4th unit DC

การส่ือสารดจิิตอลDigital Communicationรหัสวิชา EEG472

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Baseband Reception TechniquesRef. Amitabha Bhattacharya, "Digital Communication",

McGraw-Hill., 2006

Baseband Reception Techniques 2

Baseband Reception Techniques● How to safeguard a receiver system which has already been

contaminated with noise while traversing the channel.● The optimum receiving filter for accomplishing this goal is either a

matched filter or a correlator. ● An optional equalizing filter follows the receiving filter; it is only

needed for those systems where channel induced ISI has distorted the signal.

● The sampler needs precise timing info about the transmitter clock.


Baseband Reception Techniques● Noise in Communication Systems● Receiving Filter● Equalising Filter● Sampler● Detector


Noise in Communication Systems● Quantization Noise is a round-off or truncation error, present in all

digital signals.● Channel Noise is produced by varied sources, except thermal

noise, most other noises can be eliminated.● Inter Symbol Interference is always band-limited, hence it always

disperses or spreads a pulse waveform passing through it. When the channel bandwidth is close to the signal bandwidth, the spreading will exceed a symbol duration and cause signal pulses to overlap, which is called ISI.

● Timing Jitter is usually a random process and thus the sample positions cannot be accurately known.




Receiving Filter● The receiving filter places on the first line of defence against the

noise contamination by the channel.● A correlator● A matched filter

● Receiving filter delivers its best performance at the sampling instant of the sampler so that detection process becomes less errorprove.


Receiving Filter: Correlator Type Filter● Let the mth member of the N-dimensional signal set s

m(t) be

transmitted, get corrupted by noise n(t) in the channel and be received as r(t).

r(t) = sm(t) + n(t)

● the received signal r(t) can be decomposed into N components of a N-dimensional vector. This decomposition is in terms of the N basis functions {

n(t)}

● A correlator receiving filter supplies the correlated values of a received signal with all the members of the original signal set or the corresponding basis set.

● The optimum detector simply decides in favour of the symbol whose correlation with the received signal is maximum


Receiving Filter: Correlator Type Filter


Receiving Filter : Matched-Filter Type● Instead of using a bank of N correlators, we may as well use a

bank of N linear filters.● In this case, matched filters are matched to the basis functions

{n(t)}, not directly to the signal set {s

k}.

● Suppose impulse response of the kth filter amongst the N filters is :

● where {n(t)} are the N basis functions. The received signal r(t) is

passed through each of these filters and the corresponding output of the kth filter is,


Receiving Filter : Matched-Filter Type








Equalising Filter● Majority of practical digital communication channels can be

modelled as linear time-invariant (LTI) system, with a constant amplitude and linear phase frequency response.

● If we transmit the digital symbols at bandwidth slightly exceeding the channel bandwidth W, attenuation may occur, but no interference should occur.

● Practical systems are, however, non-ideal; their amplitude response is neither flat nor their phase response linear with frequency.

● Transmission of digital symbols through non-ideal channel at a transmission rate exceeding W results in interference among a number of adjacent symbols, which can tackle this inter-symbol interference by using Equalising Filter.


Equalising Filter : Inter Symbol Interference


Equalising Filter : Designing for Avoiding ISI● Nyquist Filter : [R

S = 2W]


Equalising Filter : Raised-cosine● Raised-cosine filter : [R

S < 2W]


Equalising Filter : Raised-cosine


Implementation of Equalising Filter● Linear Transversal Filter



Equalising Filter


Implementation of Equalising Filter


Graphical Display of ISI: Eye Pattern




Sampler● At this stage the signal is ready for detection.● The detector needs a discrete value representing the signal.● The precise job of the sampler is to give the detector this discrete

value of the signal. ● A sampler at a receiver has an added responsibility of

synchronization with the transmitted pulse stream.


Sampler : Synchronization




Detector● The detector should take a decision about which of the symbol has

been transmitted. ● During a symbol interval T

s, a baseband system may transmit one

out of M possible waveforms, g1(t), g

2(t), . . ., g

M(t).

● In the binary threshold detection, for a threshold level , the decision is based on the choice of one of the following two hypotheses, namely,


Detector : Maximum Likelihood Detector● Two equally likely symbols, we can safely decide in favour of a

particular transmitted symbol whose likelihood function is greater than the other.

● This strategy is called maximum likelihood detection and is quite a popular scheme due to its logical soundness and simplicity.

● A maximum likelihood detector would place the threshold for equally likely binary symbols at the intersection point of the two likelihood functions p(r | g

1) and p(r | g

2), so that to the left of the

threshold , the likelihood of g2(t) is more than that of g

1(t) and the

opposite is the case at the right of the threshold.


Detector : Maximum Likelihood Detector


Detector● What happens if the symbols are not equally likely?● For a received signal sample value of r, compare the following two

probabilities: (a) the probability that the symbol 1 was transmitted and r has been the received signal's sample value. (b) the probability that the symbol 0 was transmitted and r has been the received signal's sample value.

● The greater of the two probabilities give us the most likely symbol that was transmitted.


Detector● The probabilities (a) and (b) can also be called a posteriori

probability because they give the probability of transmission of a symbol when the received signal's sampled value r is already known.

● Detectors based on choosing the symbol whose a posteriori probability is maximum is also known as a MAP detector

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4th unit DC