arXiv subjects

Peter Jung

Publications and source records attributed to Peter Jung.

At least 73 records · Page 4Linked to original sources

arXiv2018

Derandomizing compressed sensing with combinatorial design

Compressed sensing is the art of reconstructing structured $n$-dimensional vectors from substantially fewer measurements than naively anticipated. A plethora of analytic reconstruction guarantees support this credo. The strongest among them are based on deep results from large-dimensional probability theory that require a considerable amount of randomness in the measurement design. Here, we demonstrate that derandomization techniques allow for considerably reducing the amount of randomness that is required for such proof strategies. More, precisely we establish uniform s-sparse reconstruction guarantees for $C s \log (n)$ measurements that are chosen independently from strength-four orthogonal arrays and maximal sets of mutually unbiased bases, respectively. These are highly structured families of $\tilde{C} n^2$ vectors that imitate signed Bernoulli and standard Gaussian vectors in a (partially) derandomized fashion.

cs.IT↗

arXiv2018

Generalized Approximate Message Passing for Unlimited Sampling of Sparse Signals

In this paper we consider the generalized approximate message passing (GAMP) algorithm for recovering a sparse signal from modulo samples of randomized projections of the unknown signal. The modulo samples are obtained by a self-reset (SR) analog to digital converter (ADC). Additionally, in contrast to previous work on SR ADC, we consider a scenario where the compressed sensing (CS) measurements (i.e., randomized projections) are sent through a communication channel, namely an additive white Gaussian noise (AWGN) channel before being quantized by a SR ADC. To show the effectiveness of the proposed approach, we conduct Monte-Carlo (MC) simulations for both noiseless and noisy case. The results show strong ability of the proposed algorithm to fight the nonlinearity of the SR ADC, as well as the possible additional distortion introduced by the AWGN channel.

eess.SP↗

arXiv2018

A New Scaling Law for Activity Detection in Massive MIMO Systems

In this paper, we study the problem of \textit{activity detection} (AD) in a massive MIMO setup, where the Base Station (BS) has $M \gg 1$ antennas. We consider a block fading channel model where the $M$-dim channel vector of each user remains almost constant over a \textit{coherence block} (CB) containing $D_c$ signal dimensions. We study a setting in which the number of potential users $K_c$ assigned to a specific CB is much larger than the dimension of the CB $D_c$ ($K_c \gg D_c$) but at each time slot only $A_c \ll K_c$ of them are active. Most of the previous results, based on compressed sensing, require that $A_c\le D_c$, which is a bottleneck in massive deployment scenarios such as Internet-of-Things (IoT) and Device-to-Device (D2D) communication. In this paper, we show that one can overcome this fundamental limitation when the number of BS antennas $M$ is sufficiently large. More specifically, we derive a \textit{scaling law} on the parameters $(M, D_c, K_c, A_c)$ and also \textit{Signal-to-Noise Ratio} (SNR) under which our proposed AD scheme succeeds. Our analysis indicates that with a CB of dimension $D_c$, and a sufficient number of BS antennas $M$ with $A_c/M=o(1)$, one can identify the activity of $A_c=O(D_c^2/\log^2(\frac{K_c}{A_c}))$ active users, which is much larger than the previous bound $A_c=O(D_c)$ obtained via traditional compressed sensing techniques. In particular, in our proposed scheme one needs to pay only a poly-logarithmic penalty $O(\log^2(\frac{K_c}{A_c}))$ for increasing the number of potential users $K_c$, which makes it ideally suited for AD in IoT setups. We propose low-complexity algorithms for AD and provide numerical simulations to illustrate our results. We also compare the performance of our proposed AD algorithms with that of other competitive algorithms in the literature.

cs.IT↗

arXiv2018

Noncoherent Short-Packet Communication via Modulation on Conjugated Zeros

We introduce a novel blind (noncoherent) communication scheme, called modulation on conjugate-reciprocal zeros (MOCZ), to reliably transmit short binary packets over unknown finite impulse response systems as used, for example, to model underspread wireless multipath channels. In MOCZ, the information is modulated onto the zeros of the transmitted signals $z-$transform. In the absence of additive noise, the zero structure of the signal is perfectly preserved at the receiver, no matter what the channel impulse response (CIR) is. Furthermore, by a proper selection of the zeros, we show that MOCZ is not only invariant to the CIR, but also robust against additive noise. Starting with the maximum-likelihood estimator, we define a low complexity and reliable decoder and compare it to various state-of-the art noncoherent schemes.

