Ahmed Almradi


Signal to Noise Ratio (SNR) estimation when the transmitted symbols are unknown is a common problem in many communication systems, especially those which require an accurate SNR estimation. For instance, modern wireless communication systems usually require accurate estimate of SNR without knowledge of the transmitted symbols. In addition, SNR estimation is required in order to perform efficient signal detection, power control, and adaptive modulation In this study, Non data Aided (NDA) SNR estimation for Binary Phase Shift Keying (PBSK) and Quadrature Phase Shift Keying (QPSK) using the Expectation Maximization (EM) algorithm is developed. The assumption here is that the received data samples are drawn from a mixture of Gaussians distribution and they are independent and identically distributed (i.i.d.). The quality of the proposed estimator is examined via the Cramer-Rao Lower Bound (CRLB) of NDA SNR estimator. It is also assumed that the channel gain is constant during each symbol interval, and the noise is Additive White Gaussian (AWGN). Maximum Likelihood estimator is being used if we have access to the complete data, in this case the problem would be much easier since we get the exact closed form solution, but when the observed data are incomplete or partially available, the EM algorithm will be used. This approach is an iterative method to get an approximated result which is either an approximated global maximum or local maximum. However, in the NDA SNR estimation, we only have a global maximum since our assumption is that the distribution is a mixture of Gaussians. This is being investigated for the cases of Single Input Single Output (SISO) and Single Input Multiple Output (SIMO). The main concern about the receive diversity is the cost, size, and power, that is why we resort to the transmit diversity such as Multiple Input single Output(MISO) with space time block codes (STBC). The base station usually serves hundreds to thousands of remote units which is the sole reason of using transmit diversity at the base station instead of at every remote unit covered by the base station. It is more economical in this case to add equipment to the base station instead of the remote units. Alamouti used a simple transmit diversity technique and assumed in his paper that the receiver has perfect knowledge of the channel transition matrix. However, this assumption may seem highly unrealistic. One of our contributions is to estimate the channel information, as well as the noise variance which would be used in estimating the SNR and deriving the CRLB for both DA and NDA case. The performance of our estimator would be empirically assessed using Monte-Carlo simulations, with CRLB as a performance metric.

Library of Congress Subject Headings

Signal processing--Mathematics; Wireless communication systems--Simulation methods; Signal theory (Telecommunication)

Publication Date


Document Type


Department, Program, or Center

Microelectronic Engineering (KGCOE)


Dianat, Sohail


Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: TK5102.9 .A56 2012


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