Analysis of Distributed Beamforming in Cooperative Communications Networks with Phase Shifter Based Smart Antenna Nodes by Tharunie Baleshan Thesis Submitted for the Degree of Master of Engineering Queensland University of Technology Science and Engineering Faculty 2015 QUT Verified Signature To My Parents For their endless love, support and encouragement Keywords Smart antennas, Distributed beamforming, Cooperative diversity, Power Minimisation, SNR Maximisation, Array factor, Directivity, Field intensity Abstract Performance of wireless communications systems can be significantly improved by means of multiple antennas at communicating terminals However, due to limitation of the physical size and the cost, employing large number of antennas at communicating terminals becomes infeasible As a remedy, cooperative communication was proposed where different users share their antennas and thus cooperate for the source-to-destination communication It is desirable to maximise receiver quality-of-service (QoS) in terms of Signal-to-Noise Ratio (SNR) and also to minimise the cost of transmission in terms of power Transmit power of relays and received SNR are major concerns in designing such a communication network and significant literature focusses on minimisation of the total transmit power of relays subject to received SNR or maximisation of the received SNR at the destination subject to total transmit power of relays However, most of these previous studies consider either single antenna relays or Multiple-Input-Multiple-Output (MIMO) relays Though the MIMO relays give better performance over single antenna relays, their hardware configuration is much more complex because each antenna requires a separate receiver/transmitter module Smart antenna systems can also improve the performance with only much simpler hardware, as they require only a single receiver/transmitter module Furthermore, above mentioned optimisations are often investigated separately and trade-off between those two optimisations is not fully explored Geographically separated relays can cooperatively adjust their amplitude and viii phase excitations and these excitations are calculated by optimising the performance of wireless communication An array’s radiation pattern can be continuously steered by adaptively changing the phase excitation of the antenna array without additional power in mobile communication Conventional approach to shape the beam is to maximise the field intensity at the destination However, in this research study maximising directivity is investigated for circular and linear arrays, and it is shown that directivity maximisation outperforms the field intensity maximisation to save power Hence, directivity maximisation is incorporated with distributed beamforming to analyse the performance improvement of the communication In addition to power minimisation in receive and transmit beamforming processes, directivity from each relay to the source and the destination is maximised For the transmit beamforming, the complex beamforming weight of each relay is then calculated to minimise the total transmit power of relays, while maintaining SNR at the destination above a predefined threshold We also calculated the total power gain achieved with the smart antenna system and compared it to the single antenna relays case with distributed beamforming Results show that the total power gain which exceeds the sum of the smart antenna gains can be achieved for high levels of the SNR thresholds at the destination Next, a comparison of relay power minimisation subject to received SNR at the destination and SNR maximisation subject to the total transmit power of relays for a typical wireless network with distributed beamforming is considered In this research study, it is shown that SNR maximisation subject to power constraint and power minimisation subject to SNR constraint yield the same result for a typical wireless network It is concluded that either one of the optimisation approaches is sufficient to simultaneously minimise the transmit power at the relays and to maximise the SNR at the destination 110 Appendix A MATLAB Code function direc= Directivity Bit optim(alpha m,M,q,P,phi r,phi m,theta0) AF=@(phi,theta) 0; for m=1:M x=@(phi,theta)exp(1j*(pi*q*csc(pi/M)*sin(theta).