Performance Analysis of MIMO Systems with IRM

1. Performance Analysis of MIMO Systems with IRM By Junwu Zhang Xuefeng Zhao Bin Xue Communication Theory

2. Multiple-Input Multiple-Output(MIMO)? • The use of multiple antennas at both ends of a wireless link promise significant improvements in terms of spectral efficiency. • Do all transmitter antennas use orthogonal waves? No. • Does each receiver antenna receive signals from all the transmitters? Yes. • How to detect signals from different transmitters? • Different transmission paths have different fading (or independent fading). Communication Theory

3. Example of a MIMO System (1-user) Communication Theory

4. Performance Analysis • n transmit antennas • m receiving antennas • Cti is transmitted by transmitter i at time t • Rayleigh or Rician fading, quasistatic flat fading for l time slots,ai,jis the fading coefficient from i to j, complex Gaussian variable with mean E(ai,j ) & variance 0.5 per dimension • Constellation-independent • The signal received at antenna j at time t is a noisy superposition of the n transmitted signals: Noise is zero-mean complex Gaussian random variable with variance N0/2 Communication Theory

5. Performance Analysis For code words c and e in l time slots, assume c  e. Assume the receiver has complete channel information, Communication Theory

6. Performance Analysis For code words c and e in l time slots, assume c  e. • The distance between these two code words, Communication Theory

7. Performance Analysis Communication Theory

8. Performance Analysis Notice that: • Thus matrix A is Hermitian. • From linear algebra: • Unitary Matrix:VV*=I • For a Hermitian matrix A, there exists unitary matrix V and diagonal matrix D such that VAV*=D. The rows of V,{v1, v2, … vn} are a complete orthonormal basis of Cn given by eigenvectors of A. The diagonal elements of D are eigenvalues of A. • If A=BB*, eigenvalues of A are nonnegative. Communication Theory

9. Performance Analysis Let: bi,j are independent complex Gaussian random variables with variance 0.5 and mean E(bi,j). Let Ki,j= |E(bi,j)|2, |bi,j| areindependent Rician distributions with pdf: I0(.): Bessel function of the first kind. Communication Theory

10. Performance Analysis Since |bi,j| areRician distributions, solve for the average over Rician distribution of |bi,j| : For Rayleigh fading, E(ai,j) =0 and thus Ki,j= |Ebi,j|2=0 Communication Theory

11. Performance Analysis For Rayleigh fading, Eai,j =0 and thus Ki,j= |Ebi,j|2=0 Design Criteria for Rayleigh Space–Time Codes: • The Rank Criterion: In order to achieve the maximum diversity mn, the matrix B(c,e) has to be full rank for any codewords c and e. If B(c,e) has minimum rank r over the set of distinct pairs of codewords, then a diversity of rm is achieved. • The Determinant Criterion: Suppose that a diversity benefit of rm is our target. The minimum of the absolute value of the sum of the determinants of all of all principal r×r cofactors of A(c,e) taken over all pairs of distinct codewords c and e corresponds to the coding advantage, where r is the rank of B(c,e). Communication Theory

12. Performance Analysis For Rician fading with large SNR, Design Criteria for Rician Space–Time Codes: • The Rank Criterion: Same as for Rayleigh fading. • The Determinant Criterion: Suppose that a diversity benefit of rm is our target. The minimum of the following: over distinct codewords c and e has to be maximized. Communication Theory

13. Performance: Co-channel interference Vs. diversity gain and coding gain Can we improve the performance without introducing coding or bandwidth expansion? Yes. IRM: Interference-Resistant-Modulation IRM: Interference-Resistant-Modulation Communication Theory

14. R1 R1 R2 R2 Rn Rn Basic Idea Choose the rotation matrix R such that: • Increase the rank of B(c,e) over distinct code words; • Increase the determinant of B(c,e) over distinct code words; • One possible distance-preserving transformation is to multiply this matrix by an orthogonal matrix R. the optimal matrix R maximizes the fading resistance of the transformed constellation. Communication Theory

15. Example of Rotation(L=2,3) Communication Theory

16. Rotation Matrix for High Dimension Communication Theory

17. Transmitter structure for a multiuser system with IRM Communication Theory

18. Simulation Result (1)‘Distance Matrix Determinant’ Vs. ‘Rotation Degree’ • Best Rotation angle for n=2, m=1,L=2 θ1=26.6 degree θ2=63.4 degree Communication Theory

19. Simulation Result (2)(Bit Error Ratio Vs. SNR) • Use single user BER as baseline • When SNR increases, the BER of 2 users IRM with optimum rotation angle approaches the baseline Communication Theory

20. Simulation Result (3)(Optimum IRM Vs. non-optimum IRM) • Use single user BER as baseline • Optimum IRM performs better than non-optimum IRM Communication Theory

21. References [1] V. DaSilva and E. Sousa, “Fading-resistant modulation using several transmitter antennas,” IEEE Trans. Commun., vol. 45, pp. 1236–1244, Oct. 1997. [2] V. Tarokh, N. Seshadri, and A. Calderbank, “Space–time codes for high data rate wireless communication: Performance criterion and code con-struction,” IEEE Trans. Inform. Theory, vol. 44, pp. 744–765, Mar. 1998. [3] O. Damen, J. Belfiore, K. Abed-Meraim, and A. Chkeif, “Algebraic coding/decoding multiuser scheme,” in Proc. Vehicular Technology Conf. 2000-Spring, vol. 3, 2000, pp. 2272–2274. [4] T. R. Giallorenzi and S. G. Wilson, “Multiuser ML sequence estima-tior for convolutional coded asynchronous DS-CDMA systems,” IEEE Trans. Commun., vol. 44, pp. 997–1008, Aug. 1996. [5] J. Grimm, M. P. Fitz, and J. V. Krogmeier, “Further results on space–time coding for rayleigh fading,” in Proc. Allerton Conference on Communi-cation, Control, and Computing, 1998, pp. 391–400. [6] S. Alamouti, “A simple transmit diversity technique for wireless com-munications,” IEEE J. Select. Areas Commun., vol. 16, pp. 1451–1458, Oct. 1998. Communication Theory

22. References [7] A. F. Naguib, N. Seshadri, and A. R. Calderbank, “Applications of space–time block codes and interference suppression for high capacity and high data rate wireless systems,” in Proc. 32nd Asilomar Conference, 1998, pp. 1803–1810. [8] G. Caire, G. Taricco, J. Ventura-Traveset, and E. Biglieri, “A multiuser approach to narrow-band cellular communications,” IEEE Trans. In-form. Theory, vol. 43, pp. 1503–1517, Sept. 1997. [9] E. A. Fain and M. K. Varanasi, “Diversity order gain for narrow-band multiuser communications with precombining group detection,” IEEE Trans. Commun., vol. 48, pp. 533–536, Apr. 2000. [10] J. Boutros and E. Viterbo, “Signal space diversity: A power- and band-width- efficient diversity technique for the rayleigh fading channel,” IEEE Trans. Inform. Theory, vol. 44, pp. 1453–1467, July 1998. [11] B. K. Ng,and E. S. Sousa,, “On Bandwidth-Efficient Multiuser-Space–Time Signal Design and Detection”, IEEE Jounal On Selected Areas In Communications, VOL. 20, NO. 2, Feb. 2002 [12] J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw-Hill 1995. Communication Theory

23. Thank You. Questions? Communication Theory