Maximaum likelihood timing estimation

Presented By :- Diwaker Pant ME (REGULAR 2011) NITTTR CHD June 9, 2022 1 Presented by :- Diwaker Pant

Transcript of Maximaum likelihood timing estimation

Page 1: Maximaum likelihood timing estimation

Presented By :- Diwaker PantME (REGULAR 2011)NITTTR CHD

April 13, 2023 1Presented by :- Diwaker Pant

Page 2: Maximaum likelihood timing estimation

In a digital communication system, the o/p of the demodulator must be sampled periodically at the symbol rate at the precise sampling time instants

tm = mT +τ, where

T: symbol interval τ: time delay, which accounts for the propagation time of the

signal from the transmitter to the receiver.

To perform this periodic sampling, we require a clock signal at the receiver.

The process of extracting such a clock signal at the receiver is usually called symbol synchronization or timing recovery.

April 13, 2023 2Presented by :- Diwaker Pant

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Timing recovery is one of the most critical functions that is performed at the receiver of a synchronous digital communication system.

Two important considerations are there as far as receiver is concerned

1.The receiver must know the freq. at which the o/p of the matched filter are sampled.

2.Where to take the samples within each symbol interval.

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Symbol sync. Can be achieved in many ways as follows.

In some communication systems, the transmitter and receiver clocks are synchronized to a master clock, which provides a very precise timing signal.

In this case, the receiver must estimate and compensate for the relative time delay between the transmitted and received signals.

For e.g. Radio communication system in VLF band (below 30 kHz) where precise clock signals are transmitted from a master radio station.

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In another method we simultaneously transmit the clock frequency 1/T or a multiple of 1/T along with the information signal.

The receiver may simply employ a narrowband filter tuned to the transmitted clock frequency, for extracting the clock signal for sampling.

Advantage: - simple to implement.

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1.The transmitter must allocate some of its available power to the transmission of the clock signal.

2.Some small fraction of the available channel bandwidth must be allocated for the transmission of the clock signal.

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In spite of these disadvantages, this method is frequently used in telephone transmission systems that employ large bandwidths to transmit the signals of many users.

In such a case, the transmission of a clock signal is shared in the demodulation of the signals among the many users.

Through this shared use of the clock signal, the penalty in the transmitter power and in bandwidth allocation is reduced proportionally by the number of users.

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In another method clock signal can also be obtained from the received data signal.

This method is called self synchronization.

Self synchronization is classified into two categories namely-:

1.Decision Directed Timing Estimation.

Also known as Maximum Likelihood Timing Estimation.

2.Non-Decision Directed Timing Estimation.

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Our aim is to obtain the ML estimate of time delay(τ).

Let us start with the baseband PAM waveform, it is represented as

……………(1) where ……………(2)

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In Decision-directed timing estimators the information symbols from the output of the demodulator are treated as the known transmitted sequence.

In this case, the log-likelihood function has the form as




is the coefficient of Log -Likelihood Function.

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By putting the value of eq. (2) into eq. (3) we get ……..(4)


Where …………(5)

Where Eq.(5) represents the output of Matched Filter.

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From calculus we know that for to be the ML estimate of τ:



So if the first derivative of Log-Likelihood Function w.r.t. time delay is equal to zero then ML of time delay is achieved.

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Implementation of Eq.(6) is given by fig below.

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Matched Filter g(-t)

r(t) Sampler


Sampling &Threshold Decision

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We should observed that the summation in the loop serves as the loop filter whose bandwidth is controlled by the length of the sliding window in the summation.

The output of the loop filter drives the voltage-controlled clock (VCC), or voltage-controlled oscillator, which controls the sampling times for the input of the loop.

Since the detected information sequence {In} is used in the estimation of τ, the estimate is decision-directed.

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? Querry

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REFFERENCES John G. Proakis , Masoud Salehi, Digital


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