We study the amplitude-constrained additive white Gaussian noise channel. It is well known that the capacity-achieving input distribution for this channel is discrete and supported on finitely many points. The best known bounds show that the support size of the capacity-achieving distribution is lower-bounded by a term of order $A$ and upper-bounded by a term of order $A^2$, where $A$ denotes the amplitude constraint. It was conjectured in [1] that the linear scaling is optimal. In this work, we establish a new lower bound of order $A\sqrt{\log A}$, improving the known bound and ruling out the conjectured linear scaling. To obtain this result, we quantify the fact that the capacity-achieving output distribution is close to the uniform distribution in the interior of the amplitude constraint. Next, we introduce a wrapping operation that maps the problem to a compact domain and develop a theory of best approximation of the uniform distribution by finite Gaussian mixtures. These approximation bounds are then combined with stability properties of capacity-achieving distributions to yield the final support-size lower bound.

Low-complexity detection schemes are studied for additive white Gaussian noise channels with an unknown and unbounded offset constant over each memory read. Detectors based on the Pearson distance are analyzed, and a new lower bound on the word error rate of Modified Pearson (MP) detection is derived. Three novel detectors are proposed: the Simplified Pearson (SP), the Ultra-Simplified Pearson (USP), and the Adjusted-Threshold (AT) detectors. The USP and AT detectors are designed to be robust against destructive readings. The proposed schemes are particularly suited for memory systems employing ramp-reading architectures. The analysis demonstrates that the proposed detectors achieve competitive error-rate performance with significantly reduced complexity compared to MP detection.

We study the amplitude-constrained additive white Gaussian noise channel. It is well known that the capacity-achieving input distribution for this channel is discrete and supported on finitely many points. The best known bounds show that the support size of the capacity-achieving distribution is lower-bounded by a term of orderAand upper-bounded by a term of orderA2, whereAdenotes the amplitude constraint. It was conjectured in [2] that the linear scaling is optimal. In this work, we establish a new lower bound of orderA√ logA, improving the known bound and ruling out the conjectured linear scaling. To obtain this result, we quantify the fact that the capacity-achieving output distribution is close to the uniform distribution in relative entropy. Next, we introduce a wrapping operation that maps the problem to a compact domain and develop a theory of best approximation of the uniform distribution by finite Gaussian mixtures. These approximation bounds are then combined with stability properties of capacity-achieving distributions to yield the final support-size lower bound.

In this paper, we examine the distribution and convergence properties of the estimation error $W = X - \hat X(Y)$, where $\hat X(Y)$ is the Bayesian estimator of a random variable X from a noisy observation Y = X + σZ where σ is the parameter indicating the strength of noise Z. Using the conditional expectation framework (that is, $\hat X(Y)$ is the conditional mean), we define the normalized error ${{\mathcal{E}}_\sigma } = \frac{W}{\sigma }$ and explore its properties.Specifically, in the first part of the paper, we characterize the probability density function of W and ${{\mathcal{E}}_\sigma }$. Along the way, we also find conditions for the existence of the inverse functions for the conditional expectations. In the second part, we study pointwise (i.e., almost sure) convergence of ${{\mathcal{E}}_\sigma }$ as σ → 0 under various assumptions about the noise and the underlying distributions. Our results extend some of the previous limits of ${{\mathcal{E}}_\sigma }$ as σ → 0 studied under the L2convergence, known as the MMSE dimension, to the pointwise case.

Integrated sensing and communication is regarded as a key enabler for next-generation wireless networks. To optimize the transmitted waveform for both sensing and commu-nication, various performance metrics must be considered. This work focuses on sensing, and specifically on the mean square error (MSE) of channel estimation. Given the complexity of deriving the MSE, the Bayesian Cramer-Rae Bound (BCRB) is commonly recognized as a lower bound on the minimum MSE. However, the BCRB is not applicable to channels with discrete or mixed distributions. To address this limitation, a new lower bound based on a Poincare inequality is proposed and applied to fading MIMO AWGN channels with blockage probability, and the behavior of the lower bound at high SNR is precisely characterized.

The capacity-achieving input distribution of non-coherent Rayleigh fading channels with average- and peak-power constraints is known to be discrete with a finite number of points. We sharpen this result by deriving upper and lower bounds on the number of amplitude levels. The upper bounds are based on two techniques from complex analysis: counting the number of maxima of a function that characterizes the Karush-Kuhn-Tucker conditions and an oscillation theorem. The latter provides a stronger bound but applies only if the average power constraint is inactive.