*cos(phi− phi m(m))−2*pi/2ˆP*alpha m(m))); AF=@(phi,theta) AF(phi,theta)+x(phi,theta); end y=@(phi,theta) abs(AF(phi,theta)).ˆ2.*sin(theta); den dir=integral2(y,0,2*pi,0,pi); direc= −1*abs(sum(exp(1j*−2*pi/2ˆP*alpha m).*exp(1j*pi*q *csc(pi/M)*sin(theta0)*cos(phi r−phi m))))* abs(sum(exp(1j*−2*pi/2ˆP* alpha m).*exp(1j*pi*q *csc(pi/M)*sin(theta0)*cos(phi r−phi m))))/den dir; A.3 Field Intensity Maximisation of Linear Antenna Array A.3.1 Field Intensity Linear.m %%%%%%%%% Field Intensity Maximisation clc clear M=5; q=.5; Field Intensity Linear Nobit(M,q) %%%%%%%%%% Appendix A MATLAB Code A.3.2 Field Intensity Linear Nobit.m function Field Intensity Linear Nobit(M,q) alpha m=[]; i=0; fin dir mat=[]; theta0=pi/2; for phi0=0:0.1:180 i=i+1; phi0 r=phi0*pi/180; % in radian for m=1:M if phi0 r>pi/2 phi0 r=pi−phi0 r; end b=−2*pi*(m−1)*q*cos(phi0 r); % required phase shift if b>0 b=b−2*pi; end alpha m=[alpha m b]; end %%%%%%%%%%%% E field %%%%%%%%%% m=0:M−1; c=@(phi0 1) sum(exp(1j*alpha m).*exp(1j*2*pi*m*q *sin(theta0).*cos(phi0 1))); d=@(phi0 1) abs(c(phi0 1)); num dir=d(phi0 r)ˆ2; Max F=d(phi0 r)/M; % Normalised radiation intensity %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 111 112 Appendix A MATLAB Code Max F mat(i)=Max F; Rx(i)=phi0; %%%%%%%%%%%%%%%%% Denominator of Directivity %%%%%%%%%%%%%%%%%%%% AF=@(phi,theta) 0; for m=1:M x=@(phi,theta)exp(1j*(2*pi*q*(m−1)*sin(theta).*cos(phi)+ alpha m(m))); AF=@(phi,theta) AF(phi,theta)+x(phi,theta); end y=@(phi,theta) abs(AF(phi,theta)).ˆ2.*sin(theta); den dir=integral2(y,0,2*pi,0,pi); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% fin dir=4*pi*num dir/den dir; fin dir mat=[fin dir mat fin dir]; Rx(i)=phi0; alpha m=[]; end mu=mean(fin dir mat) vari=var(fin dir mat) plot(Rx,Max F mat,'g') % Plot for normalised field intensity xlabel('Angle of Direction of the destination') ylabel('Maximum Field Intensity') title('Field Intensity of Linear antenna array') figure(2) plot(Rx,fin dir mat,'r') % Plot for Directivity xlabel('Angle of Direction of the destination') ylabel('Directivity') Appendix A MATLAB Code 113 title(['M = ' num2str(M) '; q = ' num2str(q)]) figure hist(fin dir mat,180) title(['Histogram' ' M = ' num2str(M) '; q = ' num2str(q)]) xlabel('Directivity') ylabel('Frequency') figure [f1,x1,u1]=ksdensity(fin dir mat); plot(x1,f1) xlabel('Directivity') ylabel('Probability density') title(['Probability Density Function' ' M = ' num2str(M) '; q = ' num2str(q)]) A.4 Directivity Maximisation of Linear Antenna Array A.4.1 %%%%%% Directivity Linear.m Directivity Maximisation with and without %%%%%%%%%%%% Digital Phase Shifters clc clear M=3; % number of antenna elements q=0.5; % spacing between antennas=q*lamda Directivity Linear Nobit(M,q) %%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% 114 Appendix A MATLAB Code A.4.2 Directivity Linear Nobit.m function Directivity Linear Nobit(M,q) theta0=pi/2; i=0; for phi0=0:0.1:180 % azimuth angle of direction of the destination i=i+1; phi0 r=phi0*pi/180; % in radian f=@(alpha m)Directivity Linear Nobit optim(alpha m,M,q,phi0 r, theta0); % function to optimise gs = GlobalSearch('Display','iter'); % Global seaarch optimisation if i==1 x0=zeros(1,M); gs.NumTrialPoints=4000; else x0=alpha m; gs.NumTrialPoints=200; gs.NumStageOnePoints=10; end ub=zeros(1,M); lb=zeros(1,M)−2*pi; lb(1)=0; problem = createOptimProblem('fmincon','objective', f, 'x0', x0, 'Aineq', [],'bineq', [], 'Aeq', [], 'beq', [], 'lb', lb, 'ub', ub); [alpha m,direc opti] = run(gs,problem); direc=direc opti*4*pi*−1; Rx(i)=phi0; max D nobit(i)=direc; Appendix A MATLAB Code 115 end save(['H:\MATLAB\Linear Antenna Array\Directivity\Variables\', 'M' num2str(M) ' q' 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power gain which exceeds the sum of the smart antenna. .. SNR threshold for single and multiple antenna networks with different αg for M = 3, q = 0.4 with 3-bit phase shifter in single antenna relay network and multi -antenna relay network for αf = −5