mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
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MORE DETAILS 33<br />
2.2 MORE DETAILS<br />
So how well will MF work on average? In this section we will explore performance.<br />
We start with the Alice and Bob example. Let's substitute the model equations for<br />
ri and r 2 from (1.1) into (2.1), which gives<br />
zi = 181si - 90s 0 - 90s 2 + [-10m + 9n 2 ]. (2.3)<br />
The first term on the right-hand side (r.h.s.) is the desired symbol (s\) term. We<br />
want this term to be large in magnitude, relative to the other terms. The second<br />
and third terms are ISI terms, interference from the previous and next symbols.<br />
Sometimes these terms are large (e.g., when So and s 2 have the same sign) and<br />
sometimes small (e.g., when so and s 2 have opposite signs). The last term is the<br />
noise term. Like the ISI term, it can be big or small.<br />
It is useful to have a measure or figure-of-merit that indicates how well the receiver<br />
is performing. A commonly used measure is signal-to-noise-plus-interference<br />
ratio (SINR). SINR is defined as the ratio of the signal power to the sum of the<br />
interference and noise powers, i.e., S/(I+N). For MF, we are interested in output<br />
SINR (the SINR of z u the output of MF).<br />
To compute SINR, we need to add up the power of the ISI and noise terms. Since<br />
the symbol values and noise values are unrelated (uncorrelated), we can simply add<br />
the power of the individual terms (recall power is the average of the square). From<br />
(2.3), output SINR is given by<br />
SINR = -^ J~-T, ^ = 0.955 = -0.2 dB. (2.4)<br />
90 2 +90 2 + (10 2 +9 2 v ;<br />
)100<br />
As 0 dB corresponds to S = I + N, a negative SINR (in dB) means the signal power<br />
is less than the impairment power (sum of interference and noise powers).<br />
So, could we have done better by just using r\ or r 2 alone? If we could only use<br />
one received value to detect si, we would pick r 1; as it has the stronger copy of s\.<br />
Recall that r\ is modeled as<br />
Using one-tap MF, we would form<br />
r x = -lOsi +9s 0 + ηχ. (2.5)<br />
yi = -lOri. (2.6)<br />
To analyze performance, we can substitute the model (2.5) into (2.6), obtaining<br />
yi = lOOsi - 90s,, - 10m. (2.7)<br />
Applying our definition for SINR, the output SINR in this case would be<br />
SINR = (100 2 )/(90 2 + 10 2 (100)) = 0.5525 = -2.6 dB, (2.8)<br />
which is less than the MF output SINR of 0.955 (-0.2 dB). Thus, MF does better<br />
by taking advantage of all copies of the symbol of interest. The noise and ISI powers<br />
add, whereas the signal amplitudes add (the signal power is more than the sums of