Low Signal-to-noise Ratio Regime Research Articles

Upper and lower bounds for the ergodic capacity of MIMO Jacobi fading channels.

In multi-(core/mode) optical fiber communication, the transmission channel can be modeled as a complex sub-matrix of the Haar-distributed unitary matrix (complex Jacobi unitary ensemble). In this letter, we present new analytical expressions of the upper and lower bounds for the ergodic capacity of multiple-input multiple-output Jacobi-fading channels. Recent results on the determinant of the Jacobi unitary ensemble are employed to derive a tight lower bound on the ergodic capacity. We use Jensen's inequality to provide an analytical closed-form upper bound to the ergodic capacity at any signal-to-noise ratio (SNR). Closed-form expressions of the ergodic capacity, at low and high SNR regimes, are also derived. Simulation results are presented to validate the accuracy of the derived expressions.

Empirical consideration of the effects of acquisition parameters and analysis model on clinically feasible q-ball imaging

Q-ball imaging (QBI) is a popular high angular resolution diffusion imaging (HARDI) technique used to study brain architecture in vivo. Simulation and phantom-based studies suggest that QBI results are affected by the b-value, the number of diffusion weighting directions, and the signal-to-noise ratio (SNR). However, optimal acquisition schemes for QBI in clinical settings are largely undetermined given empirical (observed) imaging considerations. In this study, we acquire a HARDI dataset at five b-values with 11 repetitions on a single subject to investigate the effects of acquisition scheme and subsequent analysis models on the accuracy and precision of measures of tissue composition and fiber orientation derived from clinically feasible QBI at 3T. Clinical feasibility entails short scan protocols - less than 5minutes in the current study - resulting in lower SNR, lower b-values, and fewer diffusion directions than are typical in most QBI protocols with research applications, where time constraints are less prevalent. In agreement with previous studies, we find that the b-value and number of diffusion directions impact the magnitude and variation of QBI indices in both white matter and gray matter regions; however, QBI indices are most heavily dependent on the maximum order of the spherical harmonic (SH) series used to represent the diffusion orientation distribution function (ODF). Specifically, to ensure numerical stability and reduce the occurrence of false peaks and inflated anisotropy, we recommend oversampling by at least 8–12 more diffusion directions than the number of estimated coefficients for a given SH order. In addition, in an equal scan time comparison of QBI accuracy, we find that increasing the directional resolution of the HARDI dataset is preferable to repeating observations; however, our results indicate that as few as 32 directions at a low b-value (1000s/mm2) captures most of the angular information in the q-ball ODF. Our findings provide guidance for determining an optimal acquisition scheme for QBI in the low SNR and low scan time regime, and suggest that care must be taken when choosing the basis functions used to represent the QBI ODF.

Secure Transmission With Aid of a Helper for MIMOME Network Having Finite Alphabet Inputs

This paper considers secure transmission with the aid of a helper for finite alphabet signals in multiple-input–multiple-output multiple antenna eavesdropper networks, where the helper transmits a jamming signal along with the confidential message sent by the source node to confuse the eavesdropper. For the scenario in which the only statistical channel-state-information (CSI) of the eavesdropper links is available at the transmitter, the ergodic secrecy rate lacks closed-form expression, and the evaluation of the ergodic secrecy rate is computationally prohibitive. To address this problem, an accurate approximation of the ergodic secrecy rate is proposed to reduce the computational complexity. Utilizing this approximation of the ergodic secrecy rate, the joint optimization of precoding design and power allocation between the source and the helper is investigated to improve the ergodic secrecy rate. Furthermore, to achieve a tradeoff between computational complexity and performance, low-complexity schemes without iteration are proposed based on the analysis at extreme signal-to-noise ratio (SNR). In the low SNR regime, we prove that it is optimal to transmit confidential messages with full power, and the beamforming design is the first-order optimal precoder. At high SNR, we transform the problem of precoding design into a semi-definite programming problem, which can be efficiently solved by the interior-point method.

