Signal to noise ratio estimation using the Expectation Maximization Algorithm

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

ML-Type EM-Based Estimation of Fast Time-Varying Frequency-Selective Channels Over SIMO OFDM Transmissions

This paper investigates the problem of fast time-varying frequency-selective (i.e., multipath) channel estimation over single-input multiple-output orthogonal frequency-division multiplexing (SIMO OFDM)-type transmissions. We do so by tracking the variations of each complex gain coefficient using a polynomial-in-time expansion. To that end, we derive the log-likelihood function (LLF) both in the data-aided (DA) and non-data-aided (NDA) cases. The DA maximum likelihood (ML) estimates over fast SIMO OFDM channels are derived here for the first time in closed-form expressions and hereby shown to be limited to applying over each receive antenna the DA least squares (LS) estimator tailored in [1] to fast SISO OFDM channels. This DA ML is used to initialize periodically, over a relatively large number of data blocks (i.e., with further reduced and relatively close-to-negligible pilot overhead compared to DA ML), a new expectation maximization (EM) ML-type solution we developed here in the NDA case to iteratively maximize the LLF. We also introduce an alternative regularized DA ML (RDM) initialization solution no longer requesting - in contrast to DA ML - more per-carrier pilot frames than the number of paths to further reduce overhead without incurring significant performance losses. Simulation results show that the proposed hybrid ML-EM estimator (i.e., combines all new NDA ML-EM and DA ML or RDM versions) converges within few iterations, thereby providing very accurate estimates of all multipath channel gains. Most importantly, this increased estimation accuracy translates into very significant BER and link-level per-carrier throughput gains over the best representative benchmark solution available so far for the problem at hand, the SISO DA LS technique in [1] with its new generalization here to SIMO systems

Active Reconfigurable Intelligent Surface Aided Wireless Communications

Reconfigurable Intelligent Surface (RIS) is a promising solution to reconfigure the wireless environment in a controllable way. To compensate for the double-fading attenuation in the RIS-aided link, a large number of passive reflecting elements (REs) are conventionally deployed at the RIS, resulting in large surface size and considerable circuit power consumption. In this paper, we propose a new type of RIS, called active RIS, where each RE is assisted by active loads (negative resistance), that reflect and amplify the incident signal instead of only reflecting it with the adjustable phase shift as in the case of a passive RIS. Therefore, for a given power budget at the RIS, a strengthened RIS-aided link can be achieved by increasing the number of active REs as well as amplifying the incident signal. We consider the use of an active RIS to a single input multiple output (SIMO) system. {However, it would unintentionally amplify the RIS-correlated noise, and thus the proposed system has to balance the conflict between the received signal power maximization and the RIS-correlated noise minimization at the receiver. To achieve this goal, it has to optimize the reflecting coefficient matrix at the RIS and the receive beamforming at the receiver.} An alternating optimization algorithm is proposed to solve the problem. Specifically, the receive beamforming is obtained with a closed-form solution based on linear minimum-mean-square-error (MMSE) criterion, while the reflecting coefficient matrix is obtained by solving a series of sequential convex approximation (SCA) problems. Simulation results show that the proposed active RIS-aided system could achieve better performance over the conventional passive RIS-aided system with the same power budget

Doppler Spread Estimation in MIMO Frequency-Selective Fading Channels

One of the main challenges in high-speed mobile communications is the presence of large Doppler spreads. Thus, accurate estimation of maximum Doppler spread (MDS) plays an important role in improving the performance of the communication link. In this paper, we derive the data-aided (DA) and non-data-aided (NDA) Cramér-Rao lower bounds (CRLBs) and maximum likelihood estimators (MLEs) for the MDS in multiple-input multiple-output (MIMO) frequency-selective fading channel. Moreover, a low-complexity NDA-moment-based estimator (MBE) is proposed. The proposed NDA-MBE relies on the second- and fourth-order moments of the received signal, which are employed to estimate the normalized squared autocorrelation function of the fading channel. Then, the problem of MDS estimation is formulated as a non-linear regression problem, and the least-squares curve-fitting optimization technique is applied to determine the estimate of the MDS. This is the first time in the literature, when DA- and NDA-MDS estimation is investigated for MIMO frequency-selective fading channel. Simulation results show that there is no significant performance gap between the derived NDA-MLE and NDA-CRLB, even when the observation window is relatively small. Furthermore, the significant reduced-complexity in the NDA-MBE leads to low root-mean-square error over a wide range of MDSs, when the observation window is selected large enough

