Phase Noise Channel Research Articles

Discrete-Time Models and Performance of Phase Noise Channels

Discrete-Time Models and Performance of Phase Noise Channels

Digital PLLs for phase noise channels: a concept based on the Tikhonov distribution

Digital PLLs for phase noise channels: a concept based on the Tikhonov distribution

RIS-Aided MIMO Systems With Hardware Impairments: Robust Beamforming Design and Analysis

Reconfigurable intelligent surface (RIS) has been anticipated to be a novel cost-effective technology to improve the performance of future wireless systems. In this paper, we investigate a practical RIS-aided multiple-input-multiple-output (MIMO) system in the presence of transceiver hardware impairments, RIS phase noise and imperfect channel state information (CSI). Joint design of the MIMO transceiver and RIS reflection matrix to minimize the total average mean-square-error (MSE) of all data streams is particularly considered. This joint design problem is non-convex and challenging to solve due to the newly considered practical imperfections. To tackle the issue, we first analyze the total average MSE by incorporating the impacts of the above system imperfections. Then, in order to handle the tightly coupled optimization variables and non-convex NP-hard constraints, an efficient iterative algorithm based on alternating optimization (AO) framework is proposed with guaranteed convergence, where each subproblem admits a closed-form optimal solution by leveraging the majorization-minimization (MM) technique. Moreover, via exploiting the special structure of the unit-modulus constraints, we propose a modified Riemannian gradient ascent (RGA) algorithm for the discrete RIS phase shift optimization. Furthermore, the optimality of the proposed algorithm is validated under line-of-sight (LoS) channel conditions, and the irreducible MSE floor effect induced by imperfections of both hardware and CSI is also revealed in the high signal-to-noise ratio (SNR) regime. Numerical results show the superior MSE performance of our proposed algorithm over the adopted benchmark schemes, and demonstrate that increasing the number of RIS elements is not always beneficial under the above system imperfections.

End-to-End Optimization of Constellation Shaping for Wiener Phase Noise Channels With a Differentiable Blind Phase Search

As the demand for higher data throughput in coherent optical communication systems increases, we need to find ways to increase capacity in existing and future optical communication links. To address the demand for higher spectral efficiencies, we apply end-to-end optimization for joint geometric and probabilistic constellation shaping in the presence of Wiener phase noise and carrier phase estimation. Our approach follows state-of-the-art bitwise auto-encoders, which require a differentiable implementation of all operations between transmitter and receiver, including the DSP algorithms. In this work, we show how to modify the ubiquitous blind phase search (BPS) algorithm, a popular carrier phase estimation algorithm, to make it differentiable and include it in the end-to-end constellation shaping. By leveraging joint geometric and probabilistic constellation shaping, we are able to obtain a robust and pilot-free modulation scheme improving the performance of 64-ary communication systems by at least 0.1 bit/symbol compared to square QAM constellations with neural demappers and by 0.05 bit/symbol compared to previously presented approaches applying only geometric constellation shaping.

Decision-directed Kalman particle filter with application to the MIMO phase noise channel

Demodulation of data transmitted over time-varying channels with a free running hidden Markov state, like the phase noise channel or the fading channel, requires that the receiver tracks the hidden channel state. The tracking technique adopted in the paper is based on non-data-aided sequential importance sampling, also known as particle filtering.The paper proposes a new particle filtering framework for data communication receivers based on an importance distribution such that each individual particle becomes a decision-directed Kalman filter relying upon its local symbol-by-symbol hard decisions. In this framework, different particles are left free to take different sequences of decisions. This leaves to the receiver the possibility of exploring different sequences of transmitted modulation symbols. The weight of the particle will be high for those particles that took in the past the correct sequence of decisions, while will be low for those particles that took wrong decisions. In the resampling procedure, particles with high weight will survive, while particles with low weight will be terminated, leaving space to the birth of new particles resampled from the surviving ones.The crucial point in importance sampling is the choice of the importance distribution and the main novelty of the paper is the proposal of an importance distribution such that the particles of the particle filter become decision-directed Kalman filters. One important benefit brought by our proposed method is that, being non-data-aided, it does not need pilot symbols, thus allowing to preserve the transmission rate. A significant application example, presented and developed in the paper, is constituted by MIMO systems affected by phase noise, where the channel state vector consists of many parameters.

