wireless communication

1. (50 points) We consider a Rayleigh fading signal. Suppose that a single branch receiver has a 10% chance of being 5 dB below a certain SNR threshold γo. a) Determine the mean of the Rayleigh fading signal as reference to the threshold mentioned in the above, i.e., γo. b) What is the probability that the receiver signal will be 8 dB below γo if b1) a single branch receiver b2) a two branch selection diversity receiver  b3) a three branch selection diversity receiver, or b4) a four branch selection diversity receiver is used, respectively.  

2. (50 points) Consider a two-tap adaptive equalizer shown below, where )/2cos( Nky k   and ) /2sin(10 N kd k   with N>2. Find the minimum MSE and the corresponding equalizer weights 1 ,ww o . 

1Z

+

ky 1 ky

0w 1 w

+k

x

kd