cs.IT↗

arXiv2018

Towards Massive Connectivity Support for Scalable mMTC Communications in 5G networks

The fifth generation of cellular communication systems is foreseen to enable a multitude of new applications and use cases with very different requirements. A new 5G multiservice air interface needs to enhance broadband performance as well as provide new levels of reliability, latency and supported number of users. In this paper we focus on the massive Machine Type Communications (mMTC) service within a multi-service air interface. Specifically, we present an overview of different physical and medium access techniques to address the problem of a massive number of access attempts in mMTC and discuss the protocol performance of these solutions in a common evaluation framework.

cs.IT↗

arXiv2018

The Szegö-Asymptotics for Doubly-Dispersive Gaussian Channels

We consider the time-continuous doubly--dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel operator is represented by a symbol which is periodic in time and fulfills some further integrability, smoothness and oscillation conditions. More precisely, we apply the well-known Holsinger-Gallager model for translating a time-continuous channel for a sequence of time--intervals of increasing length $α\rightarrow\infty$ to a series of equivalent sets of discrete, parallel channels, known at the transmitter. We quantify conditions when this procedure converges. Finally, under periodicity assumptions this result can indeed be justified as the channel capacity in the sense Shannon. The key to this is result is a new Szegö formula for certain pseudo--differential operators with real-valued symbol. The Szegö limit holds if the symbol belongs to the homogeneous Besov space $\dot{B}^1_{\infty,1}$ with respect to its time-dependency, characterizing the oscillatory behavior in time. Finally, the formula justifies the water-filling principle in time and frequency as general technique independent of a sampling scheme.

cs.IT↗

arXiv2017

Breaking Imaging Limits using Dithering Masks in 0.35 Terahertz Single-Pixel Imaging

In this contribution, we explore the imaging limits of terahertz single-pixel cameras and present a way to improve the achievable signal-to-noise ratio and spatial resolution using a technique called dithering masks. The proposed procedure is implemented on the hardware level using recent advances in the development of spatial light modulators for terahertz single-pixel cameras. Thereby, our approach offers new ways to overcome theoretical imaging limits of near wavelength resolution. We suggest that in using dithering masks the required phase retrieval driven recovery can be simplified to a robust non-negative linear model even for near wavelength terahertz single-pixel imaging.

physics.ins-det↗

arXiv2017

Mask Responses for Single-Pixel Terahertz Imaging

Terahertz (THz) radiation meaning electromagnetic radiation in the range from 0.1 THz (3 mm) to 10 THz (30 mu) has the unique advantage of easily penetrating many obstructions while being non-hazardous to organic tissue since it is non-ionizing. A shortcoming of this domain is the limited availability of high-sensitivity detector arrays respective THz cameras with >1k pixels. To overcome the imaging limitations of the THz domain, compressive imaging in combination with an optically controllable THz spatial light modulator is a promising approach especially when used in a single-pixel imaging modality. The imaging fidelity, performance and speed of this approach depend crucially on the imaging patterns also called masks and their properties used in the imaging process. Therefore, in this paper, it is investigated how the image quality after reconstruction is specifically influenced by the different mask types and their properties in a compressive imaging modality. The evaluation derives specific guidelines for the use in THz single-pixel imaging setups respective THz single-pixel cameras employing optically controllable THz spatial light modulators. As an outlook, a method is suggested that builds upon the results presented in this text and extends the discussed advantages to an improved compressive imaging setting fit for stand-off security imaging applications aka single-pixel detector Body Scanners.

physics.optics↗

arXiv2017

Blind Demixing and Deconvolution at Near-Optimal Rate

We consider simultaneous blind deconvolution of r source signals from their noisy superposition, a problem also referred to blind demixing and deconvolution. This signal processing problem occurs in the context of the Internet of Things where a massive number of sensors sporadically communicate only short messages over unknown channels. We show that robust recovery of message and channel vectors can be achieved via convex optimization when random linear encoding using i.i.d. complex Gaussian matrices is used at the devices and the number of required measurements at the receiver scales with the degrees of freedom of the overall estimation problem. Since the scaling is linear in r our result significantly improves over recent works.

cs.IT↗

arXiv2017

Robust Nonnegative Sparse Recovery and the Nullspace Property of 0/1 Measurements

