Reference no: EM131083945
In this problem, we evaluate the bit error rate (BER) performance of the CDMA communications system introduced in Problem 8.3.9. In our experiments, we will make the following additional assumptions.
- In practical systems, code vectors are generated pseudorandomly. We will assume the code vectors are random. For each transmitted data vector X, the code vector of user i will be
Where the components Sij are iid random variables such that PSij (1) = PSij (-1) = 1/2. Note that the factor 1/ √n is used so that each code vector Si has length 1: ||Si||2 = S'iSi
= 1.
- Each user transmits at 6dB SNR. For convenience, assume Pi= p = 4 and σ2= 1.
(a) Use Matlab to simulate a CDMA system with processing gain n = 16. For each experimental trial, generate a random set of code vectors {Si}, data vector X, and noise vector N. Find the ML estimate x∗ and count the number of bit errors; i.e., the number of positions in which x∗ i ≠ Xi. Use the relative frequency of bit errors as an estimate of the probability of bit error. Consider k = 2, 4, 8, 16 users. For each value of k, perform enough trials so that bit errors are generated on 100 independent trials. Explain why your simulations take so long.
(b) For a simpler detector known as the matched filter, when Y = y, the detector decision for user i is 
Where sgn (x) = 1 if x > 0, sgn (x) = -1 if x
Problem 8.3.9
In a code division multiple access (CDMA) communications system, k users share a radio channel using a set of n-dimensional code vectors {S1,..., Sk} to distinguish their signals. The dimensionality factor n is known as the processing gain. Each user i transmits independent data bits Xi such that the vector X = [X1 ··· Xn] has iid components with PXi(1) = PXi(-1) = 1/2. The received signal is
Where N is a Gaussian (0, σ2I) noise vector From the observation Y, the receiver performs a multiple hypothesis test to decode the data bit vector X.
(a) Show that in terms of vectors,
(b) Given Y = y, show that the MAP and ML detectors for X are the same and are given by
Where Bn is the set of all n dimensional vectors with ±1 elements
(c) How many hypotheses does the ML detector need to evaluate?
|
Evaluate its dft x(k)
: Given a sequence x(n), where x(0) = 0:8, x(1) = 0:6, x(2) = 0:4, and x(3) = 0:2 with two additional zero-padded data points x(4) = 0 and x(5) = 0, evaluate its DFT X(k).
|
|
Does that mean function cannot have zero between a and b
: For the intermediate value theorem why do you think it is necessary for the signs of f(a) and f(b) to be different in order to guarantee there is a zero between a and b.
|
|
Question regarding the maximum error of estimate
: In the formula for the Confidence Interval for the Mean, besides E, what group of symbol(s) represents the Maximum Error of Estimate?
|
|
What is the minimum distance that connects all the nodes
: Given the following distances between destination nodes, what is the minimum distance that connects all the nodes?
|
|
Use matlab to simulate a cdma system
: In this problem, we evaluate the bit error rate (BER) performance of the CDMA communications system introduced in Problem 8.3.9. In our experiments, we will make the following additional assumptions.
|
|
What proportion of us men
: (a) What proportion of US men are between 5 ft 7.0 in and 6 ft 1.0 in tall (67.0 and 73.0 inches, respectively)? (b) If a man is at the 14th percentile in height, how tall is he?
|
|
How fast is the ball moving
: A Doppler speed meter operating at exactly 1.02 x105 Hz emits sound waves and detects the same waves after they are reflected from a baseball thrown by the pitcher. How fast is the ball moving?
|
|
Determine if the statement is true or false
: Math 176: Algebraic Geometry, Fall 2014- Assignment 2. For each of the following, determine if the statement is true or false. If true, give a proof. If false, give a counterexample. C[x, y] is a PID
|
|
Approximate score for a student
: (a) What is the estimated percentile for a student who scores 705 on Critical Reading? (b) What is the approximate score for a student who is at the 34th percentile for Critical Reading?
|