please help in Adaptive Channel Equalisation code.

The objective of this project is to investigate the performance of an adaptive equalizer for data transmission over a channel that causes intersymbol interference. The basic configuration of the system to be simulated is shown in Figure 11.6. As we observe, five basic modules are required. Note that we have avoided carrier modulation and demodulation, which is required in a telephone channel modem. This is done to simplify the simulation program. However, all processing involves complex arithmetic operations.

FIGURE 11.6 Experiment for investigating the performance of an adaptive equalizer

The five modules are as follows:

1. The data generator module is used to generate a sequence of complex-valued information symbols {a(n)}. In particular, employ four equally probable symbols s + js, s − js, −s + js, and −s − js, where s is a scale factor that may be set to s = 1, or it can be an input parameter.

2. The channel filter module is an FIR filter with coefficients {c(n), 0 ≤ n ≤ K − 1} that simulates the channel distortion. For distortion-less transmission, set c(0) = 1 and c(n) = 0 for 1 ≤ n ≤ K − 1. The length K of the filter is an input parameter.

3. The noise generator module is used to generate additive noise that is usually present in any digital communication system. If we are modeling noise that is generated by electronic devices, the noise distribution should be Gaussian with zero mean. Use the randu function.

4. The adaptive equalizer module is an FIR filter with tap coefficients {h(k), 0 < k < N − 1}, which are adjusted by the LMS algorithm. However, due to the use of complex arithmetic, the recursive equation in the LMS algorithm is slightly modified to

where the asterisk denotes the complex conjugate.

5. The decision device module takes the estimate â(n) and quantizes it to one of the four possible signal points on the basis of the following decision rule:

The effectiveness of the equalizer in suppressing the ISI introduced by the channel filter may be seen by plotting the following relevant sequences in a two-dimensional (real–imaginary) display. The data generator output {a(n)} should consist of four points with values ±1 ±j. The effect of channel distortion and additive noise may be viewed by displaying the sequence {x(n)} at the input to the equalizer. The effectiveness of the adaptive equalizer may be assessed by plotting its output {â(n)} after convergence of its coefficients. The short-time average squared error ASE(n) may also be used to monitor the convergence characteristics of the LMS algorithm. Note that a delay must be introduced into the output of the data generator to compensate for the delays that the signal encounters due to the channel filter and the adaptive equalizer. For example, this delay may be set to the largest integer closest to (N + K)/2. Finally, an error counter may be used to count the number of symbol errors in the received data sequence, and the ratio for the number of errors to the total number of symbols (error rate) may be displayed. The error rate may be varied by changing the level of the ISI and the level of the additive noise.

It is suggested that simulations be performed for the following three channel conditions:

a. No ISI: c(0) = 1, c(n) = 0, 1 ≤ n ≤ K − 1

b. Mild ISI: c(0) = 1, c(1) = 0.2, c(2) = −0.2, c(n) = 0, 3 ≤ n ≤ K − 1

c. Strong ISI: c(0) = 1, c(1) = 0.5, c(2) = 0.5, c(n) = 0, 3 ≤ n ≤ K − 1

The measured error rate may be plotted as a function of the signal-to-noise ratio (SNR) at the input to the equalizer, where SNR is defined as Ps/Pn, where Ps is the signal power, given as Ps = s2, and Pn is the noise power of the sequence at the output of the noise generator.