We investigate recovery of nonnegative vectors from non-adaptive compressive measurements in the presence of noise of unknown power. In the absence of noise, existing results in the literature identify properties of the measurement that assure uniqueness in the non-negative orthant. By linking such uniqueness results to nullspace properties, we deduce uniform and robust compressed sensing guarantees for nonnegative least squares. No l1-regularization is required. As an important proof of principle, we establish that m x n random i.i.d. 0/1-valued Bernoulli matrices obey the required conditions with overwhelming probability provided that m=O(slog(n/s)). We achieve this by establishing the robust nullspace property for random 0/1-matrices - a novel result in its own right. Our analysis is motivated by applications in wireless network activity detection.

cs.IT↗

arXiv2017

Short-Message Communication and FIR System Identification using Huffman Sequences

Providing short-message communication and simultaneous channel estimation for sporadic and fast fading scenarios is a challenge for future wireless networks. In this work we propose a novel blind communication and deconvolution scheme by using Huffman sequences, which allows to solve three important tasks in one step: (i) determination of the transmit power (ii) identification of the discrete-time FIR channel by providing a maximum delay of less than $L/2$ and (iii) simultaneously communicating $L-1$ bits of information. Our signal reconstruction uses a recent semi-definite program that can recover two unknown signals from their auto-correlations and cross-correlations. This convex algorithm is stable and operates fully deterministic without any further channel assumptions.

cs.IT↗

arXiv2017

Blind Deconvolution with Additional Autocorrelations via Convex Programs

In this work we characterize all ambiguities of the linear (aperiodic) one-dimensional convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities can be mapped one-to-one to factorization ambiguities in the $z-$domain, which are generated by swapping the zeros of the input signals. We use this polynomial description to show a deterministic version of a recently introduced masked Fourier phase retrieval design. In the noise-free case a (convex) semi-definite program can be used to recover exactly the input signals if they share no common factors (zeros). Then, we reformulate the problem as deterministic blind deconvolution with prior knowledge of the autocorrelations. Numerically simulations show that our approach is also robust against additive noise.

cs.IT↗

arXiv2017

Spline Waveforms and Interference Analysis for 5G Random Access with Short Message Support

One of the main drivers for new waveforms in future 5G wireless communication systems is to handle efficiently the variety of traffic types and requirements. In this paper, we introduce a new random access within the standard acquisition procedures to support sporadic traffic as an enabler of the Internet of Things (IoT). The major challenge hereby is to cope with the highly asynchronous access of different devices and to allow transmission of control signaling and payload "in one shot". We address this challenge by using a waveform design approach based on bi-orthogonal frequency division multiplexing where transmit orthogonality is replaced in favor of better temporal and spectral properties. We show that this approach allows data transmission in frequencies that otherwise have to remain unused. More precisely, we utilize frequencies previously used as guard bands, located towards the standard synchronous communication pipes as well as in between the typically small amount of resources used by each IoT device. We demonstrate the superiority of this waveform approach over the conventional random access using a novel mathematical approach and numerical experiments.

cs.IT↗

arXiv2016

Compressive Random Access Using A Common Overloaded Control Channel

We introduce a "one shot" random access procedure where users can send a message without a priori synchronizing with the network. In this procedure a common overloaded control channel is used to jointly detect sparse user activity and sparse channel profiles. The detected information is subsequently used to demodulate the data in dedicated frequency slots. We analyze the system theoretically and provide a link between achievable rates and standard compressing sensing estimates in terms of explicit expressions and scaling laws. Finally, we support our findings with simulations in an LTE-A-like setting allowing "one shot" sparse random access of 100 users in 1ms.

cs.IT↗

arXiv2016

Block Compressed Sensing Based Distributed Device Detection for M2M Communications

In this work, we utilize the framework of compressed sensing (CS) for distributed device detection and resource allocation in large-scale machine-to-machine (M2M) communication networks. The devices deployed in the network are partitioned into clusters according to some pre-defined criteria. Moreover, the devices in each cluster are assigned a unique signature of a particular design that can be used to indicate their active status to the network. The proposed scheme in this work mainly consists of two essential steps: (i) The base station (BS) detects the active clusters and the number of active devices in each cluster using a novel block sketching algorithm, and then assigns a certain amount of resources accordingly. (ii) Each active device detects its ranking among all the active devices in its cluster using an enhanced greedy algorithm and accesses the corresponding resource for transmission based on the ranking. By exploiting the correlation in the device behaviors and the sparsity in the activation pattern of the M2M devices, the device detection problem is thus tackled as a CS support recovery procedure for a particular binary block-sparse signal $x\in\mathbb{B}^N$ -- with block sparsity $K_B$ and in-block sparsity $K_I$ over block size $d$. Theoretical analysis shows that the activation pattern of the M2M devices can be reliably reconstructed within an acquisition time of $\mathcal{O}(\max\{K_B\log N, K_BK_I\log d\})$, which achieves a better scaling and less computational complexity of $\mathcal{O}(N(K_I^2+\log N))$ compared with standard CS algorithms. Moreover, extensive simulations confirm the robustness of the proposed scheme in the detection process, especially in terms of higher detection probability and reduced access delay when compared with conventional schemes like LTE random access (RA) procedure and classic cluster-based access approaches.

