Moderate Signal-to-noise Ratio Research Articles

Interference Alignment and Its Applications: A Survey, Research Issues, and Challenges

The capacity of interference network is a fundamental issue that eludes the researchers for decades. Interference alignment (IA) is an emerging interference management technique that is degrees of freedom (DoFs) optimal, which means it can approach the capacity of interference network at very high signal-to-noise ratio (SNR). In IA networks, the signals are constrained into the same subspaces at the unintended receivers through cooperative precoding, and the desired signal can be recovered at each receiver by eliminating the aligned interferences using decoding matrix. Due to its promising performance in interference management, IA has successfully been applied to many kinds of multiuser wireless networks with excellent performance. Nevertheless, there are still some challenges for the practical utilization of IA, e.g., the overhead of channel state information (CSI) feedback, performance degradation at low and moderate SNRs, etc. In this review, we provide a survey on IA and its applications and discuss some research issues and challenges. The dimensions, networks topologies, and applications of IA are first introduced. Then some fundamental aspects of IA are discussed, including feasibility condition, performance metrics, iterative algorithms, and CSI. We also present some recent research issues of opportunistic IA, spectrum sharing, green IA, topology management, and physical layer security. Finally, some research challenges of IA are identified.

Energy Efficiency Optimization With Interference Alignment in Multi-Cell MIMO Interfering Broadcast Channels

Characterizing the fundamental energy efficiency (EE) performance of multiple-input–multiple-output interfering broadcast channels (MIMO-IFBC) is important for the design of green wireless system. In this paper, we propose a new network architecture proposition based on EE maximization for Multi-Cell MIMO-IFBC within the context of interference alignment (IA). Particularly, EE is maximized subject to maximum power and minimum throughput constraints. We propose two schemes to optimize EE for different signal-to-noise ratio (SNR) regions. For high-SNR operating regions, we employ a grouping-based IA scheme to jointly cancel intra- and inter-cell interferences and thus transform the MIMO-IFBC to a single-cell MIMO scenario. A gradient-based power adaptation scheme is proposed based on water-filling power adaptation and singular value decomposition to maximize EE for each cell. For moderate SNR cases, we propose an approach using dirty paper coding (DPC) with the principle of multiple access channel and broadcast channel duality to perform IA while maximizing EE in each cell. The algorithm in its dual form is solved using a subgradient method and a bisection searching scheme. Simulation results demonstrate the superior performance of the proposed schemes over several existing approaches. It also shows that interference-nulling-based IA approaches outperform hybrid DPC-IA approach in high-SNR region, and the opposite occurs in low-SNR region.

Shrinkage‐based biased signal‐to‐noise ratio estimator using pilot and data symbols for linearly modulated signals

In diverse engineering problems including wireless communications, the estimate of the signal-to-noise ratio (SNR) is required. In this study, the authors develop a shrinkage-based SNR estimator in the data-aided and non-data-aided schemes for higher M-ary phase-shift-keying (M ≥ 8) and quadrature amplitude modulations. The observed Cramer-Rao lower bound is used as the variance of the expectation maximisation estimator to determine the optimal shrinkage factor. Simulation results show that the normalised mean-squared error of the proposed method is lower than that of the expectation maximisation method for low and moderate SNR conditions.

Improving the bit error rate performance by optimising energy allocation based on union bound

A new method to improve the bit error rate (BER) performance by optimising the bit energy is proposed in this study. This method is mainly based on a formula derived from the union bound that can estimate the BER for every bit in the codeword sequence. Then by mathematical optimisation and assisted with a BER distribution, the energy for every bit can be optimised so that the average BER achieves the minimum value. Compared with other methods, this method considering all the codewords with minimum Hamming weights and their multiplicity to each bit of the codewords. The simulation examples show that the average BER is improved not only at high signal-to-noise ratio (SNR), but also at low and moderate SNRs.

