arXiv subjects

Ralf R. Müller

Publications and source records attributed to Ralf R. Müller.

At least 55 records · Page 3Linked to original sources

arXiv2018

Theoretical Bounds on MAP Estimation in Distributed Sensing Networks

The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior is proportional to the regularization term. In this paper, we study distributed sensing networks in which a set of spatially correlated signals are measured individually at separate terminals, but recovered jointly via a generic maximum-a-posterior estimator. Using the replica method, it is shown that the setting exhibits the decoupling property. For the case with jointly sparse signals, we invoke Bayesian inference and propose the "multi-dimensional soft thresholding" algorithm which is posed as a linear programming. Our investigations depict that the proposed algorithm outperforms the conventional $\ell_{2,1}$-norm regularized least squares scheme while enjoying a feasible computational complexity.

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arXiv2018

RLS Recovery with Asymmetric Penalty: Fundamental Limits and Algorithmic Approaches

This paper studies regularized least square recovery of signals whose samples' prior distributions are nonidentical, e.g., signals with time-variant sparsity. For this model, Bayesian framework suggests to regularize the least squares term with an asymmetric penalty. We investigate this problem in two respects: First, we characterize the asymptotic performance via the replica method and then discuss algorithmic approaches to the problem. Invoking the asymptotic characterization of the performance, we propose a tuning strategy to optimally tune the algorithmic approaches for recovery. To demonstrate applications of the results, the particular example of BPSK recovery is investigated and the efficiency of the proposed strategy is depicted in the shadow of results available in the literature

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arXiv2018

Iterative Antenna Selection for Secrecy Enhancement in Massive MIMO Wiretap Channels

The growth of interest in massive MIMO systems is accompanied with hardware cost and computational complexity. Antenna selection is an efficient approach to overcome this cost-plus-complexity issue which also enhances the secrecy performance in wiretap settings. Optimal antenna selection requires exhaustive search which is computationally infeasible for settings with large dimensions. This paper develops an iterative algorithm for antenna selection in massive multiuser MIMO wiretap settings. The algorithm takes a stepwise approach to find a suitable subset of transmit antennas. Numerical investigations depict a significant enhancement in the secrecy performance.

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arXiv2018

Capacity Scaling in MIMO Systems with General Unitarily Invariant Random Matrices

We investigate the capacity scaling of MIMO systems with the system dimensions. To that end, we quantify how the mutual information varies when the number of antennas (at either the receiver or transmitter side) is altered. For a system comprising $R$ receive and $T$ transmit antennas with $R>T$, we find the following: By removing as many receive antennas as needed to obtain a square system (provided the channel matrices before and after the removal have full rank) the maximum resulting loss of mutual information over all signal-to-noise ratios (SNRs) depends only on $R$, $T$ and the matrix of left-singular vectors of the initial channel matrix, but not on its singular values. In particular, if the latter matrix is Haar distributed the ergodic rate loss is given by $\sum_{t=1}^{T}\sum_{r=T+1}^{R}\frac{1}{r-t}$ nats. Under the same assumption, if $T,R\to \infty$ with the ratio $ϕ\triangleq T/R$ fixed, the rate loss normalized by $R$ converges almost surely to $H(ϕ)$ bits with $H(\cdot)$ denoting the binary entropy function. We also quantify and study how the mutual information as a function of the system dimensions deviates from the traditionally assumed linear growth in the minimum of the system dimensions at high SNR.

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arXiv2018

Optimal Transmit Antenna Selection for Massive MIMO Wiretap Channels

In this paper, we study the impacts of transmit antenna selection on the secrecy performance of massive MIMO systems. We consider a wiretap setting in which a fixed number of transmit antennas are selected and then confidential messages are transmitted over them to a multi-antenna legitimate receiver while being overheard by a multi-antenna eavesdropper. For this setup, we derive an accurate approximation of the instantaneous secrecy rate. Using this approximation, it is shown that in some wiretap settings under antenna selection the growth in the number of active antennas enhances the secrecy performance of the system up to some optimal number and degrades it when this optimal number is surpassed. This observation demonstrates that antenna selection in some massive MIMO settings not only reduces the RF-complexity, but also enhances the secrecy performance. We then consider various scenarios and derive the optimal number of active antennas analytically using our large-system approximation. Numerical investigations show an accurate match between simulations and the analytic results.

