improved error probability).