On the Distribution of SINR for Widely Linear MMSE MIMO Systems With Rectilinear or Quasi-Rectilinear Signals

• Published in: IEEE transactions on vehicular technology Vol. 71; no. 2; pp. 1643 - 1655
• Main Authors: Deng, Wei, Xia, Yili, Li, Zhe, Pei, Wenjiang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antennas; Closed form solutions; diversity gain; Diversity methods; Exact solutions; Hypergeometric functions; Interference; Mathematical analysis; MIMO communication; Multiple-input multiple-output (MIMO); outage probability; Probability density function; Probability density functions; Receiving antennas; Signal to noise ratio; signal-to-interference-and-noise ratio (SINR); Statistical analysis; symbol error rate (SER); Transmitting antennas; widely-linear minimum mean square error (WLMMSE) receivers
• ISSN: 0018-9545; 1939-9359
• DOI: 10.1109/TVT.2021.3132377

Although the widely linear least mean square error (WLMMSE) receiver has been an appealing option for multiple-input-multiple-output (MIMO) wireless systems, a statistical understanding on its pose-detection signal-to-interference-plus-noise ratio (SINR) in detail is still missing. To this end, we consider a WLMMSE MIMO transmission system with rectilinear or quasi-rectilinear (QR) signals over the uncorrelated Rayleigh fading channel and investigate the statistical properties of its SINR for an arbitrary antenna configuration with <inline-formula><tex-math notation="LaTeX">N_t</tex-math></inline-formula> transmit antennas and <inline-formula><tex-math notation="LaTeX">N_r</tex-math></inline-formula> receive ones. We first derive an analytic probability density function (PDF) of the SINR in terms of the confluent hypergeometric function of the second kind, for WLMMSE MIMO systems with an arbitrary <inline-formula><tex-math notation="LaTeX">N_r</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">N_t=2, 3</tex-math></inline-formula>. For a more general case in practice, i.e., <inline-formula><tex-math notation="LaTeX">N_t>3</tex-math></inline-formula>, we resort to the moment generating function to obtain an approximate but closed form PDF under some mild conditions, which, as expected, is more Gaussian-like as <inline-formula><tex-math notation="LaTeX">2N_r-N_t</tex-math></inline-formula> increases. The so-derived PDFs are able to provide key insights into the WLMMSE MIMO receiver in terms of the outage probability, the symbol error rate, and the diversity gain, all presented in closed form. In particular, its diversity gain and the gain improvement over the conventional LMMSE one are explicitly quantified as <inline-formula><tex-math notation="LaTeX">N_r-(N_t-1)/2</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">(N_t-1)/2</tex-math></inline-formula>, respectively. Finally, Monte Carlo simulations support the analysis.