Noncoherent Channel Research Articles

Noncoherent Channel Combining for GNSS Signal Tracking with an Adaptive Antenna Array

Adaptive antenna arrays are widely used to protect Global Navigation Satellite System (GNSS) receivers from interference. However, conventional blind anti-jamming array processing methods can cause satellite signal attenuation, which reduces signal tracking precision and measurement accuracy. To alleviate this problem, this paper proposes the noncoherent channel combining method for GNSS signal tracking with an adaptive antenna array. A two-stage processing architecture is applied in the proposed method, where the first stage implements interference suppression, and the second stage achieves noncoherent channel combining. The proposed method has the advantage of blind characteristics that can be implemented without any other auxiliary information. It also reveals a unified processing architecture for anti-jamming array processing methods. Thus, a detailed comparison and analysis of the proposed method with several typical blind anti-jamming methods is performed. Simulation results demonstrate the effectiveness of the proposed method and its superiority over existing methods in terms of tracking performance.

Revisiting the Capacity of Noncoherent Fading Channels in mmWave System

Millimeter wave (mmWave) communications use large transmission bandwidth and experience severe propagation conditions. This forces the communication system to operate in the so-called wideband regime , where signals must be increasingly “peaky” in order to attain a large fraction of the peak unconstrained wideband capacity. This paper investigates the capacity of the noncoherent channels as a function of bandwidth for signals with average and peak power constraints operating in the millimeter spectrum. Upper and lower bounds on capacity are provided, and the impact of features peculiar to mmWave channels is investigated. Numerical results for a scenario based on recent experimental campaigns are provided. It is shown that the rate achievable by a typical user in a mmWave cell with “non-peaky” signaling can be bounded away from the peak unconstrained wideband capacity. This suggests to reconsider the role of signaling “peakedness” in future mmWave communications.

Multiple-symbol noncoherent learning detection of coded QAM signals in IEEE 802.15.3 Wireless Multi-media Networks

We consider the noncoherent deep learning problem for coded signal detection under the phase noncoherent channels for remote home healthcare applications with high data rate. In particular, a multiple-symbol noncoherent learning detection (MNLD) scheme based on neural networks is proposed for low-density parity-check (LDPC) coded noncoherent quadrature amplitude modulation (QAM) signals in IEEE 802.15.3 Wireless Multi-media Networks. Our derivation shows that extensive operations for the first kind zero-order modified Bessel function is unavoidable for the implementation of the optimal bit log-likelihood ratio (LLR) for decoding in traditional multiple-symbol detection (MSD) scheme. The perfect estimation of the channel state information (CSI), i.e., a priori information about the variance of the additive white Gaussian noise (AWGN), is also required for the receiver. This is clearly not computationally practical for Wireless Multi-media Networks. Consequently, we developed an improved approach based on feed-forward neural networks to accurately calculate the bit LLR. Furthermore, to decrease the generation size of training set and thus increase the training speed of the proposed neural networks, we uniformly quantize the continuous carrier phase offset (CPO), which is random and unknown, into discrete status. Our simulation results verify the learning efficiency of this simplified training-set generation configuration. The decoding convergence is successfully accelerated and much performance gain is finally achieved when compared with traditional decoding using the perfect bit LLR. This is clearly critical for high reliable transmission of home healthcare information.

Simple and Robust Log-Likelihood Ratio Calculation of Coded MPSK Signals in Wireless Sensor Networks for Healthcare

The simple and robust log-likelihood ratio (LLR) computation of coded Multiple Phase Shift Keying (MPSK) signals in Wireless Sensor Networks (WSNs) is considered under both phase noncoherent and Rayleigh fading channels for healthcare applications. We first simplify the optimal LLR for phase noncoherent channel, the estimation of the instantaneous channel state information (CSI) for both the fading amplitude and the additive white Gaussian noise (AWGN) is successfully avoided, and the complexity-intensive process for zero-order Bessel function of the first kind is also perfectly eliminated. Furthermore, we also develop the simplified LLR under Rayleigh fading channel. Correspondingly, the variance estimation for both AWGN and the statistical characteristic of the fading amplitude is no longer required, and the complicated process for implementation of the exponential function is also successfully avoided. Compared to the calculation of optimal LLR with full complexity, the proposed method is implementation-friendly, which is practically desired for energy-limited WSNs. The simulations are developed in the context of low-density parity-check (LDPC) codes, and the corresponding results show that the detection performance is extremely close to that of the full-complexity LLR metrics. That is, the performance degradation is efficiently prevented, whereas complexity reduction is also successfully achieved.