Maximum Likelihood SNR Estimation of Linearly-Modulated Signals Over Time-Varying Flat-Fading SIMO Channels

In this paper, we tackle for the first time the problem of maximum likelihood (ML) estimation of the signal-to-noise ratio (SNR) parameter over time-varying single-input multiple-output (SIMO) channels. Both the data-aided (DA) and the non-data-aided (NDA) schemes are investigated. Unlike classical techniques where the channel is assumed to be slowly time-varying and, therefore, considered as constant over the entire observation period, we address the more challenging problem of instantaneous (i.e., short-term or local) SNR estimation over fast time-varying channels. The channel variations are tracked locally using a polynomial-in-time expansion. First, we derive in closed-form expressions the DA ML estimator and its bias. The latter is subsequently subtracted in order to obtain a new unbiased DA estimator whose variance and the corresponding Cram\'er-Rao lower bound (CRLB) are also derived in closed form. Due to the extreme nonlinearity of the log-likelihood function (LLF) in the NDA case, we resort to the expectation-maximization (EM) technique to iteratively obtain the exact NDA ML SNR estimates within very few iterations. Most remarkably, the new EM-based NDA estimator is applicable to any linearly-modulated signal and provides sufficiently accurate soft estimates (i.e., soft detection) for each of the unknown transmitted symbols. Therefore, hard detection can be easily embedded in the iteration loop in order to improve its performance at low to moderate SNR levels. We show by extensive computer simulations that the new estimators are able to accurately estimate the instantaneous per-antenna SNRs as they coincide with the DA CRLB over a wide range of practical SNRs.

On Precoding for Constant <inline-formula> <tex-math notation="TeX">$K$</tex-math></inline-formula>-User MIMO Gaussian Interference Channel With Finite Constellation Inputs

This paper considers linear precoding for the constant channel-coefficient K-user MIMO Gaussian interference channel (MIMO GIC) where each transmitter-i (Tx-i) requires the sending of d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution to receiver-i (Rx-i) for i=1,2,..., K. We define the maximum rate achieved by Tx-i using any linear precoder as the signal-to-noise ratio (SNR) tends to infinity when the interference channel coefficients are zero to be the constellation constrained saturation capacity (CCSC) for Tx-i. We derive a high-SNR approximation for the rate achieved by Tx-i when interference is treated as noise and this rate is given by the mutual information between Tx-i and Rx-i, denoted as I[X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ;Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ]. A set of necessary and sufficient conditions on the precoders under which [IX <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ; Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ] tends to CCSC for Tx-i is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Furthermore, we propose gradient-ascent-based algorithms to optimize the sum rate achieved by precoding with finite constellation inputs and treating interference as noise. A simulation study using the proposed algorithms for a three-user MIMO GIC with two antennas at each node with d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> =1 for all i and with BPSK and QPSK inputs shows more than 0.1-b/s/Hz gain in the ergodic sum rate over that yielded by precoders obtained from some known IA algorithms at moderate SNRs.

Fresnel‐assisted self‐heterodyne detection for Brillouin gain spectrum characterisation in polymer optical fibres

It has been experimentally shown that by utilising the Fresnel-reflected light as the reference light, Brillouin signals in polymer optical fibres (POFs) can be observed with a higher signal-to-noise ratio (SNR) than those measured with standard self-heterodyne detection. This method is basically the same in setup as direct detection, leading to an additional advantage of system simplicity. Moreover, it has been demonstrated that the Brillouin signal in a 1 cm-long POF can be observed with a moderate SNR using this technique, indicating a potential feasibility of POF-based distributed Brillouin measurement with a millimetre-order spatial resolution.

Capacity Region Bounds and Resource Allocation for Two-Way OFDM Relay Channels

Most of the existing works on two-way frequency division multiplexing (OFDM) relay channels was centered on per-subcarrier decode-and-forward (DF) relaying, where each subcarrier is treated as a separate channel, and channel coding is performed separately over each subcarrier. In this paper, we show that this per-subcarrier DF relay strategy is suboptimal. More specifically, we present a multi-subcarrier DF relay strategy which achieves a larger rate region by adopting cross-subcarrier channel coding. Then we develop an optimal resource allocation algorithm to characterize the achievable rate region of the proposed multi-subcarrier DF relay strategy. Compared to standard Lagrangian duality optimization algorithms, our algorithm has a much smaller computational complexity due to the use of the structure property of the optimal resource allocation solution. We further prove that our multi-subcarrier DF relay strategy tends to achieve the capacity region of the two-way OFDM relay channels in the low signal-to-noise ratio (SNR) regime, and the amplify-and-forward (AF) relay strategy tends to achieve the multiplexing gain region of the two-way OFDM relay channels in the high SNR regime. Our theoretical analysis and numerical results demonstrate that DF relaying has better performance in the low to moderate SNR regime, while AF relaying is more appropriate in the high SNR regime.

