# 7.7 Mitigation to combat frequency-selective distortion

 Page 1 / 1

Equalization can mitigate the effects of channel-induced ISI brought on by frequency-selective fading. It can help modify system performance described by the curve that is “awful” to the one that is merely “bad.” The process of equalizing for mitigating ISI effects involves using methods to gather the dispersed symbol energy back into its original time interval.

An equalizer is an inverse filter of the channel. If the channel is frequency selective, the equalizer enhances the frequency components with small amplitudes and attenuates those with large amplitudes. The goal is for the combination of channel and equalizer filter to provide a flat composite-received frequency response and linear phase.

Because the channel response varies with time, the equalizer filters must be adaptive equalizers .

The decision feedback equalizer (DFE) involves:

1) a feedforward section that is a linear transversal filter whose stage length and tap weights are selected to coherently combine virtually all of the current symbol’s energy.

2) a feedback section that removes energy remaining from previously detected symbols.

The basic idea behind the DFE is that once an information symbol has been detected, the ISI that it induces on future symbols can be estimated and subtracted before the detection of subsequent symbols.

A maximum-likelihood sequence estimation (MLSE) equalizer: tests all possible data sequences and chooses the data sequence that is the most probable of all the candidates. The MLSE is optimal in the sense that it minimizes the probability of a sequence error. Since the MLSE equalizer is implemented by using Viterbi decoding algorithm , it is often referred to as the Viterbi equalizer .

Direct-sequence spread-spectrum (DS/SS) techniques can be used to mitigate frequency-selective ISI distortion because the hallmark of spread-spectrum systems is their capability of rejecting interference, and ISI is a type of interference.

Consider a DS/SS binary phase-shift keying (PSK) communication channel comprising one direct path and one reflected path. Assume that the propagation from transmitter to receiver results in a multipath wave that is delayed by $\tau$ compared to the direct wave. The received signal, $r\left(t\right)$ , neglecting noise, can be expressed as follows:

$r\left(t\right)=\text{Ax}\left(t\right)g\left(t\right)\text{cos}\left({2\pi f}_{c}t\right)+\alpha \text{Ax}\left(t-\tau \right)g\left(t-\tau \right)\text{cos}\left({2\pi f}_{c}t+\theta \right)$

where $x\left(t\right)$ is the data signal, $g\left(t\right)$ is the pseudonoise (PN) spreading code, and $\tau$ is the differential time delay between the two paths. The angle $\theta$ is a random phase, assumed to be uniformly distributed in the range $\left(0,2\pi \right)$ , and $\alpha$ is the attenuation of the multipath signal relative to the direct path signal.

The receiver multiplies the incoming $r\left(t\right)$ by the code $g\left(t\right)$ . If the receiver is synchronized to the direct path signal, multiplication by the code signal yields the following:

$r\left(t\right)g\left(t\right)=\text{Ax}\left(t\right){g}^{2}\left(t\right)\text{cos}\left({2\pi f}_{c}t\right)+\alpha \text{Ax}\left(t-\tau \right)g\left(t\right)g\left(t-\tau \right)\text{cos}\left({2\pi f}_{c}t+\theta \right)$

where ${g}^{2}\left(t\right)=1$ . If $\tau$ is greater than the chip duration, then

$\mid \int g\left(t\right)g\left(t-\tau \right)\text{dt}\mid \le \mid \int {g}^{2}\left(t\right)\text{dt}\mid$

over some appropriate interval of integration (correlation). Thus, the spread spectrum system effectively eliminates the multipath interference by virtue of its code-correlation receiver. Even though channel-induced ISI is typically transparent to DS/SS systems, such systems suffer from the loss in energy contained in the multipath components rejected by the receiver. The need to gather this lost energy belonging to a received chip was the motivation for developing the Rake receiver .

A channel that is classified as flat fading can occasionally exhibit frequency-selective distortion when the null of the channel’s frequency-transfer function occurs at the center of the signal band. The use of DS/SS is a practical way of mitigating such distortion because the wideband SS signal can span many lobes of the selectively faded channel frequency response. This requires the spread-spectrum bandwidth ${W}_{\text{ss}}$ (or the chip rate ${R}_{\text{ch}}$ ), to be greater than the coherence bandwidth ${f}_{0}$ . The larger the ratio of ${W}_{\text{ss}}$ to ${f}_{0}$ , the more effective will be the mitigation.

Frequency-hopping spread-spectrum (FH/SS) : can be used to mitigate the distortion caused by frequency-selective fading, provided that the hopping rate is at least equal to the symbol rate. FH receivers avoid the degradation effects due to multipath by rapidly changing in the transmitter carrier-frequency band, thus avoiding the interference by changing the receiver band position before the arrival of the multipath signal.

Orthogonal frequency-division multiplexing (OFDM) : can be used for signal transmission in frequency-selective fading channels to avoid the use of an equalizer by lengthening the symbol duration. The approach is to partition (demultiplex) a high symbol-rate sequence into $N$ symbol groups, so that each group contains a sequence of a lower symbol rate (by the factor $1/N$ ) than the original sequence. The signal band is made up of $N$ orthogonal carrier waves, and each one is modulated by a different symbol group. The goal is to reduce the symbol rate (signaling rate), $W\approx 1/{T}_{s}$ , on each carrier to be less than the channel’s coherence bandwidth ${f}_{0}$ .

Pilot signal is the name given to a signal intended to facilitate the coherent detection of waveforms. Pilot signals can be implemented in the frequency domain as in-band tones, or in the time domain as digital sequences that can also provide information about the channel state and thus improve performance in fading conditions.

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!