Covert Communications With a Full-Duplex Receiver in Non-Coherent Rayleigh Fading

In a majority of research on covert communications, knowledge about channel state information (CSI) of main channel and/or warden channel is assumed to be known or partially known. However, a covert user may not afford to perform channel estimation in practice, and acquiring the warden's CSI is even impossible. In this paper, we investigate covert communications over non-coherent Rayleigh fading channels, in both i.i.d. fast fading and slow fading cases. We observe that the purpose of covert communication in many scenarios is to hide the existence of the sender, not the receiver. Therefore, we allow the receiver to work in full-duplex mode such that it can emit artificial noise (AN) while receiving signals simultaneously. We analyse the achievable covert rates with fixed and varying AN power and show that in both fast and slow fading cases, it is possible to achieve a positive covert rate. For the slow fading case, we further extend the proposed strategy to a multi-user scenario, in which multiple other users share the same spectral resource and cause interference at the warden. Extensive simulations are performed to verify the correctness of our analysis, which provide new insights on the AN design problem in non-coherent channels.

Nearest Neighbor Decoding and Pilot-Aided Channel Estimation for Fading Channels.

We study the information rates of noncoherent, stationary, Gaussian, and multiple-input multiple-output (MIMO) flat-fading channels that are achievable with nearest neighbor decoding and pilot-aided channel estimation. In particular, we investigate the behavior of these achievable rates in the limit as the signal-to-noise ratio (SNR) tends to infinity by analyzing the capacity pre-log, which is defined as the limiting ratio of the capacity to the logarithm of the SNR as the SNR tends to infinity. We demonstrate that a scheme estimating the channel using pilot symbols and detecting the message using nearest neighbor decoding (while assuming that the channel estimation is perfect) essentially achieves the capacity pre-log of noncoherent multiple-input single-output flat-fading channels, and it essentially achieves the best so far known lower bound on the capacity pre-log of noncoherent MIMO flat-fading channels. Extending the analysis to fading multiple-access channels reveals interesting relationships between the number of antennas and Doppler bandwidth in the comparative performance of joint transmission and time division multiple-access.

Closed-Form Capacity Bounds for the Exponential Version of the Dirty Paper Channel

This letter presents closed-form capacity bounds for an exponential version of the dirty paper channel (EDPC). The EDPC can be used to model the non-coherent Gaussian dirty paper channel (GDPC). First, a superposition modulation-like technique is used to obtain a capacity upper bound for the EDPC. Then, a closed-form capacity lower bound for the EDPC is obtained by using a Costa-like strategy. Using this lower bound and exploiting the asymptotic properties of high signal to noise ratios (SNRs), we obtain the high-SNR capacity of the EDPC which is intriguingly analogous to the complex-valued GDPC. Finally, a closed-form capacity lower bound for the EDPC is given which is useful in the weak interference regime.

Partially Coherent Compressive Phase Retrieval for Millimeter-Wave Massive MIMO Channel Estimation

Channel estimation is challenging for millimeter-wave (mmWave) massive MIMO systems. Leveraging the spatial sparsity of mmWave channels, compressive sensing (CS) based channel estimation been extensively studied. However, the mmWave hardware imperfections may introduce random phase distortions to the received pilots, which makes the conventional CS methods fail to estimate the channel. The compressive phase retrieval (CPR) method can be employed to solve this challenging problem. In this paper, we exploit the partial coherence in hybrid mmWave systems, i.e., the pilots sent from different radio frequency (RF) chains share the same phase distortion in the same time frame, while the phase distortions are different across different time frames. Based on this property, we propose an on-grid partially coherent CPR (PC-CPR) algorithm for mmWave channel estimation in the presence of severe phase distortions. Unlike the existing coherent channel estimation schemes that require perfect phase information or the noncoherent channel estimation schemes that ignore the phases of measurements, the proposed on-grid PC-CPR algorithm exploits the partial coherence property to estimate the sparse angle-domain channel vector. Furthermore, to solve the resolution limitation of the on-grid PC-CPR algorithm, we propose an off-grid PC-CPR algorithm that directly estimates the parameters of channel paths. The proposed partially coherent channel estimation framework subsumes the existing coherent and noncoherent channel estimation methods as special cases. Simulation results show that under the presence of random phase distortions, the proposed PC-CPR algorithms outperform noncoherent channel estimation methods with higher reliability and lower pilot overhead by leveraging the partial coherence.

