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Techniques to control noise and fading. Noise and fading are the primary sources of distortion in communication channels Techniques to reduce noise and fading are usually implemented at the receiver

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Techniques to control noise and fading
Techniques to control noise and fading

  • Noise and fading are the primary sources of distortion in communication channels

  • Techniques to reduce noise and fading are usually implemented at the receiver

  • The most common mechanism is to have a receiver filter that can cancel the effects of noise and fading, at least partially

  • Digital technology has made it possible to have adaptive filters

Principle of equalization
Principle of Equalization

  • Equalization is the process of compensation at the receiver, to reduce noise effects

  • The channel is treated as a filter with transfer function

  • Equalization is the process of creating a filter with an inverse transfer function of the channel

  • Since the channel is a varying filter, equalizer filter also has to change accordingly, hence the term adaptive.

Equalization model signal detection
Equalization Model-Signal detection





Front End

IF Stage

Message signal x(t)


Detected signal y(t)

Equalization model correction
Equalization model-Correction










Equalizer System EquationsDetected signaly(t) = x(t) * f(t) + nb(t)=> Y(f) = X(f) F(f) + Nb(f)Output of the Equalizer ^ d(t) = y(t) * heq(t)

Equalizer System EquationsDesired output ^ D(f) = Y(f) Heq(f) = X(f) => Heq(f) X(f) F(f) = X(f)=> Heq(f) F(f) = 1Heq(f) = 1/ F(f) => Inverse filter

System equations
System Equations


MSE Error =

Aim of equalizer: To minimize MSE error

Equalizer operating modes
Equalizer Operating Modes

  • Training

  • Tracking

Training and tracking functions
Training and Tracking functions

  • The Training sequence is a known pseudo-random signal or a fixed bit pattern sent by the transmitter. The user data is sent immediately after the training sequence

  • The equalizer uses training sequence to adjust its frequency response Heq (f) and is optimally ready for data sequence

  • Adjustment goes on dynamically, it is adaptable equalizer

Block diagram of digital equalizer
Block Diagram of Digital Equalizer










Adaptive Algorithm

Digital equalizer equations
Digital Equalizer equations

  • In discrete form, we sample signals at interval of ‘T’ seconds : t = k T;

  • The output of Equalizer is:

Error minimization
Error minimization

  • The adaptive algorithm is controlled by the error signal,

The equalizer weights are varied until convergence is reached.

Types of equalizers
Types of equalizers

  • Linear Equalizers.

  • Non Linear Equalizers.

Diversity techniques
Diversity techniques

  • Powerful communications receiver technique that provides wireless link improvement at relatively low cost.

  • Unlike equalization, diversity requires no training overhead.

Principle of diversity
Principle of diversity

  • Small Scale fading causes deep and rapid amplitude fluctuations as mobile moves over a very small distances.

Principle of diversity1
…Principle of diversity

  • If we space 2 antennas at 0.5 m, one may receive a null while the other receives a strong signal. By selecting the best signal at all times, a receiver can mitigate or reduce small-scale fading. This concept is Antenna Diversity.

Diversity improvement
Diversity Improvement

  • Consider a fading channel (Rayleigh)

    Input s(t) Output r(t)

  • Input-output relation

    r (t) =  (t) e -j q(t) s (t) + n (t)

  • Average value of signal to noise ratio


    SNR =  = (Eb / No) 2 (t)


Average snr improvement using diversity
Average SNR Improvement Using Diversity

  • p.d.f., p(γi) = (1 /  ) e – γi / 

    where (γi 0 ) and γi = instantaneous SNR

    Probability [γiγ]

  • M diversity branches,

    Probability [γi>γ]

Average snr improvement using diversity1
Average Snr Improvement Using Diversity

  • Average SNR improvement using selection Diversity,

  • Example : Assume that 5 antennas are used to provide space diversity. If average SNR is 20 dB, determine the probability that the SNR will be  10 dB. Compare this with the case of a single receiver.

    Solution :

     = 20 dB => 100.

    Threshold γ = 10 dB = 10.


Prob[γi>γ] = 1 – (1 – e – γ/ )M

For M = 5,

Prob= 1 – (1 – e – 0.1)5 = 0.9999

For M = 1(No Diversity),

Prob= 1 – (1 – e – 0.1)= 0.905

Maximal ratio combining mrc
Maximal Ratio Combining (MRC)

  • MRC uses each of the M branches in co-phased and weighted manner such that highest achievable SNR is available. If each branch has gain Gi,

    rM = total signal envelope


Maximal ratio combining mrc1
…Maximal Ratio Combining (MRC)

… assuming each branch has some average noise power N, total noise power NT applied to the detector is,

EXAMPLE : Repeat earlier problem for MRC case



Types of diversity
Types of diversity

  • Space Diversity

    • Either at the mobile or base station.

    • At base station, separation on order of several tens of wavelength are required.

  • Polarization Diversity

    • Orthogonal Polarization to exploit diversity

Types of diversity1
…Types of diversity

  • Frequency Diversity :

    • More than one carrier frequency is used

  • Time Diversity :

    • Information is sent at time spacings

    • Greater than the coherence time of Channel, so multiple repetitions can be resolved

Practical diversity receiver rake receiver
Practical diversity receiver – rake receiver

  • CDMA system uses RAKE Receiver to improve the signal to noise ratio at the receiver.

  • Generally CDMA systems don’t require equalization due to multi-path resolution.

Block diagram of rake receiver
Block Diagram Of Rake Receiver


M1 M2 M3α2

r(t) αM Z’ Z

Correlator 1

 ()dt

Correlator 2


Correlator M




Principle of operation
Principle Of Operation

  • M Correlators – Correlator 1 is synchronized to strongest multi-path M1. The correlator 2 is synchronized to next strongest multipath M2 and so on.

  • The weights 1 , 2 ,……,M are based on SNR from each correlator output. ( is proportional to SNR of correlator.)

  • M Z’ = M ZM

    m =1

Principle of operation1
…Principle Of Operation

  • Demodulation and bit decisions are then based on the weighted Outputs of M Correlators.