Wireless communications over fast fading channels are challenging, requiring either frequent channel tracking or complicated signaling schemes such as orthogonal time frequency space (OTFS) modulation. In this paper, we propose low-complexity frequency domain equalizations to combat fast fading, based on novel discrete delay-time and frequency-Doppler channel models. Exploiting the circular stripe diagonal nature of the frequency-Doppler channel matrix, we introduce low-complexity frequency domain minimum mean square error (MMSE) equalization for OTFS systems with fully resolvable Doppler spreads. We also demonstrate that the proposed MMSE equalization is applicable to conventional orthogonal frequency division multiplexing (OFDM) and single carrier frequency domain equalization (SC-FDE) systems with short signal frames and partially resolvable Doppler spreads. After generalizing the input-output data symbol relationship, we analyze the equalization performance via channel matrix eigenvalue decomposition and derive a closed-form expression for the theoretical bit-error-rate. Simulation results for OTFS, OFDM, and SC-FDE modulations verify that the proposed low-complexity frequency domain equalization methods can effectively exploit the time diversity over fast fading channels. Even with partially resolvable Doppler spread, the conventional SC-FDE can achieve performance close to OTFS, especially in fast fading channels with a dominating line-of-sight path.
The performance of MMSE Iterative Equalization based on MAP-SBVP and COD-MAP algorithms (for generating extrinsic information) are compared for fading and non-fading communication channels employing serial concatenated convolution codes. MAP-SBVP is a convolution decoder using a conventional soft-MAP decoder followed by a soft-convolution encoder using the soft-boolean value propagation (SBVP). From the simulations it is observed that for MMSE Iterative Equalization, MAP-SBVP performance is comparable to COD-MAP for fading and non-fading channels.
Reconfigurable intelligent surfaces (RISs), which enable tunable anomalous reflection, have appeared as a promising method to enhance wireless systems. In this paper, we propose to use an RIS as a spatial equalizer to address the well-known multi-path fading phenomenon. By introducing some controllable paths artificially against the multi-path fading through the RIS, we can perform equalization during the transmission process instead of at the receiver, and thus all the users can share the same equalizer. Unlike the beamforming application of the RIS, which aims to maximize the received energy…
We investigate channel equalization for Rayleigh fading channels under bounded channel uncertainties. We analyze three robust methods to estimate an unknown signal transmitted through a Rayleigh fading channel, where we avoid directly tuning the equalizer parameters to the available inaccurate channel information. These methods are based on minimizing certain mean-square error criteria that incorporate the channel uncertainties into the problem formulations. We present closed-form solutions to the channel equalization problems for each method and for both zero mean and nonzero mean signals. We…
Orthogonal Frequency Division Multiplexing (OFDM) has recently been applied in wireless communication systems due to its high data rate transmission capability with high bandwidth efficiency and its robustness to multi-path delay. Fading is the one of the major aspect which is considered in the receiver. To cancel the effect of fading, channel estimation and equalization procedure must be done at the receiver before data demodulation. This paper mainly deals with pilot based channel estimation techniques for OFDM communication over frequency selective fading channels. This paper proposes a spe…
This letter proposes the Faster-than-Nyquist signaling (FTNS) using overlap frequency domain equalization (FDE), which compensates the inter-symbol interference (ISI) due to band limiting filters of the FTNS at the transmitter and the receiver as well as the frequency selective fading channel. Since overlap FDE does not require any guard interval (GI) at the transmitter such as cyclic prefix (CP), higher spectral efficiency can be achieved compared to FTNS scheme using the conventional FDE. In the proposed method, the equalizer weight is derived based on minimum mean square error (MMSE) criter…