Electrical Network Frequency (ENF) Maximum-Likelihood Estimation Via a Multitone Harmonic Model

Estimation of the parameters of the electric network signal, usually present in many audio and video recordings, is known to have several important forensic applications. In this paper, we consider the problem of estimating the base frequency and signal to noise ratio (SNR). Although the electric network signal is present via its base frequency and its integer multiplies, recent estimators in the literature focus on single-tone models. In this work, we offer a multitone harmonic model for the electric network signal. We use the Cramer-Rao bound for the frequency estimation problem and show that this approach can lead to a theoretical <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) factor improvement in the estimation accuracy, where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> is the number of harmonics. We then derive the computationally efficient form of the maximum-likelihood estimator, applicable in the limit of large number of measurements. The problem of estimating the SNR of the signal is also discussed. Through extensive tests on real data and data sets reported in the current literature, the performance of the new estimators is evaluated. Results indeed show a significant gain compared to the single-tone model, and are better than previously reported estimators in the literature for moderate and high SNR values.

Optimal MSE solution for a decision feedback equalizer

Due to the inherent feedback in a decision feedback equalizer (DFE) the minimum mean square error (MMSE) or Wiener solution is not known exactly. The main difficulty in such analysis is due to the propagation of the decision errors, which occur because of the feedback. Thus in literature, these errors are neglected while designing and/or analyzing the DFEs. Then a closed form expression is obtained for Wiener solution and we refer this as ideal DFE (IDFE). DFE has also been designed using an iterative and computationally efficient alternative called least mean square (LMS) algorithm. However, again due to the feedback involved, the analysis of an LMS-DFE is not known so far. In this paper we theoretically analyze a DFE taking into account the decision errors. We study its performance at steady state. We then study an LMS-DFE and show the proximity of LMS-DFE attractors to that of the optimal DFE Wiener filter (obtained after considering the decision errors) at high signal to noise ratios (SNR). Further, via simulations we demonstrate that, even at moderate SNRs, an LMS-DFE is close to the MSE optimal DFE. Finally, we compare the LMS DFE attractors with IDFE via simulations. We show that an LMS equalizer outperforms the IDFE. In fact, the performance improvement is very significant even at high SNRs (up to 33%), where an IDFE is believed to be closer to the optimal one. Towards the end, we briefly discuss the tracking properties of the LMS-DFE.

SNR-Aided Accurate Phase Estimation in 1-Bit Software-Defined Receiver

This work investigates the high-accuracy phase discriminator in 1-bit software-defined receiver (SDR) for three signal-to-noise ratio (SNR) ranges: low SNR, high SNR and moderate SNR. Unlike traditional approaches, our approach first distinguishes which SNR range an application falls into, and this SNR information is then utilized to select a proper phase discriminator to achieve high accuracy. For low-SNR applications, traditional arctangent phase discriminator (APD) is adopted and the analysis of asymptotic performance is derived. For high-SNR applications, the noise-balanced digital phase discriminator (NB-DPD) is adopted to improve accuracy [1]. Between them, for moderate-SNR applications, a novel SNR-aided phase discriminator (SNRaPD) is proposed. The analytical and simulation results verify the superiority of the proposed approach for applications in different SNR ranges. The determination of moderate SNR range is critical and discussed finally.

Atmospheric effects on voice command intelligibility from acoustic hail and warning devices

Voice command sound pressure levels (SPLs) were recorded at distances up to 1500 m. Received SPLs were related to the meteorological condition during sound propagation and compared with the outdoor sound propagation standard ISO 9613-2. Intelligibility of received signals was calculated using ANSI S3.5. Intelligibility results for the present voice command indicate that meteorological condition imposes little to no effect on intelligibility when the signal-to-noise ratio (SNR) is low (<-9 dB) or high (>0 dB). In these two cases the signal is firmly unintelligible or intelligible, respectively. However, at moderate SNRs, variations in received SPL can cause a fully intelligible voice command to become unintelligible, depending on the meteorological condition along the sound propagation path. These changes in voice command intelligibility often occur on time scales as short as minutes during upward refracting conditions, typically found above ground during the day or upwind of a sound source. Reliably predicting the intelligibility of a voice command in a moderate SNR environment can be challenging due to the inherent variability imposed by sound propagation through the atmosphere.