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arXiv2018

Stepwise Transmit Antenna Selection in Downlink Massive Multiuser MIMO

Due to the large power consumption in RF-circuitry of massive MIMO systems, practically relevant performance measures such as energy efficiency or bandwidth efficiency are neither necessarily monotonous functions of the total transmit power nor the number of active antennas. Optimal antenna selection is however computationally infeasible in these systems. In this paper, we propose an iterative algorithm to optimize the transmit power and the subset of selected antennas subject to non-monotonous performance measures in massive multiuser MIMO settings. Numerical results are given for energy efficiency and demonstrate that for several settings the optimal number of selected antennas reported by the proposed algorithm is significantly smaller than the total number of transmit antennas. This fact indicates that antenna selection in several massive MIMO scenarios not only reduces the hardware complexity and RF-costs, but also enhances the energy efficiency of the system.

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arXiv2018

Maximum-A-Posteriori Signal Recovery with Prior Information: Applications to Compressive Sensing

This paper studies the asymptotic performance of maximum-a-posteriori estimation in the presence of prior information. The problem arises in several applications such as recovery of signals with non-uniform sparsity pattern from underdetermined measurements. With prior information, the maximum-a-posteriori estimator might have asymmetric penalty. We consider a generic form of this estimator and study its performance via the replica method. Our analyses demonstrate an asymmetric form of the decoupling property in the large-system limit. Employing our results, we further investigate the performance of weighted zero-norm minimization for recovery of a non-uniform sparse signal. Our investigations illustrate that for a given distortion, the minimum number of required measurements can be significantly reduced by choosing weighting coefficients optimally.

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arXiv2018

Oversampled Adaptive Sensing

We develop a Bayesian framework for sensing which adapts the sensing time and/or basis functions to the instantaneous sensing quality measured in terms of the expected posterior mean-squared error. For sparse Gaussian sources a significant reduction in average sensing time and/or mean-squared error is achieved in comparison to non-adaptive sensing. For compression ratio 3, a sparse 10% Gaussian source and equal average sensing times, the proposed method gains about 2 dB over the performance bound of optimum compressive sensing, about 3 dB over non-adaptive 3-fold oversampled orthogonal sensing and about 6 to 7 dB to LASSO-based recovery schemes while enjoying polynomial time complexity. We utilize that in the presence of Gaussian noise the mean-squared error conditioned on the current observation is proportional to the derivative of the conditional mean estimate with respect to this observation.

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arXiv2018

Precoding via Approximate Message Passing with Instantaneous Signal Constraints

This paper proposes a low complexity precoding algorithm based on the recently proposed Generalized Least Square Error (GLSE) scheme with generic penalty and support. The algorithm iteratively constructs the transmit vector via Approximate Message Passing (AMP). Using the asymptotic decoupling property of GLSE precoders, we derive closed form fixed point equations to tune the parameters in the proposed algorithm for a general set of instantaneous signal constraints. The tuning strategy is then utilized to construct transmit vectors with restricted peak-to-average power ratios and to efficiently select a subset of transmit antennas. The numerical investigations show that the proposed algorithm tracks the large-system performance of GLSE precoders even for a moderate number of antennas.

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arXiv2017

Statistical Mechanics of MAP Estimation: General Replica Ansatz

The large-system performance of MAP estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix to be chosen from the large class of rotationally invariant random matrices. We take a statistical mechanical approach by introducing a spin glass corresponding to the estimator, and employing the replica method for the large-system analysis. In contrast to earlier replica based studies, our analysis evaluates the general replica ansatz of the corresponding spin glass and determines the asymptotic distortion of the estimator for any structure of the replica correlation matrix. Consequently, the replica symmetric as well as the Replica Symmetry (RS) breaking ansatz with $b$ steps of breaking is deduced from the given general replica ansatz. The generality of our distortion function lets us derive a more general form of the MAP decoupling principle. Based on the general replica ansatz, we show that for any structure of the replica correlation matrix, the vector-valued system decouples into a bank of equivalent decoupled linear systems followed by MAP estimators. The structure of the decoupled linear system is further studied under both the RS and the Replica Symmetry Breaking (RSB) assumptions. For $b$ steps of RSB, the decoupled system is found to be an additive system with a noise term given as the sum of an independent Gaussian random variable with $b$ correlated impairment terms. As an application of our study, we investigate large compressive sensing systems by considering the $\ell_p$ minimization recovery schemes. Our numerical investigations show that the replica symmetric ansatz for $\ell_0$ norm recovery fails to give an accurate approximation of the mean square error as the compression rate grows, and therefore, the RSB ansätze are needed.

