mohatta2015.pdf

178 PRACTICAL CONSIDERATIONS
Figure 8.2
Complex plane.
where θ(πιΤ) is the phase noise. While the phase noise is random, it usually varies
slowly with time and can often be folded into the channel coefficients, giving rise
to time-varying channel coefficients. It can also be dealt with as part of AFC using
an approach that tracks phase and frequency error in time. In the complex plane,
the phase noise introduces a phase offset.
A third radio aspect is I/Q imbalance. With this problem, either the real part
or imaginary part has been scaled by an unknown multiplier. Thus, if rfc should be
a + jb, instead it is ka + jb, where k is the unknown multiplier. The radio front
end is designed to make k as close to one as possible.
A fourth radio aspect is DC offset. With direct conversion receivers, sometimes
the local copy of the carrier frequency used for mixing leaks into the signal path.
This gives rise to a constant term being added to the received signal. This problem
is called direct-current (DC) offset because it is analogous to power generation,
which can be DC or AC (alternating current).
Another practical aspect is sampling and quantization. An analog-to-digital
(A/D) convertor is typically used to sample the partial MF signal and represent
the samples with a finite number of bits.
8.3 THE MATH
We will use this section to explore a particular aspect of parameter estimation,
channel coefficient estimation. We will assume some initial filtering and sampling
of the signal, giving us r(mT s ).