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# Techniques to control noise and fading - PowerPoint PPT Presentation

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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Presentation Transcript

• 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

• 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.

Carrier

Transmitter

Channel

Front End

IF Stage

Message signal x(t)

Detector

Detected signal y(t)

Reconstructed

Signal

nb(t)

Decision

Maker

Equalizer

+

Equivalent

Noise

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

Error

MSE Error =

Aim of equalizer: To minimize MSE error

• Training

• Tracking

• 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

Z-1

Z-1

Z-1

w2k

w0k

w1k

wNk

-

+

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

• The output of Equalizer is:

• The adaptive algorithm is controlled by the error signal,

The equalizer weights are varied until convergence is reached.

• Linear Equalizers.

• Non Linear Equalizers.

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

• Unlike equalization, diversity requires no training overhead.

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

• 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.

• 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)

Channel

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 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

• 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

=

… 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

e-0.1

• 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

• 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

• 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.

α1

M1 M2 M3α2

r(t) αM Z’ Z

Correlator 1

 ()dt

Correlator 2

Σ

Correlator M

>

<

m’(t)

• 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

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