6.5.4 Differential-Based Statistics
This fourth quality estimation technique is based on the differential detector??™s output signal. Here we
will use the difference between adjacent time samples to determine if there is significant delay spread
or interference present in the channel. First we will rewrite the differential detector equations using
the Cartesian coordinate system.
(6.106)
(6.107)
We can clearly see if the expectation is taken on the real output signal, Xk, this resembles the sum
of the autocorrelations of the I- and Q-channels. Similarly, the expectation on the imaginary output
signal, Yk, resembles the difference of the cross-correlations of the I- and Q-channels.
Consider the real output, this is a measure of the similarity between the present symbol at time
instant k and the previous symbol at time instant k ??“ 1. Assuming an overall raised cosine pulse shaping
filter is employed in the system, then this is a measure of how much delay spread is present in the
channel. This output value should be averaged due to its discrete nature and calibrated against various
channel conditions. Let us assume a two-ray, frequency-selective fading channel where the separation
in time between the two rays is equal to sec.
Pages:
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544