Power splitting based SWIPT in network-coded two-way networks with data rate fairness: an information-theoretic perspective

This paper investigates the simultaneous wireless information and power transfer (SWIPT) for network-coded two-way relay network from an information-theoretic perspective, where two sources exchange information via an SWIPT-aware energy harvesting (EH)relay. We present a power splitting (PS)-based two-way relaying (PS-TWR) protocol by employing the PS receiver architecture. To explore the system sum rate limit with data rate fairness, an optimization problem under total power constraint is formulated. Then, some explicit solutions are derived for the problem. Numerical results show that due to the path loss effect on energy transfer, with the same total available power, PS-TWR losses some system performance compared with traditional non-EH two-way relaying, where at relatively low and relatively high signal-to-noise ratio (SNR), the performance loss is relatively small. Another observations is that, in relatively high SNR regime, PS-TWR out-performs time switching-based two-way re-laying (TS-TWR) while in relatively low SNR regime TS-TWR outperforms PS-TWR. It is also shown that with individual available power at the two sources, PS-TWR outperforms TS-TWR in both relatively low and high SNR regimes.

Performance enhancement of MPM using SNR boosting techniques

Signal to noise ratio (SNR) boosting is one of the most important research areas in signal processing. The effectiveness of SNR boosting is not limited to a specific application rather, it is widely used in image processing, signal processing, cognitive radio, MIMO systems, digital beam forming, and direction of arrival (DOA) estimation …etc. In this paper, the recursive least square (RLS) and wavelet based de-noising filters are exploited for SNR boosting in DOA estimation techniques for further performance enhancement. The matrix pencil method (MPM) as an effortlessness and high resolution DOA estimation technique is taken as a test case. That is because it suffers from performance deterioration under low SNR regimes. The simulation results reveal that the MPM based RLS de-noising filter outperforms the MPM based wavelet de-noising filter and the traditional MPM in terms of mean square error (MSE) especially at low SNR regimes.

Bandwidth efficient transceiver design for differentially encoded OFDM system

In this paper, we present a bandwidth efficient non-coherent transceiver design for single input single output orthogonal frequency division multiplexing (SISO-OFDM) modulation with differential encoding. Under fast channel fading or in low signal-to-noise ratio (SNR) regime, pilot assisted channel estimation is not feasible. In such channel conditions, conventional non-coherent detection methods are not reliable resulting in poor throughput. We propose a frequency-spread time-encoded (FSTE) method for OFDM modulation, which exploits multipath diversity and achieves target energy-per-bit to noise spectral density $${E_b}/{N_0}$$Eb/N0 in low SNR regime by spreading differentially encoded information symbols along OFDM sub-carriers. We investigate the impact of spreading on bit-error rate (BER) and throughput under relative mobility and multipath fading scenarios. In order to maximize the throughput of the proposed method, we also optimize spreading factor and modulation order. The simulation results demonstrate significant BER and throughput performance gain as compared to prevailing differential encoding methods.

Capacity Bounds on the Ergodic Capacity of Distributed MIMO Systems over K Fading Channels

The performance of D-MIMO systems is not only affected by multipath fading but also from shadowing fading, as well as path loss. In this paper, we investigate the ergodic capacity of D-MIMO systems operating in non-correlated k fading (Rayleigh/Gamma) channels. With the aid of majorization and Minkowski theory, we derive analytical closed-form expressions of the upper and lower bounds on the ergodic capacity for D-MIMO systems over non-correlated k fading channels, which are quite general and applicable for arbitrary signal-to-noise ratio (SNR) and the number of transceiver antennas. To intuitively reveal the impacts of system and fading parameters on the ergodic capacity, we deduce asymptotic approximations in the high and low SNR regimes. Finally, we pursue the massive MIMO systems analysis for the lower bound and derive closed-form expressions when the number of antennas at BS grows large, and when the number of antennas at transceivers becomes large with a fixed and finite ratio. It is demonstrated that the proposed expressions on the ergodic capacity accurately match with the theoretical analysis.