Low Complexity Non-Uniform FFT for Doppler Compensation in OFDM-Based Underwater Acoustic Communication Systems

The Doppler effect critically degrades the performance of orthogonal frequency division multiplexing (OFDM) systems in general. This problem is significantly worse for underwater acoustic (UWA) communication systems due to the distinct characteristics of the underwater channel, resulting in the loss of orthogonality among sub-carriers. In order to compensate Doppler shifts, including phase noise and multipath channels in realistic communication scenarios, the joint of channel estimation and ICI reduction is often performed. However, the accuracy depends on the channel estimation and the FFT size, while this leads to increased computational complexity at the receiver. To achieve this dual goal in the actual underwater communication environment, a novel pilot structure in the frequency domain has been applied to overcome the channel impulse response (CIR) variation in a block period. The coarse Doppler shift is firstly estimated by using the received pilot signal. Afterward, the study takes advantage of the flexibility provided by non-uniform fast Fourier transform (NFFT) in choosing the sampling points to construct a fast and stable Doppler frequency Compensation Matrix-based NFFT (DCMN) to fine compensate the Doppler phase shift. Finally, this study shows the improvement of the proposed method’s performance by actual experimental measurements and simulations.

Squeezing-enhanced communication without a phase reference

We study the problem of transmitting classical information using quantum Gaussian states on a family of phase-noise channels with a finite decoherence time, such that the phase-reference is lost after m consecutive uses of the transmission line. This problem is relevant for long-distance communication in free space and optical fiber, where phase noise is typically considered as a limiting factor. The Holevo capacity of these channels is always attained with photon-number encodings, challenging with current technology. Hence for coherent-state encodings the optimal rate depends only on the total-energy distribution and we provide upper and lower bounds for all m, the latter attainable at low energies with on/off modulation and photodetection. We generalize this lower bound to squeezed-coherent encodings, exhibiting for the first time to our knowledge an unconditional advantage with respect to any coherent encoding for m=1 and a considerable advantage with respect to its direct coherent counterpart for m>1. This advantage is robust with respect to moderate attenuation, and persists in a regime where Fock encodings with up to two-photon states are also suboptimal. Finally, we show that the use of part of the energy to establish a reference frame is sub-optimal even at large energies. Our results represent a key departure from the case of phase-covariant Gaussian channels and constitute a proof-of-principle of the advantages of using non-classical, squeezed light in a motivated communication setting.

Spectral Efficiency of a Frequency-Selective Cell-Free Massive MIMO System With Phase Noise

This letter studies spectral efficiency of a frequency-selective cell-free massive multiple-input-multiple-output (MIMO) system with phase noise (PN) and imperfect channel state information. Two linear and low-complexity receivers are considered, namely, time-reversal maximum-ratio combining (TR-MRC) and time-reversal large-scale fading decoding (TR-LSFD). For each receiver, a lower bound on the uplink achievable spectral efficiency (SE) is obtained. From the obtained bounds, it is found that, compared to the TR-MRC receiver, the TR-LSFD receiver can attain a higher SE and the performance gain of the TR-LSFD receiver depends on the number of access points (APs) and the propagation losses between APs and users. Numerical results are provided to corroborate the accuracy of our analysis and the performance superiority of TR-LSFD receiver. Results also show that the effect of PN at users is stronger than the effect of PN at APs on the achievable SE.

Analysis of SVD-Based Hybrid Schemes for Massive MIMO With Phase Noise and Imperfect Channel Estimation

In hybrid analog-digital schemes, proposed to reduce the number of RF chains especially at millimeter waves, the precoding at the transmitter and the combining at the receiver are split into digital and analog parts. We analyze the sensitivity of hybrid schemes to phase noise and channel estimation errors and we compare them to a full-digital approach. The scheme adopted for the analog part employs fixed phase shifters, then the digital part is optimized by a singular-value decomposition. We derive analytical expressions for the interference and the SNR degradation arising from the imperfect decomposition due to phase noise and the channel estimation error, for typical millimter-wave massive MIMO channels. In particular we show that when the channel estimation is made in the beam-space, this hybrid scheme is more robust to the phase noise and to the channel estimation errors than a full-digital approach.

