Maximumlikelihood estimation of admixture proportions from genetic data Jinliang Wang.
Maximaum likelihood timing estimation

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Transcript of Maximaum likelihood timing estimation
Presented By : Diwaker PantME (REGULAR 2011)NITTTR CHD
April 13, 2023 1Presented by : Diwaker Pant
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
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.
April 13, 2023 5Presented by : Diwaker Pant
Disadvantages:
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.NonDecision 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 Decisiondirected timing estimators the information symbols from the output of the demodulator are treated as the known transmitted sequence.
In this case, the loglikelihood function has the form as
Where
10
………(3)
is the coefficient of Log Likelihood Function.
April 13, 2023Presented by : Diwaker Pant
By putting the value of eq. (2) into eq. (3) we get ……..(4)
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Where …………(5)
Where Eq.(5) represents the output of Matched Filter.
April 13, 2023Presented by : Diwaker Pant
From calculus we know that for to be the ML estimate of τ:
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….…….(6)
So if the first derivative of LogLikelihood Function w.r.t. time delay is equal to zero then ML of time delay is achieved.
April 13, 2023Presented by : Diwaker Pant
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Implementation of Eq.(6) is given by fig below.
April 13, 2023Presented by : Diwaker Pant
Matched Filter g(t)
r(t) Sampler
VCC
Sampling &Threshold Decision
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 voltagecontrolled clock (VCC), or voltagecontrolled 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 decisiondirected.
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? Querry
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REFFERENCES John G. Proakis , Masoud Salehi, Digital
Communications.
www.google.com
www.wikipedia.com
April 13, 2023 16Presented by : Diwaker Pant
April 13, 2023 17Presented by : Diwaker Pant