cs.IT↗

arXiv2016

Capacity and Degree-of-Freedom of OFDM Channels with Amplitude Constraint

In this paper, we study the capacity and degree-of-freedom (DoF) scaling for the continuous-time amplitude limited AWGN channels in radio frequency (RF) and intensity modulated optical communication (OC) channels. More precisely, we study how the capacity varies in terms of the OFDM block transmission time $T$, bandwidth $W$, amplitude $A$, and the noise spectral density $N_0$. We first find suitable discrete encoding spaces for both cases, and prove that they are convex sets that have a semi-definite programming (SDP) representation. Using tools from convex geometry, we find lower and upper bounds on the volume of these encoding sets, which we exploit to drive pretty sharp lower and upper bounds on the capacity. We also study a practical Tone-Reservation (TR) encoding algorithm and prove that its performance can be characterized by the statistical width of an appropriate convex set. Recently, it has been observed that in high-dimensional estimation problems under constraints such as those arisen in Compressed Sensing (CS) statistical width plays a crucial role. We discuss some of the implications of the resulting statistical width on the performance of the TR. We also provide numerical simulations to validate these observations.

cs.IT↗

arXiv2015

OFDM Channel Estimation via Phase Retrieval

Pilot-aided channel estimation is nowadays a standard component in each wireless receiver enabling coherent transmission of complex-valued constellations, only affected by noise and interference. Whenever these disturbances are sufficiently small and long data frames are used, high data rates can be achieved and the resource overhead due to the pilots vanishes asymptotically. On the other, it is expected that for the next generation of mobile networks not only data rate is in the main focus but also low latency, short and sporadic messages, massive connectivity, distributed & adhoc processing and robustness with respect to asynchronism. Therefore a review of several well-established principles in communication has been started already. A particular implication when using complex-valued pilots is that these values have to be known at the receiver and therefore these resources can not be used simultaneously for user data. For an OFDM-like multicarrier scheme this means that pilot tones (usually placed equidistantly according to the Nyquist theorem) are allocated with globally known amplitudes and phases to reconstruct the channel impulse response. Phases are designed and allocated globally which is in contrast to a distributed infrastructure. In this work we present therefore a new phaseless pilot scheme where only pilot amplitudes need to be known at the receiver, i.e., phases are available again and can be used for various other purposes. The idea is based on a phase retrieval result for symmetrized and zero-padded magnitude Fourier measurements obtained by two of the authors. The phases on the pilot tones can now be used to carry additional user-specific data or compensate for other signal characteristics, like the PAPR.

cs.IT↗

arXiv2015

Compressive Rate Estimation with Applications to Device-to-Device Communications

We develop a framework that we call compressive rate estimation. We assume that the composite channel gain matrix (i.e. the matrix of all channel gains between all network nodes) is compressible which means it can be approximated by a sparse or low rank representation. We develop and study a novel sensing and reconstruction protocol for the estimation of achievable rates. We develop a sensing protocol that exploits the superposition principle of the wireless channel and enables the receiving nodes to obtain non-adaptive random measurements of columns of the composite channel matrix. The random measurements are fed back to a central controller that decodes the composite channel gain matrix (or parts of it) and estimates individual user rates. We analyze the rate loss for a linear and a non-linear decoder and find the scaling laws according to the number of non-adaptive measurements. In particular if we consider a system with $N$ nodes and assume that each column of the composite channel matrix is $k$ sparse, our findings can be summarized as follows. For a certain class of non-linear decoders we show that if the number of pilot signals $M$ scales like $M \sim k \log(N/k)$, then the rate loss compared to perfect channel state information remains bounded. For a certain class of linear decoders we show that the rate loss compared to perfect channel state information scales like $1/\sqrt{M}$.

cs.IT↗