Performance Analysis of MIMO Systems with IRM By Junwu Zhang Xuefeng Zhao Bin Xue 2018/11/14 Communication Theory

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). 2018/11/14 Communication Theory

Example of a MIMO System (1-user) 2018/11/14 Communication Theory

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,j is 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 2018/11/14 Communication Theory

Performance Analysis For code words c and e in l time slots, assume c  e. Assume the receiver has complete channel information, 2018/11/14 Communication Theory

Performance Analysis The distance between these two code words, For code words c and e in l time slots, assume c  e. The distance between these two code words, 2018/11/14 Communication Theory

Performance Analysis 2018/11/14 Communication Theory

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. 2018/11/14 Communication Theory

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| are independent Rician distributions with pdf: I0(.): Bessel function of the first kind. 2018/11/14 Communication Theory

Performance Analysis Since |bi,j| are Rician 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 2018/11/14 Communication Theory

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). 2018/11/14 Communication Theory

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. 2018/11/14 Communication Theory

IRM: Interference-Resistant-Modulation 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 2018/11/14 Communication Theory

Basic Idea Choose the rotation matrix R such that: Rn R1 R2 Rn 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. 2018/11/14 Communication Theory

Example of Rotation(L=2,3) 2018/11/14 Communication Theory

Rotation Matrix for High Dimension 2018/11/14 Communication Theory

Transmitter structure for a multiuser system with IRM 2018/11/14 Communication Theory

Simulation Result (1) ‘Distance Matrix Determinant’ Vs 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 2018/11/14 Communication Theory

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 2018/11/14 Communication Theory

Simulation Result (3) (Optimum IRM Vs. non-optimum IRM) Use single user BER as baseline Optimum IRM performs better than non-optimum IRM 2018/11/14 Communication Theory

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. 2018/11/14 Communication Theory

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.   2018/11/14 Communication Theory

Thank You. Questions? 2018/11/14 Communication Theory