Equalization - Digital Communication: Principles and System Modelling - page 105

Thus, set of (2N + 1) linear equations are obtained for coefficients of zero forcing
equalization . Equation ( 5.26 ) also may be expressed in matrix form as

Pc = q (5.27)

where, P is a (2 N , c is

the (2 N+1) coefficient vector, and q is the (2 N+1) column vector with non-zero
elements.

+ 1) × (2 N + 1) matrix with elements { p ( mT B − n τ ) }

5.6 Adaptive Equalizer

From the previous sections, we have found that, by adjusting the tap gains, proper
equalization can be obtained. For practical systems, the situation is somewhat more
critical. In practice, the channel response is time-variant and may be non-linear.
Therefore, the tap gains need to be adjusted automatically time to time. These type
equalizers with the provision of automatic and adaptive tap-gain adjustment are the
adaptive equalizers . As shown in the Fig. 5.11 , 16 point QAM signal is transmitted
through a dispersed channel. The eye diagram suggests, proper choice of sampling
instant is almost impossible in this case, and in the constellation diagram also, it is
showing more than 16 points in the I-Q plane. After passing through an adaptive

Fig. 5.11 ( a )and( c ) Eye plot and constellation diagram of 16 point QAM passed through distorted
channel, ( b )and( d ) Eye plot and constellation diagram of the signal when passed through an
adaptive equalizer