Secure Transmission in Cooperative Relaying Networks With Multiple Antennas

We investigate the secrecy performance of dual-hop amplify-and-forward multi-antenna relaying systems over Rayleigh fading channels, considering the direct link between the source and the destination. In order to exploit the available direct link and the multiple antennas for secrecy improvement, different linear processing schemes at the relay and different diversity combining techniques at the destination are proposed, namely: 1) zero-forcing/maximal ratio combining (ZF/MRC); 2) ZF/selection combining (ZF/SC); 3) maximal ratio transmission/MRC (MRT/MRC); and 4) MRT/SC. For all these schemes, we present new closed-form approximations for the secrecy outage probability. Moreover, we investigate a benchmark scheme, i.e., cooperative jamming/ZF (CJ/ZF), where the secrecy outage probability is obtained in exact closed-form. In addition, we present asymptotic secrecy outage expressions for all the proposed schemes in the high signal-to-noise ratio (SNR) regime, in order to characterize key design parameters, such as secrecy diversity order and secrecy array gain. The outcomes of this paper can be summarized as follows: 1) MRT/MRC and MRT/SC achieve a full diversity order of $M+1$ , ZF/MRC and ZF/SC achieve a diversity order of $M$ , while CJ/ZF only achieves unit diversity order, where $M$ is the number of antennas at the relay; 2) ZF/MRC (ZF/SC) outperforms the corresponding MRT/MRC (MRT/SC) in the low SNR regime, while becomes inferior to the corresponding MRT/MRC (MRT/SC) in the high SNR; and 3) all the proposed schemes tend to outperform the CJ/ZF with moderate number of antennas, and linear processing schemes with MRC attain better performance than those with SC.

On the Minimax Risk of Dictionary Learning

We consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying dictionary. In particular, we derive lower bounds on the minimum achievable worst case mean squared error (MSE), regardless of computational complexity of the dictionary learning (DL) schemes. By casting DL as a classical (or frequentist) estimation problem, the lower bounds on the worst case MSE are derived following an established information-theoretic approach to minimax estimation. The main contribution of this paper is the adaption of these information-theoretic tools to the DL problem in order to derive lower bounds on the worst case MSE of any DL algorithm. We derive three different lower bounds applying to different generative models for the observed signals. The first bound only requires the existence of a covariance matrix of the (unknown) underlying coefficient vector. By specializing this bound to the case of sparse coefficient distributions and assuming the true dictionary satisfies the restricted isometry property, we obtain a lower bound on the worst case MSE of DL methods in terms of the signal-to-noise ratio (SNR). The third bound applies to a more restrictive subclass of coefficient distributions by requiring the non-zero coefficients to be Gaussian. Although the applicability of this bound is the most limited, it is the tightest of the three bounds in the low SNR regime. A particular use of our lower bounds is the derivation of necessary conditions on the required number of observations (sample size), such that DL is feasible, i.e., accurate DL schemes might exist. By comparing these necessary conditions with sufficient conditions on the sample size such that a particular DL technique is successful, we are able to characterize the regimes, where those algorithms are optimal in terms of required sample size.

High Diversity Transceiver for Low Power Differentially Encoded OFDM System

In this work, we investigate differentially encoded blind transceiver design in low signal-to-noise ratio (SNR) regimes for orthogonal frequency-division multiplexing (OFDM) signaling. Owing to the fact that acquisition of channel state information is not viable for short coherence times or in low SNR regimes, we propose a time-spread frequency-encoded method under OFDM modulation. The repetition (spreading) of differentially encoded symbols allows us to achieve a target energy per bit to noise ratio and higher diversity. Based on the channel order, we optimize subcarrier assignment for spreading (along time) to achieve frequency diversity of an OFDM modulated signal. We present the performance of our proposed transceiver design and investigate the impact of Doppler frequency on the performance of the proposed differentially encoded transceiver design. To further improve reliability of the decoded data, we employ capacity-achieving low-density parity-check forward error correction encoding to the information bits.

On the Capacity of MIMO Weibull-Gamma Fading Channels in Low SNR Regime

We present capacity analysis for multiple-input multiple-output (MIMO) system under a low signal-to-noise ratio (SNR) regime. We have selected a composite fading channel that considers Weibull fading for multipath and gamma fading for shadowing. We have presented the analysis in a detailed form for three different techniques, namely, spatial multiplexing (SM) with optimal detection, SM with minimum mean square error (MMSE) detection, and orthogonal space-time block codes (OSTBC). Because capacity analysis at arbitrary signal-to-noise (SNR) is stringent, a low SNR regime is considered to achieve a positive rate and wideband slope. The improvement is the result of minimizing energy per information bit (Eb). For the first time, closed-form expressions are evaluated for the capacity of MIMO systems at low SNR under WG fading channels which facilitate the performance comparison for proposed techniques.

