In the context of satellite communications, random access (RA) methods can significantly increase throughput and reduce latency over the network. The recent RA methods are based on multi-user multiple access transmission at the same time and frequency combined with interference cancellation and iterative decoding at the receiver. Generally, it is assumed that perfect knowledge of the interference is available at the receiver. In practice, the interference term has to be accurately estimated to avoid performance degradation. Several estimation techniques have been proposed lately in the case of superimposed signals. In this paper, we present an improved channel estimation technique that combines estimation using an autocorrelation based method and the Expectation-Maximization algorithm, and uses Pilot Symbol Assisted Modulation to further improve the performance and achieve optimal interference cancellation.
The EM algorithm @cite_0 is a two-step iterative estimation method that has been proposed in @cite_8 to perform channel estimation in case of superimposed signals. In a first step called Expectation'' (E step), the preamble part is extracted from the received signal. Then for each user @math , vector @math is derived as the preamble of user @math ( @math ) multiplied by its estimated channel coefficient @math (of previous iteration) and additioned with a certain percentage @math of the difference between the received preamble part ( @math ) and the reconstructed preambles of both users @math and @math , as shown below where @math refers to the index of the preamble.
@cite_0 @cite_8
2154191559 2011277999 1510028821 2591812953
A computationally efficient algorithm for parameter estimation of superimposed signals based on the two-step iterative EM (estimate-and-maximize, with an E step and an M step) algorithm is developed. The idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately. The algorithm iterates back and forth, using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates. The application of the algorithm to the multipath time delay and multiple-source location estimation problems is considered. > The Expectation-Maximization (EM) algorithm is an iterative approach to maximum likelihood parameter estimation. Jordan and Jacobs (1993) recently proposed an EM algorithm for the mixture of experts architecture of Jacobs, Jordan, Nowlan and Hinton (1991) and the hierarchical mixture of experts architecture of Jordan and Jacobs (1992). They showed empirically that the EM algorithm for these architectures yields significantly faster convergence than gradient ascent. In the current paper we provide a theoretical analysis of this algorithm. We show that the algorithm can be regarded as a variable metric algorithm with its searching direction having a positive projection on the gradient of the log likelihood. We also analyze the convergence of the algorithm and provide an explicit expression for the convergence rate. In addition, we describe an acceleration technique that yields a significant speedup in simulation experiments. In this paper, we extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its application to matrix completion, robust PCA, dictionary learning, and related matrix-factorization problems. Here, in Part I of a two-part paper, we derive our Bilinear G-AMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, where central-limit theorem arguments and Taylor-series approximations apply, and under the assumption of statistically independent matrix entries with known priors. In addition, we propose an adaptive damping mechanism that aids convergence under finite problem sizes, an expectation-maximization (EM)-based method to automatically tune the parameters of the assumed priors, and two rank-selection strategies. In Part II of the paper, we will discuss the specializations of EM-BiG-AMP to the problems of matrix completion, robust PCA, and dictionary learning, and we will present the results of an extensive empirical study comparing EM-BiG-AMP to state-of-the-art algorithms on each problem. In this paper, we develop a low-complexity channel estimation for hybrid millimeter wave (mmWave) systems, where the number of radio frequency (RF) chains is much less than the number of antennas equipped at each transceiver. The proposed mmWave channel estimation algorithm first exploits multiple frequency tones to estimate the strongest angle-of-arrivals (AoAs) at both base station (BS) and user sides for the design of analog beamforming matrices. Then, all the users transmit orthogonal pilot symbols to the BS along the directions of the estimated strongest AoAs in order to estimate the channel. The estimated channel will be adopted to design the digital zero-forcing (ZF) precoder at the BS for the multi-user downlink transmission. The proposed channel estimation algorithm is applicable to both the non-sparse and sparse mmWave channel environments. Furthermore, we derive a tight achievable rate upper bound of the digital ZF precoding with the proposed channel estimation algorithm scheme. Our analytical and simulation results show that the proposed scheme obtains a considerable achievable rate of fully digital systems, where the number of RF chains equipped at each transceiver is equal to the number of antennas. Besides, considering the effect of various types of errors, i.e., random phase errors, transceiver analog beamforming errors, and equivalent channel estimation errors, we derive a closed-form approximation for the achievable rate of the considered scheme. We illustrate the robustness of the proposed channel estimation and multi-user downlink precoding scheme against the system imperfection.