Once the
carrier frequency and phase offsets have been removed, the conventional next step would be to use a
symbol- (or bit-) based detector. What we will present in this section is the performance gain in
widening the number of symbols (or bits) used to perform a decision on a single information signal.
We will maintain the naming convention of MBO [26]. This technique differs from the multiple symbol
differential detection (MSDD), to be discussed latter, in that as the observation window is made
larger, we still make a decision on a single bit of information rather than a sequence of bits.
In particular, we will observe n bits of a continuous phase FSK (CPFSK) waveform and perform
a decision on 1 bit, specifically the first bit in this observation window. For sake of simplicity let us
use binary CPFSK waveform with modulation index, b 0.5 or MSK modulation.
(4.40) (0 t T ) s(t) A(t) # cos cvct
pt
2T
# a1 u1 d
Here a1 data {1, 1} and u1 phase at the beginning of the observation interval. We can also
write down the FSK waveform during the ith bit time as
(4.41)
In the following interval
Since we have used the coherent detection receiver we will assume u1 is known to us and therefore
we will set it to zero for simplification.
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