Medicaps Institute of Technology & Management

Submitted by :-Prasanna PansePriyanka ShuklaSavita Deshmukh

Guided by :-Mr. Anshul ShrotriyaAssistant Professor

Department of Electronics and Communication

OPTIMUM RECEIVERS FOR CHANNELSWITH ISI AND AWGN

INTRODUCTION

In order to transmit digital information over bandpass channels, we have to transfer information to a carrier wave of appropriate frequency.

OPTIMUM RECEIVER

The performance of the receiver is usually measured in terms of the probability of error and the receiver is said to be optimum if it yields the minimum probability of error .

OPTIMUM RECEIVER FOR AN AWGN CHANNELWITH ISI

MatchedFilterh(t)

Sampler MLSE

Clockt=KT

Outputdata

ReceivedSignalR1(t)

Maximum Likelihood Sequence Estimation

• When the signal has no memory, the symbol-by-symbol detector described in the preceding section is optimum in the sense of minimizing the probability of a symbol error.

• When the transmitted signal has memory, i.e., the signals transmitted in successive symbol intervals are interdependent.

• MLSE criterion is equivalent to the problem of estimating the state of a discrete time finite state machine.

• The finite state machine in this case is the equivalent discrete time channel.

• To develop the maximum-likelihood sequence detection algorithm, let us consider, as an example, the NRZI signal.

• Its memory is characterized by the trellis shown in the following figure:

• The signal transmitted in each signal interval is binary PAM.

•Since the channel noise is assumed to be white and Gaussian and f(t= iT), f(t =jT) for i≠j are orthogonal.

•Hence, the noise sequence n1, n2, …, nk is also white.

•Then, given the received sequence r1,r2,…,rk at the output , ,the detector determines the sequence s(m)={s1(m),s2(m),..,sK (m)}. Such a detector is called the maximum-likelihood (ML) sequence detector.

•For the NRZI example, which employs binary modulation, the total number of sequence is 2K , where K is the number of outputs obtained from the demodulator.

• However, this is not the case. We may reduce the number of the sequences in the trellis search by using the Viterbi algorithm to eliminate sequences as new data is received from the demodulator.

Viterbi Algorithm

•The Viterbi algorithm is a sequence trellis search algorithm for performing ML sequence detection.

Basic concept –

• Generate the code trellis at the decoder.

• The decoder penetrates through the code trellis level by level in search for the transmitted code sequence.

• At each level of the trellis, the decoder computes and compares the metrics of all the partial paths entering a node.

• The decoder stores the partial path with the larger metric and eliminates all the other partial paths.

The corresponding trellis is shown in the following figure :

At time t=T, we receive r1=s1+n1 from the demodulator, and at t=2T, we receive r2=s2+n2.

• For the two paths entering node S(0), we compute the two Euclidean distance metrics.

• The Viterbi algorithm compares these two metrics and discards the path having the larger metrics. The other path with the lower metric is saved.

• Similarly, for two paths entering node S1 at t=2T, we compute the two Euclidean distance metrics by using the output r1 and r2 from the demodulator.

• The two metrics are compared and the signal path with the larger metric is eliminated.

• Thus, at t=2T, we are left with two survivor paths, one at node S0 and the other at node S1 , and their corresponding metrics.

Discrete time model for a channel with ISI

• ISI is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as effect as noise, It making the communication less reliable.

• The transmitter sends discrete time symbols at a rate of 1/T per second and the sampled output of match filter at the receiver is also discrete time signal with samples rate 1/T per second.

• Major difficulty with discrete model occurs in the evaluation of performance of equalization techniques.

• The major difficulty is caused by correlation in the noise sequence V(k) at the out put of match filter.

• More convenient to deal with the white noise sequence when calculating error rate performance.

Thank you