Nondata-Aided Rician Parameters Estimation With Redundant GMM for Adaptive Modulation in Industrial Fading Channel

Wireless networks have been widely utilized in industries, where wireless links are challenged by the severe nonstationary Rician fading channel, which requires online link quality estimation to support high-quality wireless services. However, most traditional Rician estimation approaches are designed for channel measurements and work only with nonmodulated symbols. Then, the online Rician estimation usually requires a priori aiding pilots or known modulation order to cancel the modulation interference. This article proposes a nondata-Aided method with redundant Gaussian mixture model (GMM). The convergence paradigm of GMM with redundant subcomponents has been analyzed, guided by which the redundant subcomponents can be iteratively discriminated to approach the global optimization. By further adopting the constellation constraint, the probability to identify the redundant subcomponent is significantly increased. As a result, accurate estimation of the Rician parameters can be achieved without additional overhead. Experiments illustrate not only the feasibility but also the near-optimal accuracy

MIMO Systems: Principles, Iterative Techniques, and advanced Polarization

International audienceThis chapter considers the principles of multiple-input multiple-output (MIMO) wireless communication systems as well as some recent accomplishments concerning their implementation. By employing multiple antennas at both transmitter and receiver, very high data rates can be achieved under the condition of deployment in a rich-scattering propagation medium. This interesting property of MIMO systems suggests their use in the future high-rate and high-quality wireless communication systems. Several concepts in MIMO systems are reviewed in this chapter. We first consider MIMO channel models and recall the basic principles of MIMO structures and channel modeling. We next study the MIMO channel capacity and present the early developments in these systems concerning the information theory aspect. Iterative signal detection is considered next; it considers iterative techniques for space-time decoding. As the capacity is inversely proportional to the spatial channel correlation, MIMO antennas should be sufficiently separated, usually by several wavelengths. In order to minimize antennas' deployment, we present advanced polarization diversity techniques for MIMO systems and explain how they can help to reduce the spatial correlation in order to achieve high transmission rates. We end the chapter by considering the application of MIMO systems in local area networks, as well as their potential in enhancing range, localization, and power efficiency of sensor networks

Hybrid solutions to instantaneous MIMO blind separation and decoding: narrowband, QAM and square cases

Future wireless communication systems are desired to support high data rates and high quality transmission when considering the growing multimedia applications. Increasing the channel throughput leads to the multiple input and multiple output and blind equalization techniques in recent years. Thereby blind MIMO equalization has attracted a great interest.Both system performance and computational complexities play important roles in real time communications. Reducing the computational load and providing accurate performances are the main challenges in present systems. In this thesis, a hybrid method which can provide an affordable complexity with good performance for Blind Equalization in large constellation MIMO systems is proposed first. Saving computational cost happens both in the signal sep- aration part and in signal detection part. First, based on Quadrature amplitude modulation signal characteristics, an efficient and simple nonlinear function for the Independent Compo- nent Analysis is introduced. Second, using the idea of the sphere decoding, we choose the soft information of channels in a sphere, and overcome the so- called curse of dimensionality of the Expectation Maximization (EM) algorithm and enhance the final results simultaneously. Mathematically, we demonstrate in the digital communication cases, the EM algorithm shows Newton -like convergence.Despite the widespread use of forward -error coding (FEC), most multiple input multiple output (MIMO) blind channel estimation techniques ignore its presence, and instead make the sim- plifying assumption that the transmitted symbols are uncoded. However, FEC induces code structure in the transmitted sequence that can be exploited to improve blind MIMO channel estimates. In final part of this work, we exploit the iterative channel estimation and decoding performance for blind MIMO equalization. Experiments show the improvements achievable by exploiting the existence of coding structures and that it can access the performance of a BCJR equalizer with perfect channel information in a reasonable SNR range. All results are confirmed experimentally for the example of blind equalization in block fading MIMO systems