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arXiv2017

Optimal Number of Transmit Antennas for Secrecy Enhancement in Massive MIMOME Channels

This paper studies the impact of transmit antenna selection on the secrecy performance of massive MIMO wiretap channels. We consider a scenario in which a multi-antenna transmitter selects a subset of transmit antennas with the strongest channel gains. Confidential messages are then transmitted to a multi-antenna legitimate receiver while the channel is being overheard by a multi-antenna eavesdropper. For this setup, we approximate the distribution of the instantaneous secrecy rate in the large-system limit. The approximation enables us to investigate the optimal number of selected antennas which maximizes the asymptotic secrecy throughput of the system. We show that increasing the number of selected antennas enhances the secrecy performance of the system up to some optimal value, and that further growth in the number of selected antennas has a destructive effect. Using the large-system approximation, we obtain the optimal number of selected antennas analytically for various scenarios. Our numerical investigations show an accurate match between simulations and the analytic results even for not so large dimensions.

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arXiv2017

On User Pairing in NOMA Uplink

User pairing in Non-Orthogonal Multiple-Access (NOMA) uplink based on channel state information is investigated considering some predefined power allocation schemes. The base station divides the set of users into disjunct pairs and assigns the available resources to these pairs. The combinatorial problem of user pairing to achieve the maximum sum rate is analyzed in the large system limit for various scenarios, and some optimum and sub-optimum algorithms with a polynomial-time complexity are proposed. In the first scenario, $2M$ users and the base station have a single-antenna and communicate over $M$ subcarriers. The performance of optimum pairing is derived for $M\rightarrow \infty$ and shown to be superior to random pairing and orthogonal multiple access techniques. In the second setting, a novel NOMA scheme for a multi-antenna base station and single carrier communication is proposed. In this case, the users need not be aware of the pairing strategy. Furthermore, the proposed NOMA scheme is generalized to multi-antenna users. It is shown that random and optimum user pairing perform similarly in the large system limit, but optimum pairing is significantly better in finite dimensions. It is shown that the proposed NOMA scheme outperforms a previously proposed NOMA scheme with signal alignment.

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arXiv2017

Asymptotics of Nonlinear LSE Precoders with Applications to Transmit Antenna Selection

This paper studies the large-system performance of Least Square Error (LSE) precoders which~minimize~the~input-output distortion over an arbitrary support subject to a general penalty function. The asymptotics are determined via the replica method in a general form which encloses the Replica Symmetric (RS) and Replica Symmetry Breaking (RSB) ansätze. As a result, the "marginal decoupling property" of LSE precoders for $b$-steps of RSB is derived. The generality of the studied setup enables us to address special cases in which the number of active transmit antennas are constrained. Our numerical investigations depict that the computationally efficient forms of LSE precoders based on "$\ell_1$-norm" minimization perform close to the cases with "zero-norm" penalty function which have a considerable improvements compared to the random antenna selection. For the case with BPSK signals and restricted number of active antennas, the results show that RS fails to predict the performance while the RSB ansatz is consistent with theoretical bounds.

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arXiv2017

A New Class of Nonlinear Precoders for Hardware Efficient Massive MIMO Systems

A general class of nonlinear Least Square Error (LSE) precoders in multi-user multiple-input multiple-output systems is analyzed using the replica method from statistical mechanics. A single cell downlink channel with $N$ transmit antennas at the base station and $K$ single-antenna users is considered. The data symbols are assumed to be iid Gaussian and the precoded symbols on each transmit antenna are restricted to be chosen from a predefined set $\mathbb{X}$. The set $\mathbb{X}$ encloses several well-known constraints in wireless communications including signals with peak power, constant envelope signals and finite constellations such as Phase Shift Keying (PSK). We determine the asymptotic distortion of the LSE precoder under both the Replica Symmetry (RS) and the one step Replica Symmetry Breaking (1-RSB) assumptions. For the case of peak power constraint on each transmit antenna, our analyses under the RS assumption show that the LSE precoder can reduce the peak to average power ratio to 3dB without any significant performance loss. For PSK constellations, as $N/K$ grows, the RS assumption fails to predict the performance accurately and therefore, investigations under the 1-RSB assumption are further considered. The results show that the 1-RSB assumption is more accurate.

