A practical limitation of an adaptive antenna array using the LMS algorithm is the dynamic range over which the array can operate. This limitation is due to the fact that the speed of response of the weights in the [MS algorithm is proportional to the average signal power at the array input.

(a) Justify the assertion that the dynamic range of average signal power at the array input is proportional to R_b/f _max where R_b is the data rate in b/s and f _max is the maximum fade rate in Hz.

(b) Assuming a proportionality factor of 0.2, by which the ratio R_b/f _max is scaled, calculate the dynamic range of an adaptive antenna array using the LMS algorithm for R_b = 32 kb/s and f _max = 70 Hz. Comment on your result. (The proportionality factor of 0.2 is a reasonable choice for systems using PSK.)