youssef123456
Newbie level 2
HELP PLEASE
I NEED HELP IN MY PROJCTE PLEASE ANY ONE
THIS IS THE PROJCTE
BACKGROUND:
In wireless environments, each transmitted signal is received via different paths because of reflectors located between the transmitter and receiver. This phenomenon is called multipath fading, which causes the amplitude of the received signal to vary randomly. Frequently, the signal amplitude is modeled as a Rayleigh random variable. A key performance measure in fading environments is the outage probability defined as the probability that the received signal power falls below a specified threshold. The threshold is the power level below which the receiver fails to recognize and detect the signal. Clearly, it depends on the modulation and channel coding schemes employed.
Multipath fading degrades the performance of wireless systems significantly. Diversity is a technique that reduces this degradation by providing the receiver with independent copies of the signal. Diversity can be provided using time, frequency or space domains. The receiver can process (combine) the obtained copies (branches) differently. The optimal solution is the maximum-ratio combining (MRC), in which the receiver scales each branch by its amplitude and sums the results. The simplest solution is the selection combining (SC) where the receiver selects the branch whose instantaneous power is the maximum.
PROCEDURE:
PLEASE IMPLEMENT THE FOLLOWING TASKS USING MATLAB:
I. Design for Rayleigh Fading:
(a) Generate two zero-mean independent Gaussian random vectors (say of length 5x104 each) using “randn” command, call them n1 and n2. Set the variance of n1 and n2 according to the signal average power ( to be determined below.
(b) Form the vector r = (n12 +n22)1/2. This is a Rayleigh random vector. Plot the histograms of n1, n2 and r using “hist” command (use 50 columns at least) for = E(r2) = 10,20 dB. Comment on your results. Here, r describes the random variation of the signal amplitude.
(c) Form = r2, which is an exponential random vector, and plot its histogram for = 10,20 dB. Comment on your results. Here, describes the random variations in the signal power.
(d) Calculate the outage probability Po = Pr(<b) for b = 10, 20 dB. This is just a number.
(e) Generate n1, n2 and vectors and calculate Po as in (a)-(d) by varying from 0-30 dB with a step size of 5 dB. Plot Po versus for b = 10,20 dB. Comment on your results.
(f) For b= 10,20 dB, design the minimum signal power levels required for Po not to exceed 1% and 5%. Comment on your results.
II. SC for Rayleigh Fading:
(a) Generate L independent Rayleigh random vectors, with an average power , call them rl, l=1,2, …,L. Form the vectors l = rl2, l=1,2, …,L.
(b) Form the output of the SC receiver as SC = max(1,2,…,L). Draw its histogram for = 10 dB and L=2,3,4. Compare with the histogram of found in part (I-c).
(c) Plot Po = Pr(SC<b) versus (0-20 dB with a step of 5 dB) for b = 10 dB and L=2,3,4. Compare with results found in part (I-e).
(d) For L=2,3,4 and b = 10 dB, design the minimum signal power levels required for Po not to exceed 1% and 5%. Compare with results found in part (I-f).
III. MRC for Rayleigh Fading:
(a) Repeat part II-(a).
(b) Form the output of the MRC receiver as MRC = sum(1,2,…,L). Draw its histogram for = 10 dB and L=2,3,4. Compare with results found in parts (I-c) and (II-b).
(c) Plot Po = Pr(MRC<b) versus (0-20 dB with a step of 5 dB) for b = 10 dB and L=2,3,4. Compare with results found in parts (I-e) and (II-c).
(d) For L=2,3,4 and b = 10 dB, design the minimum signal power levels required for Po not to exceed 1% and 5%. Compare with results found in parts (I-f) and (II-d).
PLEASE HELP ME URGNT
I NEED HELP IN MY PROJCTE PLEASE ANY ONE
THIS IS THE PROJCTE
BACKGROUND:
In wireless environments, each transmitted signal is received via different paths because of reflectors located between the transmitter and receiver. This phenomenon is called multipath fading, which causes the amplitude of the received signal to vary randomly. Frequently, the signal amplitude is modeled as a Rayleigh random variable. A key performance measure in fading environments is the outage probability defined as the probability that the received signal power falls below a specified threshold. The threshold is the power level below which the receiver fails to recognize and detect the signal. Clearly, it depends on the modulation and channel coding schemes employed.
Multipath fading degrades the performance of wireless systems significantly. Diversity is a technique that reduces this degradation by providing the receiver with independent copies of the signal. Diversity can be provided using time, frequency or space domains. The receiver can process (combine) the obtained copies (branches) differently. The optimal solution is the maximum-ratio combining (MRC), in which the receiver scales each branch by its amplitude and sums the results. The simplest solution is the selection combining (SC) where the receiver selects the branch whose instantaneous power is the maximum.
PROCEDURE:
PLEASE IMPLEMENT THE FOLLOWING TASKS USING MATLAB:
I. Design for Rayleigh Fading:
(a) Generate two zero-mean independent Gaussian random vectors (say of length 5x104 each) using “randn” command, call them n1 and n2. Set the variance of n1 and n2 according to the signal average power ( to be determined below.
(b) Form the vector r = (n12 +n22)1/2. This is a Rayleigh random vector. Plot the histograms of n1, n2 and r using “hist” command (use 50 columns at least) for = E(r2) = 10,20 dB. Comment on your results. Here, r describes the random variation of the signal amplitude.
(c) Form = r2, which is an exponential random vector, and plot its histogram for = 10,20 dB. Comment on your results. Here, describes the random variations in the signal power.
(d) Calculate the outage probability Po = Pr(<b) for b = 10, 20 dB. This is just a number.
(e) Generate n1, n2 and vectors and calculate Po as in (a)-(d) by varying from 0-30 dB with a step size of 5 dB. Plot Po versus for b = 10,20 dB. Comment on your results.
(f) For b= 10,20 dB, design the minimum signal power levels required for Po not to exceed 1% and 5%. Comment on your results.
II. SC for Rayleigh Fading:
(a) Generate L independent Rayleigh random vectors, with an average power , call them rl, l=1,2, …,L. Form the vectors l = rl2, l=1,2, …,L.
(b) Form the output of the SC receiver as SC = max(1,2,…,L). Draw its histogram for = 10 dB and L=2,3,4. Compare with the histogram of found in part (I-c).
(c) Plot Po = Pr(SC<b) versus (0-20 dB with a step of 5 dB) for b = 10 dB and L=2,3,4. Compare with results found in part (I-e).
(d) For L=2,3,4 and b = 10 dB, design the minimum signal power levels required for Po not to exceed 1% and 5%. Compare with results found in part (I-f).
III. MRC for Rayleigh Fading:
(a) Repeat part II-(a).
(b) Form the output of the MRC receiver as MRC = sum(1,2,…,L). Draw its histogram for = 10 dB and L=2,3,4. Compare with results found in parts (I-c) and (II-b).
(c) Plot Po = Pr(MRC<b) versus (0-20 dB with a step of 5 dB) for b = 10 dB and L=2,3,4. Compare with results found in parts (I-e) and (II-c).
(d) For L=2,3,4 and b = 10 dB, design the minimum signal power levels required for Po not to exceed 1% and 5%. Compare with results found in parts (I-f) and (II-d).
PLEASE HELP ME URGNT