Orthogonal time frequency and space (OTFS) modulation is a promising technology that satisfies high Doppler requirements for future mobile systems. OTFS modulation encodes information symbols and pilot symbols into the two-dimensional (2D) delay-Doppler (DD) domain. The received symbols suffer from inter-Doppler interference (IDI) in the fading channels with fractional Doppler shifts that are sampled at noninteger indices in the DD domain. IDI has been treated as an unavoidable effect because the fractional Doppler shifts cannot be obtained directly from the received pilot symbols. In this pap…
This paper proposes a low-complexity algorithm for blind equalization of data in OFDM-based wireless systems with general constellations. The proposed algorithm is able to recover data even when the channel changes on a symbol-by-symbol basis, making it suitable for fast fading channels. The proposed algorithm does not require any statistical information of the channel and thus does not suffer from latency normally associated with blind methods. We also demonstrate how to reduce the complexity of the algorithm, which becomes especially low at high SNR. Specifically, we show that in the high SN…
The use of low resolution Analog to Digital Converters (ADCs) can significantly reduce the power consumption for massive Multiple Input Multiple Output (MIMO) systems. The existing literature on quantized massive MIMO systems deals with Cyclic Prefix (CP) transmission schemes in frequency-selective fading channels. In this paper, we propose a block processing Frequency Domain Equalization (FDE) technique in CP-free transmission schemes for massive MIMO systems having low resolution ADCs. The optimal block length for FDE is found by minimizing a computational complexity cost function and taking…
In this paper, we propose a serially concatenated turbo-encoded faster-than-Nyquist signaling (FTNS) transceiver that takes into account FTNS-specific colored noise effects. The proposed low-complexity receiver carries out soft-decision frequency-domain equalization with the aid of the minimum-mean square error criterion while whitening the colored noise. Simulation results demonstrate that the proposed multi-stage-concatenated FTNS system achieves a better error-ratio performance than previous systems that do not consider colored noise effects in the high-symbol-packing FTNS regime. Furthermo…
Programmable radio environments parametrized by reconfigurable intelligent surfaces (RISs) are emerging as a new wireless communications paradigm, but currently used channel models for the design and analysis of signal-processing algorithms cannot include fading in a manner that is faithful to the underlying wave physics. To overcome this roadblock, we introduce a physics-based end-to-end model of RIS-parametrized wireless channels with adjustable fading (coined PhysFad) which is based on a first-principles coupled-dipole formalism. PhysFad naturally incorporates the notions of space and causa…
For ergodic fading, a lattice coding and decoding strategy is proposed and its performance is analyzed for the single-input single-output (SISO) and multiple-input multiple-output (MIMO) point-to-point channel as well as the multiple-access channel (MAC), with channel state information available only at the receiver (CSIR). At the decoder a novel strategy is proposed consisting of a time-varying equalization matrix followed by decision regions that depend only on channel statistics, not individual realizations. Our encoder has a similar structure to that of Erez and Zamir. For the SISO channel…
In this article, a fractional-norm constrained blind adaptive algorithm is presented for sparse channel equalization. In essence, the algorithm improves on the minimization of the constant modulus (CM) criteria by adding a sparsity inducing \(\ell_p\)-norm penalty. Simulation results demonstrate that the proposed regularized equalizer exploits the inherent channel sparsity effectively and exhibits faster convergence compared to its counterparts.
