Micro-programmed Adaptive Filtering Applications - Digital Design of Signal Processing Systems: A Practical Approach - page 458

channel effects. One of the most challenging problems in wireless communication is to device
algorithms and techniques that mitigate the impairments caused by multi-path fading effects of
a wireless channel. These paths result in multiple and time-delayed echoes of the transmitted signal
at the receiver. These delay spreads are up to tens of microseconds and result in inter-symbol
interference spreading over many data symbols. To cater for the multi-path effects, either multi-
carrier techniques like OFDM are used, or single sarrier (SC) techniques with more sophisticated
time and frequency equalizations are performed.
A transmitted signal in a typical wireless communication system can be represented as:

fs b ðtÞe j 2 pf c t sðtÞ¼ Re

where s b (t) and s(t) are baseband and passband signals, respectively, and f c is the carrier frequency.
This transmitted signal goes through multiple propagation paths and experiences different delays
t n (t) and attenuation a n (t) while propagating to a receiver antenna. The received signal at the antenna
is modeled as:

X

rðtÞ¼ a n ðtÞsðtt n ðtÞÞ

n

There are different channel models that statistically study the variability of the multi-path effects
in a mobile environment. Rayleigh and Ricean fading distributions [10-13] are generally used for
channel modeling. A time-varying tap delay-line system can model most of the propagation
environment. The model assumes L multiple paths and expresses the channel as:

L 1

h i ½n¼

0 h l d½nt l

l¼

where h l and t l are the complex-valued path gain and the path delay of the lth path, respectively.
There are a total of L paths that are modeled for a particular channel environment.
The time-domain equalizer implements a transversal filter. The length of the filter should be
greater than the maximumdelay that spreads over many symbols. In many applications this amounts
to hundreds of coefficients.

11.4.2 Example: NLMS Algorithm to Update Coefficients
This example demonstrates the use of an NLMS algorithm to update the coefficients of an equalizer.
Each frame of communication appends a training sequence. The sequence is designed such that it
helps in determining the start of a burst at the receiver. The sequence can also help in computing
frequency offset and an initial channel estimation. This channel estimation can also be used as the
initial guess for the equalizer. The receiver updates the equalizer coefficients and the rest of the data
is passed through the updated equalizer filter. In many applications a blind equalizer is also used for
generating the error signal from the transmitted data. This equalizer type compares the received
symbol with closest ideal symbol in the transmitted constellation. This error is then used for updating
the coefficients of the equalizer.
In this example, a transmitter periodically sends a training sequence t[n], with n N t 1 , for

the receiver to adapt the equalizer coefficients using the NLMS algorithm. The transmitter then
appends the data d[n] to form a frame. The frame consisting of data and the training is modulated
using QAM modulation technique. The modulated signal is transmitted. The signal goes through

¼ 0 ...