Deterministic Equivalents for the Performance Analysis of Isometric Random Precoded Systems

Jakob Hoydis (1) , Romain Couillet (2) , Merouane Debbah (3)

1 E3S - Supélec Sciences des Systèmes
2 SSEC - Chaire Sciences des Systèmes et Défis Energétiques EDF/ECP/Supélec
3 Chaire Radio Flexible - Chaire Radio Flexible Alcatel-Lucent/Supélec

We consider a general wireless channel model for different types of code-division multiple access (CDMA) and space-division multiple-access (SDMA) systems with isometric random signature/precoding matrices over frequency-selective and flat fading channels. We derive deterministic approximations of the Stieltjes transform, the mutual information and the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver and provide a simple fixed-point algorithm for their computation, which is proved to converge. The deterministic approximations are asymptotically tight, almost surely, but shown by simulations to be very accurate for even small system dimensions. Our analysis requires neither arguments from free probability theory nor the asymptotic freeness or the convergence of the spectral distribution of the involved matrices. The results presented in this work are, therefore, also a novel contribution to the field of random matrix theory and might be useful to further applications involving isometric random matrices.

Keywords: random matrix theory; deterministic equivalents; mutual information; random beamforming; isometric precoding; SINR; frequency-selective fading

Domains: Computer Science [cs]; Networking and Internet Architecture [cs.NI]; Computer Science [cs]; Information Theory [cs.IT]; Mathematics [math]; Information Theory [math.IT]

Jakob Hoydis, Romain Couillet, Merouane Debbah. Deterministic Equivalents for the Performance Analysis of Isometric Random Precoded Systems. IEEE International Conference on Communications 2011, Jun 2011, Kyoto, Japan. 5 p., ⟨10.1109/icc.2011.5962503⟩. ⟨hal-00648021⟩