In this work, we consider the problem of distributed approximation of functions over multiple-access channels with additive noise. In contrast to previous works, we take fast fading into account and give explicit probability bounds for the approximation error allowing us to derive bounds on the number of channel uses that are needed to approximate a function up to a given approximation accuracy. Neither the fading nor the noise process is limited to Gaussian distributions. Instead, we consider sub-gaussian random variables which include Gaussian as well as many other distributions of practical…
In this paper, we study a new intelligent refracting surface (IRS)-assisted high-mobility communication with the IRS deployed in a high-speed moving vehicle to assist its passenger's communication with a static base station (BS) on the roadside. The vehicle's high Doppler frequency results in a fast fading channel between the BS and the passenger/user, which renders channel estimation for the IRS with a large number of refracting elements a more challenging task as compared to the conventional case with low-mobility users only. In order to mitigate the Doppler effect and reap the full IRS pass…
The "Writing onto Fast Fading Dirt" (WFFD) channel is investigated to study the effects of partial channel knowledge on the capacity of the "writing on dirty paper" channel. The WFFD channel is the Gel'fand-Pinsker channel in which the output is obtained as the sum of the input, white Gaussian noise and a fading-times-state term. The fading-times-state term is equal to the element-wise product of the channel state sequence, known only at the transmitter, and a fast fading process, known only at the receiver. We consider the case of Gaussian distributed channel states and derive an approximate …
User selection (US) with Zero-forcing beamforming is considered in fast fading Gaussian vector broadcast channels with perfect channel state information (CSI) at the transmitter. A novel criterion for US is proposed, which depends on both CSI and the data symbols, while conventional criteria only depend on CSI. Since the optimization of US based on the proposed criterion is infeasible, a greedy algorithm of data-dependent US is proposed to perform the optimization approximately. An overhead issue arises in fast fading channels: On every update of US, the transmitter might inform each user whet…
In this work we extend the setting of communication without power constraint, proposed by Poltyrev, to fast fading channels with channel state information (CSI) at the receiver. The optimal codewords density, or actually the optimal normalized log density (NLD), is considered. Poltyrev's capacity for this channel is the highest achievable NLD, at possibly large block length, that guarantees a vanishing error probability. For a given finite block length n and a fixed error probability, there is a gap between the highest achievable NLD and Poltyrev's capacity. As in other channels, this gap asym…
Secret sharing over the fast-fading MIMO wiretap channel is considered. A source and a destination try to share secret information over a fast-fading MIMO channel in the presence of a wiretapper who also makes channel observations that are different from but correlated to those made by the destination. An interactive authenticated unrestricted public channel is also available for use by the source and destination in the secret sharing process. This falls under the "channel-type model with wiretapper" considered by Ahlswede and Csiszar. A minor extension of their result (to continuous channel a…
We develop a characterization of fading models, which assigns a number called logarithmic Jensen's gap to a given fading model. We show that as a consequence of a finite logarithmic Jensen's gap, approximate capacity region can be obtained for fast fading interference channels (FF-IC) for several scenarios. We illustrate three instances where a constant capacity gap can be obtained as a function of the logarithmic Jensen's gap. Firstly for an FF-IC with neither feedback nor instantaneous channel state information at transmitter (CSIT), if the fading distribution has finite logarithmic Jensen's…
A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, without using pilot symbols. We derive an approximate maximum likelihood estimate to the channel parameters and reconstruct the transmitted data. We demonstrate significant and consistent improvements in the error rate of the reconstructed symbols, compared to existing blind equaliza…
This paper presents adaptive bidirectional minimum mean-square error (MMSE) parameter estimation algorithms for fast-fading channels. The time correlation between successive channel gains is exploited to improve the estimation and tracking capabilities of adaptive algorithms and provide robustness against time-varying channels. Bidirectional normalized least mean-square (NLMS) and conjugate gradient (CG) algorithms are devised along with adaptive mixing parameters that adjust to the time-varying channel correlation properties. An analysis of the proposed algorithms is provided along with a dis…