Capacity Scaling in a Non-Coherent Wideband Massive SIMO Block Fading Channel

The scaling of coherent and non-coherent channel capacity is studied in a single-input multiple-output (SIMO) block Rayleigh fading channel as both the bandwidth and the number of receiver antennas go to infinity jointly with the transmit power fixed. The transmitter has no channel state information (CSI), while the receiver may have genie-provided CSI (coherent receiver), or the channel statistics only (non-coherent receiver). Our results show that if the available bandwidth is smaller than a threshold bandwidth which is proportional (up to leading order terms) to the square root of the number of antennas, there is no gap between the coherent capacity and the non-coherent capacity in terms of capacity scaling behavior. On the other hand, when the bandwidth is larger than this threshold, there is a capacity scaling gap. Since achievable rates using pilot symbols for channel estimation are subject to the non-coherent capacity bound, this work reveals that pilot-assisted coherent receivers in systems with a large number of receive antennas are unable to exploit excess spectrum above a given threshold for capacity gain.

Noncoherent Detection With Polar Codes

Polar codes (PCs) have attracted significant attention in the last decade, especially after their adoption in the forthcoming 5G wireless networks. However, previous studies focused on coherent polar codes, which always rely on the strong assumption of available perfect channel state information. Instead, in this paper, we investigate the use of PCs in noncoherent systems. First, a binary differential phase shift keying (BDPSK) demodulator is concatenated with a polar decoder to form the noncoherent detector, where successive cancellation (SC) is applied. The simulation results demonstrate that the SC-based PCs for noncoherent detection have approximately a discrepancy of only 3 dB compared with the coherent counterpart in noncoherent channels. Furthermore, in order to further decrease this discrepancy, we replace the BDPSK demodulator with a soft-input soft-output (SISO) multiple symbol differential sphere decoding demodulator. Similarly, the SC-based PC decoder is replaced by the SISO belief propagation-based PC decoder, and by using this novel architecture, an iterative noncoherent detector is constructed. Benefiting from further invoking extrinsic information transfer chart tool and the dynamic window-size detection scheme, the performance of the proposed iterative noncoherent detector becomes competitive with its coherent one in practical applications, since the performance degradation is reduced to 1 dB.

On Cooperation and Interference in the Weak Interference Regime

Handling interference is one of the main challenges in the design of wireless networks. In this paper, we study the application of cooperation for interference management in the weak interference (WI) regime, focusing on the Z-interference channel with a causal relay (Z-ICR), in which the channel coefficients are subject to ergodic phase fading, all transmission powers are finite, and the relay is full-duplex. The phase fading model represents many practical communications systems in which the transmission path impairments mainly affect the phase of the signal, such as non-coherent wireless communications and fiber optic channels. In order to provide a comprehensive understanding of the benefits of cooperation in the WI regime, we characterize, for the first time, two major performance measures for the ergodic phase fading Z-ICR in the WI regime: the sum-rate capacity and the maximal generalized degrees-of-freedom (GDoF). In the capacity analysis, we obtain conditions on the channel coefficients, subject to which the sum-rate capacity of the ergodic phase fading Z-ICR is achieved by treating interference as noise at each receiver, and explicitly state the corresponding sum-rate capacity. In the GDoF analysis, we derive conditions on the exponents of the magnitudes of the channel coefficients, under which treating interference as noise achieves the maximal GDoF, which is explicitly characterized as well. It is shown that under certain conditions on the channel coefficients, relaying strictly increases both the sum-rate capacity and the maximal GDoF of the ergodic phase fading Z-interference channel in the WI regime. Our results demonstrate for the first time the gains from relaying in the presence of interference, when interference is weak and the relay power is finite , both in increasing the sum-rate capacity and in increasing the maximal GDoF, compared with the channel without a relay.

Revisiting the Capacity of Noncoherent Fading Channels in mmWave System

Millimeter wave (mmWave) communications use large transmission bandwidth and experience severe propagation conditions. This forces the communication system to operate in the so-called wideband regime , where signals must be increasingly “peaky” in order to attain a large fraction of the peak unconstrained wideband capacity. This paper investigates the capacity of the noncoherent channels as a function of bandwidth for signals with average and peak power constraints operating in the millimeter spectrum. Upper and lower bounds on capacity are provided, and the impact of features peculiar to mmWave channels is investigated. Numerical results for a scenario based on recent experimental campaigns are provided. It is shown that the rate achievable by a typical user in a mmWave cell with “non-peaky” signaling can be bounded away from the peak unconstrained wideband capacity. This suggests to reconsider the role of signaling “peakedness” in future mmWave communications.

