Multiuser detection in a dynamic environment Part I: User identification and data detection

In random-access communication systems, the number of active users varies with time, and has considerable bearing on receiver's performance. Thus, techniques aimed at identifying not only the information transmitted, but also that number, play a central role in those systems. An example of application of these techniques can be found in multiuser detection (MUD). In typical MUD analyses, receivers are based on the assumption that the number of active users is constant and known at the receiver, and coincides with the maximum number of users entitled to access the system. This assumption is often overly pessimistic, since many users might be inactive at any given time, and detection under the assumption of a number of users larger than the real one may impair performance. The main goal of this paper is to introduce a general approach to the problem of identifying active users and estimating their parameters and data in a random-access system where users are continuously entering and leaving the system. The tool whose use we advocate is Random-Set Theory: applying this, we derive optimum receivers in an environment where the set of transmitters comprises an unknown number of elements. In addition, we can derive Bayesian-filter equations which describe the evolution with time of the a posteriori probability density of the unknown user parameters, and use this density to derive optimum detectors. In this paper we restrict ourselves to interferer identification and data detection, while in a companion paper we shall examine the more complex problem of estimating users' parameters.Comment: To be published on IEEE Transactions on Information Theor

A Variational Inference Framework for Soft-In-Soft-Out Detection in Multiple Access Channels

We propose a unified framework for deriving and studying soft-in-soft-out (SISO) detection in interference channels using the concept of variational inference. The proposed framework may be used in multiple-access interference (MAI), inter-symbol interference (ISI), and multiple-input multiple-outpu (MIMO) channels. Without loss of generality, we will focus our attention on turbo multiuser detection, to facilitate a more concrete discussion. It is shown that, with some loss of optimality, variational inference avoids the exponential complexity of a posteriori probability (APP) detection by optimizing a closely-related, but much more manageable, objective function called variational free energy. In addition to its systematic appeal, there are several other advantages to this viewpoint. First of all, it provides unified and rigorous justifications for numerous detectors that were proposed on radically different grounds, and facilitates convenient joint detection and decoding (utilizing the turbo principle) when error-control codes are incorporated. Secondly, efficient joint parameter estimation and data detection is possible via the variational expectation maximization (EM) algorithm, such that the detrimental effect of inaccurate channel knowledge at the receiver may be dealt with systematically. We are also able to extend BPSK-based SISO detection schemes to arbitrary square QAM constellations in a rigorous manner using a variational argument.Comment: Submitted to Transactions on Information Theor

Soft-decision equalization techniques for frequency selective MIMO channels

Multi-input multi-output (MIMO) technology is an emerging solution for high data rate wireless communications. We develop soft-decision based equalization techniques for frequency selective MIMO channels in the quest for low-complexity equalizers with BER performance competitive to that of ML sequence detection. We first propose soft decision equalization (SDE), and demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered, and linear in the signal constellation size. Building upon the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Motivated by the need for low-complexity receiver processing, we further present an alternative low-complexity soft-decision equalization approach for frequency selective MIMO communication systems. With the help of iterative processing, two detection and estimation schemes based on second-order statistics are harmoniously put together to yield a two-part receiver structure: local multiuser detection (MUD) using soft-decision Probabilistic Data Association (PDA) detection, and dynamic noise-interference tracking using Kalman filtering. The proposed Kalman-PDA detector performs local MUD within a sub-block of the received data instead of over the entire data set, to reduce the computational load. At the same time, all the inter-ference affecting the local sub-block, including both multiple access and inter-symbol interference, is properly modeled as the state vector of a linear system, and dynamically tracked by Kalman filtering. Two types of Kalman filters are designed, both of which are able to track an finite impulse response (FIR) MIMO channel of any memory length. The overall algorithms enjoy low complexity that is only polynomial in the number of information-bearing bits to be detected, regardless of the data block size. Furthermore, we introduce two optional performance-enhancing techniques: cross- layer automatic repeat request (ARQ) for uncoded systems and code-aided method for coded systems. We take Kalman-PDA as an example, and show via simulations that both techniques can render error performance that is better than Kalman-PDA alone and competitive to sphere decoding. At last, we consider the case that channel state information (CSI) is not perfectly known to the receiver, and present an iterative channel estimation algorithm. Simulations show that the performance of SDE with channel estimation approaches that of SDE with perfect CSI

Correcting the Bias of Subtractive Interference Cancellation in CDMA: Advanced Mean Field Theory

In this paper we introduce an advanced mean field method to correct the inherent bias of conventional subtractive interference cancellation in Code Division Multiple Access (CDMA). In simulations, we get a performance quite close to that of the individual optimal exponential complexity detector and significant improvements over current state-of-the-art subtractive interference cancellation in all setups tested, for example in one case doubling the number of user at a bit error rate of. To obtain such a good performance for finite size systems, where the performance is normally degraded by the presence of suboptimal fix-point solutions, it is crucial to use the method in conjunction with mean field annealing, i.e. solving the fixed point equations at decreasing temperatures (noise levels). In the limit of infinite large system size, the new subtractive interference cancellation scheme is expected to be identical to the individual optimal detector. The computational complexity is cubic in the number of users whereas conventional (naive mean field) subtractive interference cancellation is quadratic. We also present a quadratic complexity approximation to our new method that also gives performance improvements, but in addition requires knowledge of the spreading code statistics. The proposed methodology is quite general and is expected to be applicable to other digital communication problems