Reliable and prompt identification of active users is critical for enabling random access in massive machine-to-machine type networks which typically operate within stringent access delay and energy constraints. In this paper, an energy efficient active user identification protocol is envisioned in which the active users simultaneously transmit On-Off Keying (OOK) modulated preambles whereas the base station uses non-coherent detection to avoid the channel estimation overheads. The minimum number of channel-uses required for active user identification in the asymptotic regime of total number o…
In this paper we consider the capacity of the cognitive radio channel in different fading environments under a low interference regime. First we derive the probability that the low interference regime holds under shadow fading as well as Rayleigh and Rician fast fading conditions. We demonstrate that this is the dominant case, especially in practical cognitive radio deployment scenarios. The capacity of the cognitive radio channel depends critically on a power loss parameter, $α$, which governs how much transmit power the cognitive radio dedicates to relaying the primary message. We derive a s…
Semantic Channel Equalization Strategies for Deep Joint Source-Channel Coding
DIAG Department, Sapienza University of Rome（罗马大学DIAG系）；Consorzio Nazionale Interuniversitario per le Telecomunicazioni (CNIT)（国家跨大学电信合作机构）；CEA Leti, University Grenoble Alpes（CEA Leti与格勒诺布尔阿尔卑斯大学）；DIET Department, Sapienza University of Rome（罗马大学DIET系）
Irregular repeat-accumulate Root-Check LDPC codes based on Progressive Edge Growth (PEG) techniques for block-fading channels are proposed. The proposed Root-Check LDPC codes are {both suitable for channels under $F = 2, 3$ independent fadings per codeword and} for fast fading channels. An IRA(A) Root-Check structure is devised for $F = 2, 3$ independent fadings. The performance of the new codes is investigated in terms of the Frame Error Rate (FER). Numerical results show that the IRAA LDPC codes constructed by the proposed algorithm {outperform by about 1dB the existing} IRA Root-Check LDPC …
The "writing dirty paper" capacity result crucially dependents on the perfect channel knowledge at the transmitter as the presence of even a small uncertainty in the channel realization gravely hampers the ability of the transmitter to pre-code its transmission against the channel state. This is particularly disappointing as it implies that interference pre-coding in practical systems is effective only when the channel estimates at the users have very high precision, a condition which is generally unattainable in wireless environments. In this paper we show that substantial improvements are po…
Costa`s "writing on dirty paper" result establishes that full state pre-cancellation can be attained in the Gel`fand-Pinsker problem with additive state and additive white Gaussian noise. This result holds under the assumptions that full channel knowledge is available at both the transmitter and the receiver. In this work we consider the scenario in which the state is multiplied by an ergodic fading process which is not known at the encoder. We study both the case in which the receiver has knowledge of the fading and the case in which it does not: for both models we derive inner and outer boun…
In this work, we present a framework analysis of millimeter waves (mmWaves) vehicular communications systems. Communications between vehicles take place through a cooperative relay which acts as an intermediary base station (BS). The relay is equipped with multiple transmit and receive antennas and it employs decode-and-forward (DF) to process the signal. Also, the relay applies maximal ratio combining (MRC), and maximal ratio transmission (MRT), respectively, to receive and forward the signal. As the vehicles' speeds are relatively high, the channel experiences a fast fading and this time var…
This paper presents a novel efficient receiver design for wireless communication systems that incorporate orthogonal frequency division multiplexing (OFDM) transmission. The proposed receiver does not require channel estimation or equalization to perform coherent data detection. Instead, channel estimation, equalization, and data detection are combined into a single operation, and hence, the detector is denoted as a direct data detector (D^{3}). The performance of the proposed system is thoroughly analyzed theoretically in terms of bit error rate (BER), and validated by Monte Carlo simulations…
In this paper we consider the capacity of the cognitive radio channel in a fading environment under a "low interference regime". This capacity depends critically on a power loss parameter, $α$, which governs how much transmit power the cognitive radio dedicates to relaying the primary message. We derive a simple, accurate approximation to $α$ which gives considerable insight into system capacity. We also investigate the effects of system parameters and propagation environment on $α$ and the cognitive radio capacity. In all cases, the use of the approximation is shown to be extremely accurate. …
Deterministic identification (DI) is addressed for Gaussian channels with fast and slow fading, where channel side information is available at the decoder. In particular, it is established that the number of messages scales as $2^{n\log(n)R}$, where $n$ is the block length and $R$ is the coding rate. Lower and upper bounds on the DI capacity are developed in this scale for fast and slow fading. Consequently, the DI capacity is infinite in the exponential scale and zero in the double-exponential scale, regardless of the channel noise.