On the Benefits of Partial Channel State Information for Repetition Protocols in Block Fading Channels

This paper studies the throughput performance of HARQ (hybrid automatic repeat request) protocols over block fading Gaussian channels. It proposes new protocols that use the available feedback bit(s) not only to request a retransmission, but also to inform the transmitter about the instantaneous channel quality. An explicit protocol construction is given for any number of retransmissions and any number of feedback bits. The novel protocol is shown to simultaneously realize the gains of HARQ and of power control with partial CSI (channel state information). Remarkable throughput improvements are shown, especially at low and moderate SNR (signal to noise ratio), with respect to protocols that use the feedback bits for retransmission request only. In particular, for the case of a single retransmission and a single feedback bit, it is shown that the repetition is not needed at low $\snr$ where the throughput improvement is due to power control only. On the other hand, at high SNR, the repetition is useful and the performance gain comes form a combination of power control and ability of make up for deep fades.

Zero-Forcing DFE Transceiver Design Over Slowly Time-Varying MIMO Channels Using ST-GTD

This paper considers the optimization of transceivers with decision feedback equalizers (DFE) for slowly time-varying memoryless multi-input multi-output (MIMO) channels. The data vectors are grouped into space-time blocks (ST-blocks) for the spatial and temporal precoding to take advantage of the diversity offered by time-varying channels. The space-time generalized triangular decomposition (ST-GTD) is proposed for application in time-varying channels. Under the assumption that the instantaneous channel state information at the transmitter (CSIT) and receiver (CSIR), and the channel prediction are available, we also propose the space-time geometric mean decomposition (ST-GMD) system based on ST-GTD. Under perfect channel prediction, the system minimizes both the arithmetic MSE at the feedback detector, and the average un-coded bit error rate (BER) in moderate high signal to noise ratio (SNR) region. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD system is also proposed. At the moderate high SNR region, our analysis and numerical results show that all the proposed systems have better BER performance than the conventional GMD-based systems over time-varying channels; the average BERs of the proposed systems are non-increasing functions of the ST-block size.

Cramer-Rao Lower Bounds for NDA SNR Estimates of Square QAM Modulated Transmissions

In this paper, we derive for the first time analytical expressions for the exact Cramér-Rao lower bounds on the variance of unbiased non-data-aided (NDA) signal-to-noise ratio (SNR) estimators of square QAM-modulated signals. The channel is assumed to be constant over the observation interval and the received signal is supposed to be corrupted by additive white Gaussian noise (AWGN). The derived expressions corroborate previous attempts to numerically compute the considered CRLBs. It will be shown that the NDA CRLBs differ widely from one modulation order to another especially at moderate SNR levels.

Accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors-in-variables and output error identification

For identifying errors-in-variables models, the time domain maximum likelihood (TML) method and the sample maximum likelihood (SML) method are two approaches. Both methods give optimal estimation accuracy but under different assumptions. In the TML method, an important assumption is that the noise-free input signal is modelled as a stationary process with rational spectrum. For SML, the noise-free input needs to be periodic. It is interesting to know which of these assumptions contain more information to boost the estimation performance. In this paper, the estimation accuracy of the two methods is analyzed statistically for both errors-in-variables (EIV) and output error models (OEM). Numerical comparisons between these two estimates are also done under different signal-to-noise ratios (SNRs). The results suggest that TML and SML have similar estimation accuracy at moderate or high SNR for EIV. For OEM identification, these two methods have the same accuracy at any SNR.