Raptor Codes in the Low SNR Regime

In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise (BIAWGN) channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approximations. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime.

Optimal Multinode Sensing in a Malicious Cognitive Radio Network

Spectrum sensing is an essential function in cognitive radio systems for dynamic spectrum access. Multinode sensing is a technique being used in cognitive radio networks to enhance the sensing performance using space diversity concept. The challenges in multinode spectrum sensing are the prediction of signal status in multiple frequency bands in a low signal-to-noise ratio (SNR) regime and sensing reliability. The weighted gain combining (WGC) and the equal gain combining are the two soft decision cooperative sensing techniques being used frequently in literature. In this paper, we introduce weighted gain cooperative sensing using differential evolution (DE) and adjusted box-plot methods to exalt the sensing reliability together with the sensing performance. The main advantage of the WGC method using DE is that it can generate optimal weights independent of received signal characteristics, which is an indispensable condition to realize the system in real time. The proposed optimal cooperative sensing method with entropy and cyclic features enhances the sensing performance, and it is less severe to noise uncertainties compared with the traditional sensing methods. It can detect the low SNR signals up to $-$ 24 dB at desired sensing performance ( $P_{f} = 0.1$ and $P_{d} = 0.9$ ) with a frame size of 256 and using five nodes in cooperation. It is a significant improvement for IEEE 802.22 WRAN systems, which work under low SNR regime.

Ergodic Capacity Analysis of Free-Space Optical Links With Nonzero Boresight Pointing Errors

A unified capacity analysis of a free-space optical (FSO) link that accounts for nonzero boresight pointing errors and both types of detection techniques (i.e. intensity modulation/direct detection as well as heterodyne detection) is addressed in this work. More specifically, an exact closed-form expression for the moments of the end-to-end signal-to-noise ratio (SNR) of a single link FSO transmission system is presented in terms of well-known elementary functions. Capitalizing on these new moments expressions, we present approximate and simple closed-form results for the ergodic capacity at high and low SNR regimes. All the presented results are verified via computer-based Monte-Carlo simulations.

Spectrum Efficiency Evaluation with Multiuser Scheduling and MRC Antenna Diversity with Effects of Combining Errors for Rayleigh Fading Channels with Feedback

In this paper, we present an analytical framework to jointly investigate MRC diversity and multiuser scheduling under Rayleigh fading channels with the effect of combining errors under a low SNR regime. We derive spectrum efficiency expressions for multiuser scheduling systems with two different cases of multiuser scheduling, (1) Full feedback user scheduling (2) Limited feedback user scheduling with effects of combining errors. A signal to noise ratio (SNR) based user selection scheme is considered. For combining errors, correlation is defined as the magnitude of the complex cross-correlation between the transmission coefficients of the medium associated with pilot and message frequencies. We derive the probability density function and cumulative density function for the above cases. Adaptation policies like (1) Optimal power and rate adaptation policy (OPRA), (2) Optimal rate adaptation policy, (3) Channel inversion with fixed rate policy, (4) Truncated channel inversion with fixed rate policy are employed to improve system performance. It is observed that limited feedback user scheduling along with employment of adaptation policies yields better system performance compared to full feedback user scheduling. Further, OPRA policy yields maximum capacity among the four policies.

Impact of Antenna Correlation on Optimum Improved Energy Detector in Cognitive Radio

This paper investigates the detection performance of an improved energy detector for a secondary user with spatially correlated multiple antennas. In an improved energy detector, an arbitrary positive power operation p replaces the squaring operation in a conventional energy detector, and the optimum value of p that gives the best detection performance may be different from 2. Firstly, for a given value of p, we derive closed-form expressions for the probability of detection and the probability of false alarm when antennas at the secondary user are exponentially correlated. We then find the optimum value of p for two different detection criteria−maximizing the probability of detection for a target probability of false alarm, and minimizing the probability of false alarm for a target probability of detection. We show that the optimum p is strongly dependent on system parameters like number of antennas, antenna correlation coefficient among multiple antennas, and average received signal-to-noise ratio (SNR). From results, we infer that, in low SNR regime, the effect of antenna correlation is less pronounced on the optimum p. Finally, we find the optimum values of p and threshold jointly that minimize the total error rate. key words: cognitive radio; correlation, improved energy detector, multiple antennas, total error rate