When a channel model is available, learning how to communicate on fading noisy channels can be formulated as the (unsupervised) training of an autoencoder consisting of the cascade of encoder, channel, and decoder. An important limitation of the approach is that training should be generally carried out from scratch for each new channel. To cope with this problem, prior works considered joint training over multiple channels with the aim of finding a single pair of encoder and decoder that works well on a class of channels. As a result, joint training ideally mimics the operation of non-coherent…
In this paper, fading Gaussian multiuser channels are considered. If the channel is perfectly known to the transmitter, capacity has been established for many cases in which the channels may satisfy certain information theoretic orders such as degradedness or strong/very strong interference. Here, we study the case when only the statistics of the channels are known at the transmitter which is an open problem in general. The main contribution of this paper is the following: First, we introduce a framework to classify random fading channels based on their joint distributions by leveraging three …
The performance of integer-forcing equalization for communication over the compound multiple-input multipleoutput channel is investigated. An upper bound on the resulting outage probability as a function of the gap to capacity has been derived previously, assuming a random precoding matrix drawn from the circular unitary ensemble is applied prior to transmission. In the present work a simple and explicit lower bound on the worst-case outage probability is derived for the case of a system with two transmit antennas and two or more receive antennas, leveraging the properties of the Jacobi ensemb…
We propose iterative detection and decoding (IDD) algorithms with Low-Density Parity-Check (LDPC) codes for Multiple Input Multiple Output (MIMO) systems operating in block-fading and fast Rayleigh fading channels. Soft-input soft-output minimum mean-square error receivers with successive interference cancellation are considered. In particular, we devise a novel strategy to improve the bit error rate (BER) performance of IDD schemes, which takes into account the soft \textit{a posteriori} output of the decoder in a block-fading channel when Root-Check LDPC codes are used. A MIMO IDD receiver w…
We propose an Iterative Detection and Decoding (IDD) scheme with Low Density Parity Check (LDPC) codes for Multiple Input Multiple Output (MIMO) systems for block-fading $F = 2$ and fast fading Rayleigh channels. An IDD receiver with soft information processing that exploits the code structure and the behaviour of the log likelihood ratios (LLR)'s is developed. Minimum Mean Square Error (MMSE) with Successive Interference Cancellation (SIC) and with Parallel Interference Cancellation (PIC) schemes are considered. The soft \textit{a posteriori} output of the decoder in a block-fading channel wi…
A reconfigurable intelligent surface (RIS) is capable of manipulating electromagnetic waves with its flexibly configurable unit cells, thus is an appealing technology to resist fast fading caused by multi-path in wireless communications. In this paper, a two-path propagation model for RIS-assisted wireless communications is proposed by considering both the direct path from the transmitter to the receiver and the assisted path provided by the RIS. The proposed propagation model unveils that the phase shifts of RISs can be optimized by appropriate configuration for multi-path fading mitigation. …
There are currently a plurality of capacity theories of fading channels, including the ergodic capacity for fast fading channels and outage capacity for slow fading channels. However, analyses show that the outage capacity is a misconception. In this paper we use the 1st order Gaussian-Markov process with coherence coefficient $α$ as the unified model for slow and fast fading channels, the capacity of which without channel side information is studied. We demonstrate that the information rate of a fading channel has a structure that the rate of user message is always accompanied by a rate of ch…
This paper studies dual-hop amplify-and-forward relaying system employing differential encoding and decoding over time-varying Rayleigh fading channels. First, the convectional "two-symbol" differential detection (CDD) is theoretically analysed in terms of the bit-error-rate (BER). The obtained analysis clearly shows that performance of two-symbol differential detection severely degrades in fast-fading channels and reaches an irreducible error floor at high signal-to-noise ratio region. To overcome the error floor experienced with fast-fading, a practical suboptimal "multiple-symbol" detection…
In this paper we study the problem of half-duplex active eavesdropping in fast fading channels. The active eavesdropper is a more powerful adversary than the classical eavesdropper. It can choose between two functional modes: eavesdropping the transmission between the legitimate parties (Ex mode), and jamming it (Jx mode) -- the active eavesdropper cannot function in full duplex mode. We consider a conservative scenario, when the active eavesdropper can choose its strategy based on the legitimate transmitter-receiver pair's strategy -- and thus the transmitter and legitimate receiver have to p…