On the limits of communication with low-precision analog-to-digital conversion at the receiver

As communication systems scale up in speed and bandwidth, the cost and power consumption of high-precision (e.g., 8-12 bits) analog-to-digital conversion (ADC) becomes the limiting factor in modern transceiver architectures based on digital signal processing. In this work, we explore the impact of lowering the precision of the ADC on the performance of the communication link. Specifically, we evaluate the communication limits imposed by low-precision ADC (e.g., 1-3 bits) for transmission over the real discrete-time additive white Gaussian noise (AWGN) channel, under an average power constraint on the input. For an ADC with K quantization bins (i.e., a precision of log2 K bits), we show that the input distribution need not have any more than K+1 mass points to achieve the channel capacity. For 2-bin (1-bit) symmetric quantization, this result is tightened to show that binary antipodal signaling is optimum for any signal-to- noise ratio (SNR). For multi-bit quantization, a dual formulation of the channel capacity problem is used to obtain tight upper bounds on the capacity. The cutting-plane algorithm is employed to compute the capacity numerically, and the results obtained are used to make the following encouraging observations : (a) up to a moderately high SNR of 20 dB, 2-3 bit quantization results in only 10-20% reduction of spectral efficiency compared to unquantized observations, (b) standard equiprobable pulse amplitude modulated input with quantizer thresholds set to implement maximum likelihood hard decisions is asymptotically optimum at high SNR, and works well at low to moderate SNRs as well.

Turbo equalization with cancelation of nonlinear distortion for CP-assisted and zero-padded MC-CDM schemes

In this paper, we consider MC-CDM schemes (MultiCarrier Code Division Multiplexing) where clipping techniques are employed to reduce the envelope fluctuations of the transmitted signals. Both CP-assisted (Cyclic Prefix) and ZP (Zero- Padded) MC-CDM schemes are studied. We develop frequencydomain turbo equalizers combined with an iterative estimation and cancelation of nonlinear distortion effects, with relatively low complexity since they allow FFT-based (Fast Fourier Transform), frequency-domain implementations. Our performance results show that the proposed receivers allow significant performance improvements at low and moderate SNR (Signal-to-Noise Ratio), even when strongly nonlinear transmitters are employed. The receiver for ZP MC-CDM is of special interest for systems where the duration of the channel impulse response is not a small fraction of the duration of the MC-CDM blocks, being suitable to MC-CDM systems with very large blocks (hundreds or even thousands of subcarriers), since they do not require the inversion nor the multiplication of large matrixes.

A Simple Dual-Mode Limited Feedback Multiuser Downlink System

Generally limited feedback systems that multiplex multiple user signals are noise power limited in the low signal-tonoise- ratio (SNR) regime and interference power limited in the high SNR regime. If the amount of feedback does not grow with SNR, then there is a sum rate ceiling that increasing the transmit power alone cannot surpass. This paper proposes a simple dual mode system where the base station serves either one user or as many users as the number of transmit antennas. The switching mechanism is smooth and is based on instantaneous system conditions. The mobile determines its preferred transmission mode by using a very simple signal-to-interference-and-noiseratio (SINR) threshold. Based on the mobiles' feedback, the base station chooses the method of signalling accordingly. With a finite number of feedback bits per mobile, it is shown that the proposed system achieves close to the maximum of the sum-rate for single user and multiuser modes. We identify the preferrable mode for an asymptotically large number of users and/or SNR. This proposed architecture is suitable for systems with moderate coherence time, a moderate to large number of users, and a moderate SNR that cannot afford complex processing at the base station or at the mobile.

Outage Probability-Based Power and Time Optimization for Relay Networks

In the context of cooperative wireless networks that convey data on slow fading channels, outage probability P o is the relevant performance index from the point of view of information theory. Derivation and minimization of this probability with respect to the relaying protocol parameters is of central importance. However, it is often hard to derive its expression, let alone to find its exact minimum for all possible values of the signal-to-noise ratio (SNR). This problem can be simplified by studying the behavior of P o in the asymptotic regime where the SNR rho converges to infinity. In this regime, usually rho N+1 P o converges to a constant xi where N is the number of relays. In this paper, a simple and general method for deriving and minimizing xi with respect to the power distribution between the source and the relays, and with respect to the durations of the slots specified by the relaying protocol, is developed. While the proposed approach is designed for the high SNR regime, simulations show that outage probability is reduced in a similar proportion at moderate SNR. The method applies to a general class of radio channels that includes the Rayleigh and the Rice channels as particular cases. Convexity of xi with respect to the design parameters is shown. Decode-and-forward, as well as amplify-and-forward protocols are considered in the half duplex mode.