1. EEE-752 Emerging Wireless Networks MIMO Simulation Riaz Hussain FA08-PCE-003 rhussain@comsats.edu.pk Ph.D. Student Department of Electrical Engineering COMSATS Institute of Information Technology Islamabad, Pakistan Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation1rhussain@comsats.edu.pk

2. MIMO Simulation Matlab Comparison with theoretical values BER Vs SNR (dB) 64 QAM OFDM Simulink Understanding Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation2rhussain@comsats.edu.pk

3. MIMO Simulation Input Parameters N = No of bits for simulation M = ? In MPSK 2, 4, 8, 16, 32, and 64 Output Graph BER Vs SNR (dB) Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation3rhussain@comsats.edu.pk

4. Model Alamouti OSTBC Time Slot :1 Time Slot :2 Ant: 1S1-S2* Ant: 2S2S1* Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation4rhussain@comsats.edu.pk

5. Model Channel Response (h) h = [h1h2]for time slots Signals(s) |------| | s1 -s2* | s = | | for two time slots | s2 s1* | |------| Noise (n) n = [n1n2]for two time slots Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation5rhussain@comsats.edu.pk

6. Received Signal r = h * s + n |------| | s1 -s2* |  r = [h1h2] * | | + [n1n2] | s2 s1* | |------|  r = [h1s1+h2s2h2S1* - h1s2*] + [n1 n2]  Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation6rhussain@comsats.edu.pk

7. Decode Signal Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation7rhussain@comsats.edu.pk y_hat = |--- ---| | h1*r1 h2*r1 | | | | h2r2* -h1r2* | |--- ---|

8. Implementation (1) Generating Bit Stream Uniformly distributed random variable ip = rand(1,N) > 0.5; Equal probability for 0s and 1s Map bits to symbols BPSK sym_map=2*ip - 1; 0 -> -1 and 1 -> 1 Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation8rhussain@comsats.edu.pk

9. Implementation (2) Map symbols to s matrix Change the dimensions from 1 X N to 2 X N/2 A = reshape(sym_map, 2, N/2); Repeat s1 and s2 for two time slots sym_code = kron(A,ones(1,2)); Take conjugate, inverse-conjugate and rearrange accordingly sym_code(1,[2:2:end]) = -conj( sym_code(2,[1:2:end]) ); sym_code(2,[2:2:end]) = conj(sym_code(1,[1:2:end])); Keeping signal energy unchanged sym_code = (1/sqrt(2))*sym_code; s1 -s2* s2s1* Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation9rhussain@comsats.edu.pk

10. Implementation (3) Create Rayleigh Channel h = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)]; Normally distributed Generate normally distributed random noise n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)]; White Gausian Nois e Repeating same channel for two symbols A = reshape(h,2,N/2); hMod = kron(A,ones(1,2)); Add Channel and Noise y = sum(hMod.*sym_code,1) + 10^(-Eb_No_dB(ii)/10)*n; Element by element multiplication and adding each column ii ranges from 0 to 30 Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation10rhussain@comsats.edu.pk

11. Implementation (4) Decoding the received signals Map y, the received signal array y_mod = kron(reshape(y,2,N/2),ones(1,2)); y_mod(2,[1:1:end]) = conj(y_mod(2,[1:1:end])); Modify h to map to required condition h_mod = kron(A,ones(1,2)); h_mod(1,[1:2:end]) = conj(h_mod(1,[1:2:end])); h_mod(1,[2:2:end]) = conj(h_mod(2,[2:2:end])); h_mod(2,[2:2:end]) = -conj(h_mod(1,[1:2:end])); Obtain y_hat y_hat = sum(h_mod.*y_mod,1); Equalize hEqPower = sum(h.*conj(h),1); y_hat = y_hat./hEqPower; Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation11rhussain@comsats.edu.pk y_hat = |--- ---| | h1*r1 h2*r1 | | | h2r2* -h1r2* | |------|

12. Implementation (5) Extracting the bits Using hard decision decoding ipHat = real(y_hat) > 0 Counting the errors nErr(ii) = size(find([ip - ipHat]),2); Simulating for SNR (dB); ii ranges from 0 to 30 Finding BER simBer = nErr/N; Plot the graph Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation12rhussain@comsats.edu.pk

13. Simulation BPSK N = 10^6 Riaz Hussainrhussain@comsats.edu.pkEEE752-EWN: MIMO-Simulation13rhussain@comsats.edu.pk