Differential distributed space-time coding (D-DSTC) technique has been considered for relay networks to provide both diversity gain and high throughput in the absence of channel state information. Conventional differential detection (CDD) or two-symbol non-coherent detection over slow -fading channels has been examined and shown to suffer 3-4 dB loss when compared to coherent detections. Moreover, it has also been shown that the performance of CDD severely degrades in fast-fading channels and an irreducible error floor exists at high signal-to-noise ratio region. To overcome the error floor ex…
In this study, a cross-layer design which combines adaptive modulation and coding (AMC) and hybrid automatic repeat request (HARQ) techniques for a cooperative wireless network is investigated analytically. Previous analyses of such systems in the literature are confined to the case where the fading channel is independent at each retransmission, which can be unrealistic unless the channel is varying very fast. On the other hand, temporal channel correlation can have a significant impact on the performance of HARQ systems. In this study, utilizing a Markov channel model which accounts for the t…
This paper presents a tool for the analysis, and simulation of direction-of-arrival (DOA) estimation in wireless mobile communication systems over the fading channel. It reviews two methods of Direction of arrival (DOA) estimation algorithm. The standard Multiple Signal Classification (MUSIC) can be obtained from the subspace based methods. In improved MUSIC procedure called Cyclic MUSIC, it can automatically classify the signals as desired and undesired based on the known spectral correlation property and estimate only the desired signal's DOA. In this paper, the DOA estimation algorithm usin…
This study will present the design, construction and implementation of Algebraic Geometric Irregular Block Turbo Codes (AGIBTCs). Furthermore, we will evaluate its performance over fast fading channels using different modulation schemes (BPSK, QPSK, 16QAM and 64QAM). The idea behind the design of AGIBTC is to overcome the high system complexity of Algebraic Geometric Block Turbo Codes (AGBTCs) while maintaining a high Bit-Error Rate (BER) performance. This design is inspired by the idea of unequal protection of information symbols which is the core of IBTCs. Our experiments conducted over the …
Intelligent reflecting/refracting surface (IRS) has recently emerged as a promising solution to reconfigure wireless propagation environment for enhancing the communication performance. In this paper, we study a new IRS-aided high-mobility communication system by employing the intelligent refracting surface with a high-speed vehicle to aid its passenger's communication with a remote base station (BS). Due to the environment's random scattering and vehicle's high mobility, a rapidly time-varying channel is typically resulted between the static BS and fast-moving IRS/user, which renders the chan…
In this paper we address the problem of transmission of correlated sources over a fast fading multiple access channel (MAC) with partial channel state information available at both the encoders and the decoder. We provide sufficient conditions for transmission with given distortions. Next these conditions are specialized to a Gaussian MAC (GMAC). We provide the optimal power allocation strategy and compare the strategy with various levels of channel state information. Keywords: Fading MAC, Power allocation, Partial channel state information, Correlated sources.
The covert capacity is characterized for a non-coherent fast Rayleigh-fading wireless channel, in which a legitimate user wishes to communicate reliably with a legitimate receiver while escaping detection from a warden. It is shown that the covert capacity is achieved with an amplitude-constrained input distribution that consists of a finite number of mass points including one at zero and numerically tractable bounds are provided. It is also conjectured that distributions with two mass points in fixed locations are optimal.
This is the first part of a two-part paper that studies the problem of jamming in a fixed-rate transmission system with fading. Both transmitter and jammer are subject to power constraints which can be enforced over each codeword short-term / peak) or over all codewords (long-term / average), hence generating different scenarios. All our jamming problems are formulated as zero-sum games, having the probability of outage as pay-off function and power control functions as strategies. The paper aims at providing a comprehensive coverage of these problems, under fast and slow fading, peak and aver…
We present nonasymptotic bounds on the maximum coding rate achievable over a Rician block-fading channel for a fixed packet size and a fixed packet error probability. Our bounds, which apply to the scenario where no a priori channel state information is available at the receiver, allow one to quantify the tradeoff between the rate gains resulting from the exploitation of time-frequency diversity and the rate loss resulting from fast channel variations and pilot-symbol overhead.
We extend the idea of end-to-end learning of communications systems through deep neural network (NN)-based autoencoders to orthogonal frequency division multiplexing (OFDM) with cyclic prefix (CP). Our implementation has the same benefits as a conventional OFDM system, namely singletap equalization and robustness against sampling synchronization errors, which turned out to be one of the major challenges in previous single-carrier implementations. This enables reliable communication over multipath channels and makes the communication scheme suitable for commodity hardware with imprecise oscilla…