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arXiv2017

Asymptotics of Transmit Antenna Selection: Impact of Multiple Receive Antennas

Consider a fading Gaussian MIMO channel with $N_\mathrm{t}$ transmit and $N_\mathrm{r}$ receive antennas. The transmitter selects $L_\mathrm{t}$ antennas corresponding to the strongest channels. For this setup, we study the distribution of the input-output mutual information when $N_\mathrm{t}$ grows large. We show that, for any $N_\mathrm{r}$ and $L_\mathrm{t}$, the distribution of the input-output mutual information is accurately approximated by a Gaussian distribution whose mean grows large and whose variance converges to zero. Our analysis depicts that, in the large limit, the gap between the expectation of the mutual information and its corresponding upper bound, derived by applying Jensen's inequality, converges to a constant which only depends on $N_\mathrm{r}$ and $L_\mathrm{t}$. The result extends the scope of channel hardening to the general case of antenna selection with multiple receive and selected transmit antennas. Although the analyses are given for the large-system limit, our numerical investigations indicate the robustness of the approximated distribution even when the number of antennas is not large.

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arXiv2017

Nonlinear Precoders for Massive MIMO Systems with General Constraints

We introduce a class of nonlinear least square error precoders with a general penalty function for multiuser massive MIMO systems. The generality of the penalty function allows us to consider several hardware limitations including transmitters with a predefined constellation and restricted number of active antennas. The large-system performance is then investigated via the replica method under the assumption of replica symmetry. It is shown that the least square precoders exhibit the "marginal decoupling property" meaning that the marginal distributions of all precoded symbols converge to a deterministic distribution. As a result, the asymptotic performance of the precoders is described by an equivalent single-user system. To address some applications of the results, we further study the asymptotic performance of the precoders when both the peak-to-average power ratio and number of active transmit antennas are constrained. Our numerical investigations show that for a desired distortion at the receiver side, proposed forms of the least square precoders need to employ around %35\%$ fewer number of active antennas compared to cases with random transmit antenna selection.

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arXiv2017

Asymptotic Performance Analysis of Spatially Reconfigurable Antenna Arrays

A spatially reconfigurable antenna arrays consists of an antenna array of finite length and fixed geometry which is displaced within a given area. Using these reconfigurable components, the performance of MIMO systems is remarkably improved by effectively positioning the array in its displacement area. This paper studies the large-system performance of MIMO setups with spatially reconfigurable antenna arrays when the displacement area is large. Considering fading channels, the distribution of the input-output mutual information is derived, and the asymptotic hardening property is demonstrated to hold. As the size of the displacement area grows large, the mutual information is shown to converge in distribution to a type-one Gumbel random variable whose mean grows large proportional to the displacement size, and whose variance tends to zero. Our numerical investigations depict that the type-one Gumbel approximation closely tracks the empirical distribution even for a finite displacement size.

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arXiv2016

Phase Shift Keying on the Hypersphere: Peak Power-Efficient MIMO Communications

Phase Shift Keying on the Hypersphere (PSKH), a generalization of conventional Phase Shift Keying (PSK) for Multiple-Input Multiple-Output (MIMO) systems, is introduced. In PSKH, constellation points are distributed on a multidimensional hypersphere. The use of such constellations with a Peak-To-Average-Sum-Power-Ratio (PASPR) of 1 allows to use load-modulated transmitters which can cope with a small backoff, which in turn results in a high power efficiency. In this paper, we discuss several methods how to generate PSKH constellations and compare their performance. After applying conventional Pulse-Amplitude Modulation (PAM), the PASPR of the continuous time PSKH signal depends on the choice of the pulse shaping method. This choice also influences bandwidth and power efficiency of a PSKH system. In order to reduce the PASPR of the continuous transmission signal, we use spherical interpolation to generate a smooth signal over the hypersphere and present corresponding receiver techniques. Additionally, complexity reduction techniques are proposed and compared. Finally, we discuss the methods presented in this paper regarding their trade-offs with respect to PASPR, bandwidth, power efficiency and receiver complexity.

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