Design of Digital Communications for Strong Phase Noise Channels

To meet the requirements of beyond 5G networks, the significant amount of unused spectrum in sub-TeraHertz frequencies is contemplated for high-rate wireless communications. Yet, the performance of sub-TeraHertz systems is severely degraded by strong oscillator phase noise. We investigate in this paper the design of digital communications robust to phase noise. This problem is addressed in three steps: the characterization of the phase noise channel, the design of the optimum receiver, and the optimization of the modulation scheme. This paper proposes a joint performance and implementation optimization. First, we address the design of the demodulation scheme for phase noise channels and propose the polar metric, a soft-decision rule for symbol detection. It is shown that performance gains are achieved for coded and uncoded systems with valuable complexity reductions of the receiver. Second, we investigate the optimization of the modulation scheme for phase noise. We demonstrate that using a constellation defined upon a lattice in the amplitude-phase domain leads to significant performance gains and a low-complexity implementation. Thereupon, we propose the Polar-QAM scheme with efficient binary labeling and demodulation. Numerical simulation results show that the proposed modulation and demodulation schemes offer valuable solutions to achieve high-rate communications on systems strongly impaired by phase noise.

Study and Implementation of Phase Noise Channels using Independant Oscillators for Mimo by using Unscented Kalman Filter

Study and Implementation of Phase Noise Channels using Independant Oscillators for Mimo by using Unscented Kalman Filter

Approximate ML Decoding of Short Convolutional Codes Over Phase Noise Channels

We propose a decoding algorithm for tail-biting convolutional codes over phase noise channels. It can be seen as a reduced complexity approximation of maximum likelihood decoding. We target short blocks and extend the wrap-around Viterbi algorithm to trellises describing the random evolution of the phase impairment, for which we adopt two different models: a blockwise non-coherent and a blockwise Wiener channel model. Numerical results show that the performance of the proposed algorithm is within a few tenths of dB or less from maximum likelihood decoding for the setup studied in this letter.

Spiral Constellations for Phase Noise Channels

In this paper, we consider the design of spiral constellations for channels affected by phase noise. The strength of the proposed constellations resides both on the performance and on the extreme simplicity of the design. The symbols can in fact be expressed in analytical form, and are uniquely defined through a single parameter that accounts for the phase and thermal noise variances. The structure of the proposed constellations allows to easily determine the points that are closest to any point in the complex plane, therefore we also propose a low complexity detector that is suitable for phase noise channels in medium-high signal-to-noise ratio conditions. The performance of the proposed constellations are assessed in terms of information rate and error rate. Despite their simplicity, the new spiral constellations have excellent performance, especially when the constellation size grows large.

Optimized communication strategies with binary coherent states over phase noise channels

The achievable rate of information transfer in optical communications is determined by the physical properties of the communication channel, such as the intrinsic channel noise. Bosonic phase noise channels, a class of non-Gaussian channels, have emerged as a relevant noise model in quantum information and optical communication. However, while the fundamental limits for communication over Gaussian channels have been extensively studied, the properties of communication over Bosonic phase noise channels are not well understood. Here we propose and demonstrate experimentally the concept of optimized communication strategies for communication over phase noise channels to enhance information transfer beyond what is possible with conventional methods of modulation and detection. Two key ingredients are generalized constellations of coherent states that interpolate between standard on-off keying and binary phase-shift keying formats, and non-Gaussian measurements based on photon number resolving detection of the coherently displaced signal. For a given power constraint and channel noise strength, these novel strategies rely on joint optimization of the input alphabet and the measurement to provide enhanced communication capability over a non-Gaussian channel characterized in terms of the error rate as well as mutual information.

Short Non-Binary Low-Density Parity-Check Codes for Phase Noise Channels

This work considers the design of short non-binary low-density parity-check (LDPC) codes over finite fields of order m, for channels with phase noise. In particular, m-ary differential phase-shift keying (DPSK) modulated code symbols are transmitted over an additive white Gaussian noise (AWGN) channel with Wiener phase noise. At the receiver side, non-coherent detection takes place, with the help of a multi-symbol detection algorithm, followed by a non-binary decoding step. Both the detector and decoder operate on a joint factor graph. As a benchmark, finite length bounds and information rate expressions are computed and compared with the codeword error rate (CER) performance, as well as the iterative threshold of the obtained codes. As a result, performance within 1:2 dB from finite-length bounds is obtained, down to a CER of 1e-3.

Reduced-complexity sparsity-aware joint phase noise mitigation and channel equalization in OFDM receivers

A major performance and complexity limitation in direct-conversion broadband wireless transceivers is the phase noise (PN) resulting from the inevitable imperfections in the fabrication process of the crystal oscillator. PN induces inter-carrier interference in orthogonal frequency division multiplexing (OFDM) transceivers. Assuming the availability of inaccurate PN and channel estimates, in this paper, we propose an efficient low-complexity sparsity-based design for joint PN mitigation and channel equalization in OFDM systems. Moreover, we analyze the maximum expected coherence metric for the sparsifying matrix that is used in our approach which provides some insight into its performance. Finally, our numerical simulations demonstrate the effectiveness of our proposed compensation approach compared to the state-of-the-art designs in terms of both performance and computational complexity.