Wireless multiuser communication systems: diversity receiver performance analysis, GSMuD design, and fading channel simulator

Multipath fading phenomenon is central to the design and analysis of wireless communication systems including multiuser systems. If untreated, the fading will corrupt the transmitted signal and often cause performance degradations such as increased communication error and decreased data rate, as compared to wireline channels with little or no multipath fading. On the other hand, this multipath fading phenomenon, if fully utilized, can actually lead to system designs that provide additional gains in system performance as compared to systems that experience non-fading channels.;The central question this thesis tries to answer is how to design and analyze a wireless multiuser system that takes advantage of the benefits the diversity multipath fading channel provides. Two particular techniques are discussed and analyzed in the first part of the thesis: quadrature amplitude modulation (QAM) and diversity receivers, including maximal ratio combining (MRC) and generalized selection combining (GSC). We consider the practical case of imperfect channel estimation (ICE) and develop a new decision variable (DV) of MRC receiver output for M-QAM. By deriving its moment generating function (MGF), we obtain the exact bit error rate (BER) performance under arbitrary correlated Rayleigh and Rician channels, with ICE. GSC provides a tradeoff between receiver complexity and performance. We study the effect of ICE on the GSC output effective SNR under generalized fading channels and obtain the exact BER results for M-QAM systems. The significance of this part lies in that these results provide system designers means to evaluate how different practical channel estimators and their parameters can affect the system\u27s performance and help them distribute system resources that can most effectively improve performance.;In the second part of the thesis, we look at a new diversity technique unique to multiuser systems under multipath fading channels: the multiuser diversity. We devise a generalized selection multiuser diversity (GSMuD) scheme for the practical CDMA downlink systems, where users are selected for transmission based on their respective channel qualities. We include the effect of ICE in the design and analysis of GSMuD. Based on the marginal distribution of the ranked user signal-noise ratios (SNRs), we develop a practical adaptive modulation and coding (AMC) scheme and equal power allocation scheme and statistical optimal 1-D and 2-D power allocation schemes, to fully exploit the available multiuser diversity. We use the convex optimization procedures to obtain the 1-D and 2-D power allocation algorithms, which distribute the total system power in the waterfilling fashion alone the user (1-D) or both user and time (2-D) for the power-limited and energy-limited system respectively. We also propose a normalized SNR based GSMuD scheme where user access fairness issues are explicitly addressed. We address various fairness-related performance metrics such as the user\u27s average access probability (AAP), average access time (AAT), and average wait time (AWT) in the absolute- and normalized-SNR based GSMuD. These metrics are useful for system designers to determine parameters such as optimal packet size and delay constraints.;We observe that Nakakagami-m fading channel model is widely applied to model the real world multipath fading channels of different severity. In the last part of the thesis, we propose a Nakagami-m channel simulator that can generate accurate channel coefficients that follow the Nakagami-m model, with independent quadrature parts, accurate phase distribution and arbitrary auto-correlation property. We demonstrate that the proposed simulator can be extremely useful in simulations involving Nakagami-m fading channel models, evident from the numerous simulation results obtained in earlier parts of the thesis where the fading channel coefficients are generated using this proposed simulator

Federated Edge Learning with Misaligned Over-The-Air Computation

Over-the-air computation (OAC) is a promising technique to realize fast model aggregation in the uplink of federated edge learning. OAC, however, hinges on accurate channel-gain precoding and strict synchronization among the edge devices, which are challenging in practice. As such, how to design the maximum likelihood (ML) estimator in the presence of residual channel-gain mismatch and asynchronies is an open problem. To fill this gap, this paper formulates the problem of misaligned OAC for federated edge learning and puts forth a whitened matched filtering and sampling scheme to obtain oversampled, but independent, samples from the misaligned and overlapped signals. Given the whitened samples, a sum-product ML estimator and an aligned-sample estimator are devised to estimate the arithmetic sum of the transmitted symbols. In particular, the computational complexity of our sum-product ML estimator is linear in the packet length and hence is significantly lower than the conventional ML estimator. Extensive simulations on the test accuracy versus the average received energy per symbol to noise power spectral density ratio (EsN0) yield two main results: 1) In the low EsN0 regime, the aligned-sample estimator can achieve superior test accuracy provided that the phase misalignment is non-severe. In contrast, the ML estimator does not work well due to the error propagation and noise enhancement in the estimation process. 2) In the high EsN0 regime, the ML estimator attains the optimal learning performance regardless of the severity of phase misalignment. On the other hand, the aligned-sample estimator suffers from a test-accuracy loss caused by phase misalignment.Comment: 17 pages, 11 figure