### Project Description

### Matlab Professional Assignment help sample

**Problem?Solving Task**

**Multiple?Antennas?and?Space-time?Communications?**

**Consider a 2??2 MIMO system with channel gain matrix ?? given by**

**?? = ?**

**0.3 0.8**

**0.4 1.5**

**?**

**Assume that ?? is known at both transmitter and receiver and that there is a total transmit**

**power of ?? = 12 ???? across the two transmit antennas, AWGN with ??0 = 10-9 ??/???? at**

**each receive antenna, and bandwidth ?? = 1??????.**

**Write a MATLAB script that can,**

**a) Find the SVD for ??.**

**(20 marks)**

**b) Find the capacity of this channel.**

**(20 marks)**

**c) Assume that transmit precoding and receiver shaping have been used to transform**

**this channel into two parallel independent channels with a total power constraint ??.**

**Use MATLAB to find the maximum data rate that can be transmitted over this**

**parallel set assuming MQAM modulation on each channel, with optimal power**

**allocation across the channels subject to power constraint ??. Assume a target BER**

**of 10-3 on each channel and that the BER is bounded ???? = 0.2??- 1.5??**

**?? -1.**

**(20 marks)**

**d) Suppose now that the antennas at the transmitter and receiver are all used for**

**diversity (with optimal weighting at the transmitter and receiver) to maximize the SNR of**

**the combiner output. Using MATLAB, find the SNR of the combiner output as well as the**

**BER of a BPSK modulated signal transmitted over this diversity system. Compare the data**

**rate and BER of this BPSK signalling with diversity (assuming ?? = 1/????) to the rate**

**and BER from part c.**

**(20 marks)**

**e) Discuss the diversity-multiplexing trade-offs between the systems in parts c and d.**

**(20 marks)**

**Submission Requirements**

**1. This is an individual assignment; please ensure the submitted work is your own as each**

**assignment will be tested for academic integrity.**

**2. The assignment report is to be submitted electronically through QUT Blackboard (due 31st**

**May 2016).**

**3. The written report should provide responses to all required tasks, as well as the MATLAB**

**scripts used to produce your results.**

**4. The electronic files submitted must be in a pdf file format. This ensures that your document**

**formatting is preserved.**

**5. Do not zip or archive your submissions.**

**6. It is permissible to submit your assignment to Blackboard multiple times.**

**7. However, only the latest submission will be marked.**

**8. It is the student’s responsibility to check that files submitted to Blackboard have not been**

**corrupted in the process. All uploaded files can be reviewed post submission.**

%%%%%%%%%%%%%%%%%%%%%%%%%%%

%ENN522

%Assignment

%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%% Variables declaration %%%%%%%%%%%%

clear all

close all

clc

H = [0.3 0.8; 0.4 1.5]; % Matrix H

B = 1e6; % Bandwidth

P = 12e-3; % Transmit power

No = 1e-9; % AWGN Channel

Pb = 1e-3; %Bit error probability ~ BER

%%%%%%%%%%%% Question a %%%%%%%%%%%%

[U,S,V] = svd(H); % Computing (SVD)

Hcmp = U*S*V’; % Checking the relation H = U*S*V’

%%%%%%%%%%%% Qestion b %%%%%%%%%%%%%

gamma1 = (S(1)^2*P)/(No*B); % Gamma1 coefficent

gamma2 = (S(4)^2*P)/(No*B); % Gamma1 coefficent

gamma0 = (2*gamma1*gamma2)/(gamma1 + gamma2 + gamma1*gamma2); %Gamma0 coefficent

C = B * log2(gamma1/gamma0) + B * log2(gamma2/gamma0); % Channel capacity

%%%%%%%%%%%% Qestion c %%%%%%%%%%%%%

K = -1.5/(log(5*Pb)); % M-1 value

gamma0k = 2/(1 + (1/K)*(1/gamma1 + 1/gamma2)); %gamma0k value

gammak = gamma0/K;

R = B*(log2(gamma1/gammak) + log2(gamma2/gammak)); %Bit rate R

%%%%%%%%%%%% Qestion d %%%%%%%%%%%%%

lambdamax = 0.7592; % Max Wishart Matrix value

Tb = 1e-6; %Bit time

rho = P/(No*B); %Adimenssional factor

gamma_s = lambdamax*rho; %Gamma for QPSK scheme

PbBPSK = qfunc(sqrt(2*gamma_s)); %Probability bit error Pb

R_QPSK = 1/Tb; %Bit Rate R

**Report**

### Project Details

**Date**December 6, 2016**Tags**Matlab, Programming