Performance of the optimal ESP is a function of ρ, and the performance of the optimal PIC with an OIB is dependent on ρ and γo. Thus, performance comparison of the two processors depends on the relative values of these two constants.
First, consider a case where the precise interference direction is known. Let the interference beam be formed using an OIB given by
A simple calculation indicates that for the interference beamformer weights given by (6.91) and (6.92), γ
o attains its maximum value and
 |
(6.93) |
A comparison of the results derived in
optimal beamformer and
PIC beamformer reveals that for this case the output powers and the SNRs of the two processors are identical (see
(4.42) and
(6.75)). Thus, if the interference beam of the PIC is formed by an OIB for which (6.93) holds, then the performance of the optimal PIC is identical to the performance of the optimal ESP.
| However, if the interference beam of the PIC is formed by an OIB for which |
|
 |
(6.94) |
then a comparison of the results for the two processors (an expression for Pˆ
N results using
(4.20) and
(4.41) reveals that
 |
(6.95) |
| and |
|
 |
(6.96) |
Thus, the total noise power at the output of the optimal PIC in this case is more than the total noise power at the output of the optimal ESP, and the SNR achievable by the optimal PIC is less than that achievable by the optimal ESP. It follows from
(4.42) and
(6.75) that the ratio of the two SNRs is given by
 |
(6.97) |
| For σn^2/LP1<<γo, this ratio reduces to |
|
 |
(6.98) |
and depends on the relative values of ρ and γo. Furthermore, if ρ = 1, then it follows from (6.98) that the output SNRs of the two processors are approximately the same. Plots of (6.98) for four values of ρ as a function of γo are shown in Figure 20. The figure shows that the difference in the output SNRs of the two processors is smaller for the larger values of these constants and increases as these constants decrease.
In the next page Comparison in Presence of Look Direction Errors is discussed.
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