On the capacity and energy efficiency of non‐coherent Rayleigh fading channels with additive Gaussian mixture noise

This paper studies the capacity and energy efficiency of non-coherent Rayleigh fading channels with Gaussian mixture noise where neither the transmitter nor the receiver has the knowledge of channel state information. The channel under consideration is suited for cellular networks having multi-tier heterogeneous architectures in which the channel conditions change rapidly. In the first part of the paper, we characterize the structure of a capacity-achieving input signal. Specifically, we establish an integrable upper bound on the integrand in the output entropy and demonstrate that there exists a unique optimal input. By formulating the Kuhn-Tucker condition and establishing a diverging lower bound on it, we show that the optimal input is discrete having a finite number of mass points. Using this result, we investigate the capacity and energy efficiency of the considered channel in the second part of the paper. In particular, we first develop a numerical method to evaluate the optimal input and compute the capacity. The energy efficiency, which is related to the capacity and optimal input in low-power regimes, is examined by calculating the minimum bit energy and wideband slope of the spectral-efficiency curve. We also analytically show the optimality of an on-off signal in this regime.

Data and pilot optimised combining method for new composite global navigation satellite system signal acquisition

With the increasing adoption of high bit rate navigation signals, the performance of detection is significantly affected by sign transition. To reduce the correlation loss caused by the sign transition, three optimised channel combining methods, which include the optimised non-coherent channel combining, optimised coherent channel combining and optimised differential channel combining, are proposed in this study. Three corresponding analytical expressions of probabilities of detection for the authors methods are derived. To better evaluate the performance of their methods, three corresponding analytical expressions of probabilities of detection for conventional channel combining methods in the presence of sign transition are also derived. Comparing with conventional channel combining and zero padding methods, although increasing the computational cost, their methods can achieve 2–2.5 and 4–6 dB acquisition sensitivity improvements according to the analytic and simulated results. Moreover, experiments on real data from global positioning system L5 further evaluate the detection performance of their methods.

A Simple Recursively Computable Lower Bound on the Noncoherent Capacity of Highly Underspread Fading Channels

Real-world wireless communication channels are typically highly underspread: their coherence time is much greater than their delay spread. In such situations, it is common to assume that, with sufficiently high bandwidth, the capacity without channel state information (CSI) at the receiver (termed the noncoherent channel capacity) is approximately equal to the capacity with perfect CSI at the receiver (termed the coherent channel capacity). In this paper, we propose a lower bound on the noncoherent capacity of highly underspread fading channels, which assumes only that the delay spread and coherence time are known. Furthermore, our lower bound can be calculated recursively, with each increment corresponding to a step increase in bandwidth. These properties, we contend, make our lower bound an excellent candidate as a simple method to verify that the noncoherent capacity is indeed approximately equal to the coherent capacity for typical wireless communication applications. We precede the derivation of the aforementioned lower bound on the information capacity with a rigorous justification of the mathematical representation of the channel. Furthermore, we also provide a numerical example for an actual wireless communication channel and demonstrate that our lower bound does indeed approximately equal the coherent channel capacity.

Capacity investigation of on–off keying in noncoherent channel settings at low SNR

AbstractOn–off keying (OOK) has repossessed much new research interest to realize green communication for establishing autonomous sensor networks. To realize ultra‐low power wireless design, we investigate the minimum energy per bit required for reliable communication of using OOK in a noncoherent channel setting where envelope detection is applied at the receiver. By defining different OOK channels with average transit power constraints, the achievability of the Shannon limit for both cases of using soft and hard decisions at the channel output is evaluated based on the analysis of the capacity per unit‐cost at low signal‐to‐noise ratio. We demonstrate that in phase fading using hard decisions cannot destroy the capacity only if extremely asymmetric OOK inputs are used with a properly chosen threshold. The corresponding pulse‐position modulation scheme is explicitly studied and demonstrated to be a Shannon‐type solution. Moreover, we also consider a slow Rayleigh fading scenario where the transmitter and receiver have no access to channel realizations. Throughput per unit‐cost results are developed to explore the tradeoff between power efficiency and channel quality for noncoherent OOK using soft and hard decisions. Copyright © 2015 John Wiley & Sons, Ltd.