Extended Kalman Filter for MIMO Phase Noise Channels With Independent Oscillators

The Kalman filter is proposed here to track the phase noise introduced by independent transmit and receive oscillators in multiple-input multiple-output transmission. To take advantage of pilot symbols that are transmitted before and after the time instant where one wants to estimate the vector of phases, a forward–backward Kalman filter is proposed. To reduce the complexity of the Kalman filter, suboptimal methods are introduced and their performance is compared with that of the full complexity Kalman filter by computer simulation.

Phase noise in broadcasting: an outer bound for capacity region and corresponding simulations

Point-to-point communication channels with phase noise have been studied extensively. To the best of the authors’ knowledge, the broadcast channel (BC) with phase noise has not been studied yet. In this study, having reviewed definitions of the channels with phase noise, the authors analyse capacity region of the BC impaired by Wiener phase noise and additive white Gaussian noise and obtain an outer bound for the capacity region. Also, its high signal-to-noise ratio analysis is presented. Their outer bound includes the known outer bound for the point-to-point phase noise channel as its special case. Mathematical findings are explained more by simulation results.

On the Multiplexing Gain of Discrete-Time MIMO Phase Noise Channels

The capacity of a point-to-point discrete-time multi-input-multiple-output (MIMO) channel with phase uncertainty (MIMO phase noise channel) is still open. As a matter of fact, even the pre-log (multiplexing gain) of the capacity in the high signal-to-noise ratio (SNR) regime is unknown in general. We make some progress in this direction for two classes of such channels. With phase noise on the individual paths of the channel (model A), we show that the multiplexing gain is $\frac {1}{2}$ , which implies that the capacity does not scale with the channel dimension at high SNR. With phase noise at both the input and output of the channel (model B), the multiplexing gain is upper-bounded by $\frac {1}{2} \min \{{ n_{\text {t}}}, (n_{\text {r}}-2)^{+}\! + 1\}$ , and lower-bounded by $\frac {1}{2} \min \left\{{ n_{\text {t}}, \lfloor \frac {n_{\text {r}}+1}{2} \rfloor }\right\}$ , where $n_{\text {t}}$ and $n_{\text {r}}$ are the number of transmit and receive antennas, respectively. The multiplexing gain is enhanced to $\frac {1}{2}\min \{ n_{\text {t}}, n_{\text {r}}\}$ without receive phase noise, and to $\frac {1}{2}\min \{2 n_{\text {t}}-1, n_{\text {r}}\}$ without transmit phase noise. In all the cases of model B, the multiplexing gain scales linearly with $\min \{ n_{\text {t}}, n_{\text {r}}\}$ . Our main results rely on the derivation of non-trivial upper and lower bounds on the capacity of such channels.

Models and Information Rates for Wiener Phase Noise Channels

A waveform channel is considered where the transmitted signal is corrupted by Wiener phase noise and additive white Gaussian noise. A discrete-time channel model that takes into account the effect of filtering on the phase noise is developed. The model is based on a multi-sample receiver, i.e., an integrate-and-dump filter whose output is sampled at a rate higher than the signaling rate. It is shown that, at high Signal-to-Noise Ratio (SNR), the multi-sample receiver achieves a rate that grows logarithmically with the SNR if the number of samples per symbol (oversampling factor) grows with the cubic root of the SNR. Moreover, the pre-log factor is at least 1/2 and can be achieved by amplitude modulation. For an approximate discrete-time model of the multi-sample receiver, the capacity pre-log at high SNR is shown to be at least 3/4 if the number of samples per symbol grows with the square root of the SNR. The analysis shows that phase modulation achieves a pre-log of at least 1/4 while amplitude modulation still achieves a pre-log of 1/2. This is strictly greater than the capacity pre-log of the (approximate) discrete-time Wiener phase noise channel with only one sample per symbol, which is 1/2. Numerical simulations are used to compute lower bounds on the information rates achieved by the multi-sample receiver. The simulations show that oversampling is beneficial for both strong and weak phase noise at high SNR. In fact, the information rates are sometimes substantially larger than when using commonly-used approximate discrete-time models.