mohatta2015.pdf

MORE DETAILS 33
2.2 MORE DETAILS
So how well will MF work on average? In this section we will explore performance.
We start with the Alice and Bob example. Let's substitute the model equations for
ri and r 2 from (1.1) into (2.1), which gives
zi = 181si - 90s 0 - 90s 2 + [-10m + 9n 2 ]. (2.3)
The first term on the right-hand side (r.h.s.) is the desired symbol (s\) term. We
want this term to be large in magnitude, relative to the other terms. The second
and third terms are ISI terms, interference from the previous and next symbols.
Sometimes these terms are large (e.g., when So and s 2 have the same sign) and
sometimes small (e.g., when so and s 2 have opposite signs). The last term is the
noise term. Like the ISI term, it can be big or small.
It is useful to have a measure or figure-of-merit that indicates how well the receiver
is performing. A commonly used measure is signal-to-noise-plus-interference
ratio (SINR). SINR is defined as the ratio of the signal power to the sum of the
interference and noise powers, i.e., S/(I+N). For MF, we are interested in output
SINR (the SINR of z u the output of MF).
To compute SINR, we need to add up the power of the ISI and noise terms. Since
the symbol values and noise values are unrelated (uncorrelated), we can simply add
the power of the individual terms (recall power is the average of the square). From
(2.3), output SINR is given by
SINR = -^ J~-T, ^ = 0.955 = -0.2 dB. (2.4)
90 2 +90 2 + (10 2 +9 2 v ;
)100
As 0 dB corresponds to S = I + N, a negative SINR (in dB) means the signal power
is less than the impairment power (sum of interference and noise powers).
So, could we have done better by just using r\ or r 2 alone? If we could only use
one received value to detect si, we would pick r 1; as it has the stronger copy of s\.
Recall that r\ is modeled as
Using one-tap MF, we would form
r x = -lOsi +9s 0 + ηχ. (2.5)
yi = -lOri. (2.6)
To analyze performance, we can substitute the model (2.5) into (2.6), obtaining
yi = lOOsi - 90s,, - 10m. (2.7)
Applying our definition for SINR, the output SINR in this case would be
SINR = (100 2 )/(90 2 + 10 2 (100)) = 0.5525 = -2.6 dB, (2.8)
which is less than the MF output SINR of 0.955 (-0.2 dB). Thus, MF does better
by taking advantage of all copies of the symbol of interest. The noise and ISI powers
add, whereas the signal amplitudes add (the signal power is more than the sums of