A Log-Det Inequality for Random Matrices

We prove a new inequality for the expectation $E\left[\log\det\left(\mathbf{W}\mathbf{Q}+\mathbf{I}\right)\right]$, where $\mathbf{Q}$ is a nonnegative definite matrix and $\mathbf{W}$ is a diagonal random matrix with identically distributed nonnegative diagonal entries. A sharp lower bound is obtained by substituting $\mathbf{Q}$ by the diagonal matrix of its eigenvalues $\mathbf{\Gamma}$. Conversely, if this inequality holds for all $\mathbf{Q}$ and $\mathbf{\Gamma}$, then the diagonal entries of $\mathbf{W}$ are necessarily identically distributed. From this general result, we derive related deterministic inequalities of Muirhead- and Rado-type. We also present some applications in information theory: We derive bounds on the capacity of parallel Gaussian fading channels with colored additive noise and bounds on the achievable rate of noncoherent Gaussian fading channels.

Nearest-Neighbor Distributed Learning by Ordered Transmissions

The problem of distributed learning in wireless sensor networks is addressed, with the perspective of implementing nearest-neighbor (NN) regression in a decentralized way, with communication constraints. Elaborating on the ordered-transmission idea of Blum and Sadler , a universal channel access policy is designed that, without inter-sensor coordination, enables the fusion center to recover exactly the training-set labels it needs, while less informative labels are not delivered at all. Exploiting the aforementioned access policy, two different paradigms are then considered. In the first one, a constraint is imposed on the number of channel accesses, and a distributed regression algorithm is proposed reaching an asymptotic performance of twice the minimum achievable mean-squared error, while requiring just a single channel access. In the second one, a constraint is imposed on the number of quantization bits, and the focus is on devising consistent kn-NN regression rules. The noiseless case with quantized data is preliminarily addressed. Then, the role of the channel is explicitly taken into account, and a scheme with one-bit quantizers is proposed, reaching consistency over binary symmetric channels. Finally, it is argued that the inference task can be naturally suited to uncoded communications. Accordingly, two schemes are proposed, ensuring consistency over coherent and noncoherent channels, respectively; possible gains over the coded schemes are discussed.

Low-Rate Non-Binary LDPC Codes for Coherent and Blockwise Non-Coherent AWGN Channels

Low-rate non-binary low-density parity-check (LDPC) codes for coherent and blockwise non-coherent additive white Gaussian noise (AWGN) channels are developed. The proposed construction is based on the concatenation of non-binary outer LDPC codes with inner binary codes. In case the binary codes are chosen to be Hadamard or Reed-Muller (RM) codes, the complexity of the decoding scheme is considerably reduced. An asymptotic analysis of the concatenation with help of composite capacity considerations anddensity evolution (DE) is provided, from which guidelines on the choice of both inner and outer codes are devised. Finite length designs presented in this work confirm the excellent performance of the proposed codes.

Phase-Quantized Block Noncoherent Communication

Analog-to-digital conversion (ADC) is a key bottleneck in scaling DSP-centric receiver architectures to multiGigabit/s speeds. Recent information-theoretic results, obtained under ideal channel conditions (perfect synchronization, no dispersion), indicate that low-precision ADC (1-4 bits) could be a suitable choice for designing such high speed systems. In this work, we study the impact of employing low-precision ADC in a carrier asynchronous system. Specifically, we consider transmission over the block noncoherent additive white Gaussian noise channel, and investigate the achievable performance under low-precision output quantization. We focus attention on an architecture in which the receiver quantizes only the phase of the received signal: this has the advantage of being implementable without automatic gain control, using multiple 1-bit ADCs preceded by analog multipliers. For standard uniform Phase Shift Keying (PSK) modulation, we study the structure of the transition density of the phase-quantized block noncoherent channel. Several results, based on the symmetry inherent in the channel model, are provided to characterize this transition density. Low-complexity procedures for computing the channel information rate, and for block demodulation, are obtained using these results. Numerical computations are performed to compare the performance of quantized and unquantized systems, for different quantization precisions, and different block lengths. With QPSK modulation, it is observed, for example, that for SNR larger than 2-3 dB, 8-bin phase quantization of the received signal recovers about 80-85% of the mutual information attained with unquantized observations, while 12-bin phase quantization recovers more than 90% of the unquantized mutual information. Dithering the constellation is shown to improve the performance in the face of drastic quantization.