Space-frequency channel pairing and power allocation for OFDM- based multi-pair two-way relay wireless networks

To improve multi-pair two-way relay wideband wireless networks using orthogonal frequency-division multiplexing, this paper proposes a space-frequency (SF) joint channel pairing (CP) that maximizes the sum-rate (MSR) after block diagonalization beamforming at a relay station (RS). Following this, a space-frequency (SF) joint water lling power allocation (WFPA) is designed to further improve the performance of the system. Simula- tion results illustrate that, compared to space channel pairing without CP, the proposed MSR-SFCP can achieve substantial performance gains, including improvements in the sum-rate and bit error rate (BER) for a given signal-to-noise ratio (SNR). In contrast, the SF-WFPA can improve BER performance in the low and medium SNR regimes, compared to equal power allocation.

Reducing the effects of the noise uncertainty in energy detectors for cognitive radio networks

SummaryBecause of its ease of implementation and minimum requirements about the primary signals' information, energy detection is broadly considered for signal detection in spectrum sensing algorithms. However, the noise uncertainty phenomenon, caused by the random variations in the noise power, degrades the performance of an energy detector, particularly when the signal‐to‐noise ratio (SNR) is low. In this work, we propose to reduce the negative effects of the noise uncertainty in the performance of an energy detector by dynamically adapting its detection threshold to the noise conditions experienced at each sensing epoch. The noise power is estimated from the received signal samples using an algorithm based on a high‐pass filters bank and median filtering. With our proposal, it is possible to maintain a constant and low false alarm rate in the presence of noise uncertainty, without increasing the probability of misdetection, even in the low SNR regime, and without increasing the number of samples considered for spectrum sensing. Copyright © 2014 John Wiley & Sons, Ltd.

Comparison of fringe-tracking algorithms for single-mode near-infrared long-baseline interferometers

To enable optical long baseline interferometry toward faint objects, long integrations are necessary despite atmospheric turbulence. Fringe trackers are needed to stabilize the fringes and thus increase the fringe visibility and phase signal-to-noise ratio (SNR), with efficient controllers robust to instrumental vibrations, and to subsequent path fluctuations and flux drop-outs. We report on simulations, analysis and comparison of the performances of a classical integrator controller and of a Kalman controller, both optimized to track fringes under realistic observing conditions for different source magnitudes, disturbance conditions, and sampling frequencies. The key parameters of our simulations (instrument photometric performance, detection noise, turbulence and vibrations statistics) are based on typical observing conditions at the Very Large Telescope observatory and on the design of the GRAVITY instrument, a 4-telescope single-mode long baseline interferometer in the near-infrared, next in line to be installed at VLT Interferometer. We find that both controller performances follow a two-regime law with the star magnitude, a constant disturbance limited regime, and a diverging detector and photon noise limited regime. Moreover, we find that the Kalman controller is optimal in the high and medium SNR regime due to its predictive commands based on an accurate disturbance model. In the low SNR regime, the model is not accurate enough to be more robust than an integrator controller. Identifying the disturbances from high SNR measurements improves the Kalman performances in case of strong optical path difference disturbances.

On the Low SNR Capacity of MIMO Fading Channels With Imperfect Channel State Information

The capacity of multiple-input multiple-output (MIMO) Rayleigh fading channels with full knowledge of channel state information (CSI) at both the transmitter and the receiver (CSI-TR) has been shown recently to scale at low signal-to-noise ratio (SNR) essentially as SNR log(1/SNR), independently of the number of transmit and receive antennas. In this paper, we investigate the ergodic capacity of MIMO Rayleigh fading channel with estimated channel state information at the transmitter (CSI-T) and possibly imperfect channel state information at the receiver (CSI-R). Our framework can be seen as a generalization of previous works as it can capture the perfect CSI-TR as a special case when the estimation error variance goes to zero. In this paper, we mainly focus on the low SNR regime, and we show that the capacity scales as (1 - α) SNR log(1/SNR), where α is the estimation error variance. This characterization shows the loss of performance due to error estimation over the perfect channel state information at both the transmitter and the receiver. As a by-product of our new analysis, we show that our framework can be also extended to characterize the capacity of MIMO Rician fading channels at low SNR with possibly imperfect CSI-T and CSI-R.