This work considers a discrete-time Poisson noise channel with an input amplitude constraint A and a dark current parameter A. It is known that the capacity-achieving distribution for this channel is discrete with finitely many points. Recently, for$A$= 0, a lower bound of order ✓A and an upper bound of order A log2 (A) have been demonstrated on the cardinality of the support of the optimal input distribution. In this work, we improve these results in several ways. First, we provide upper and lower bounds that hold for non-zero dark current. Second, we produce a sharper upper bound with a far simpler technique. In particular, for$A$= 0, we sharpen the upper bound from the order of A log2 (A) to the order of A. Finally, some other additional information about the location of the support is provided.

This work considers a binomial noise channel. The paper can be roughly divided into two parts. The first part is concerned with the properties of the capacity-achieving distribution. In particular, for the binomial channel, it is not known if the capacity-achieving distribution is unique since the output space is finite (i.e., supported on integers 0, …, n) and the input space is infinite (i.e., supported on the interval [0, 1 D, and there are multiple distributions that induce the same output distribution. This paper shows that the capacity-achieving input distribution is unique by appealing to the total positivity property of the binomial kernel. In addition, we provide upper and lower bounds on the cardinality of the support of the capacity-achieving distribution. Specifically, an upper bound of order n/2 is shown, which improves on the previous upper bound of order$n$due to Witsenhausen. Moreover, a lower bound of order yin is shown. Finally, additional results about the locations and probability values of the support points are established.

A multi-input multi-output (MIMO) Gaussian chan-nel with two transmit antennas and two receive antennas is studied that is subject to an input peak-power constraint. The ca-pacity and the capacity-achieving input distribution are unknown in general. The problem is shown to be equivalent to a channel with an identity matrix but where the input lies inside and on an ellipse with principal axis length$r_{p}$and minor axis length$r_{m}$. If$r_{p}\leq\sqrt{2}$, then the capacity-achieving input has support on the ellipse. A sufficient condition is derived under which a two-point distribution is optimal. Finally, if$r_{m} < r_{p}\leq\sqrt{2}$, then the capacity-achieving distribution is discrete.

This work investigates the error performance of detection schemes based on the minimum Pearson distance in the context of additive white Gaussian noise channels with unknown and unbounded offset, constant throughout each channel use. We derive a lower bound on the word error rate under modified Pearson (MP) detection. Additionally, we introduce a new and low-complexity detection strategy, namely the Simplified Pearson (SP) detector. We analyze and compare the error performance of the SP detector with that of the MP detector.

This work studies non-coherent Rayleigh fading channels subject to average- and peak-power constraints. Several properties of the optimal input distribution are derived based on the Karush-Kuhn- Tucker conditions. In particular, the capacity-achieving distribution is characterized in the small peak and average power regimes, upper and lower bounds on the optimal input probabilities are presented, insights about the locations of the support points are provided, and bounds on the channel capacity are established.

In this paper, we investigate the capacity of the$b- \mathbf{modulated}$nonlinear frequency division multiplexing (NFDM) systems. Recently, a tractable channel model was proposed for such optical fiber communication systems, describing the received$b-\mathbf{Modulated}$signal by an input-dependent complex Gaussian distributed noise. Considering this channel model, we prove that the capacity achieving input distribution has discrete amplitude, uniform independent phase (DAUIP). Noting that this distribution is supported on a finite number of concentric shells, we find a lower bound for the capacity by assuming a single shell support. The corresponding output distribution and mutual information expressions are derived in closed-form.

An upper bound on the capacity of multiple-input multiple-output (MIMO) Gaussian fading channels is derived under peak amplitude constraints. The upper bound is obtained borrowing concepts from convex geometry and it extends to MIMO channels notable results from the geometric analysis on the capacity of scalar Gaussian channels. Relying on a sphere packing argument and on the renowned Steiner’s formula, the proposed upper bound depends on the intrinsic volumes of the constraint region, i.e., functionals defining a measure of the geometric features of a convex body. The tightness of the bound is investigated at high signal-to-noise ratio (SNR) for any arbitrary convex amplitude constraint region, for any channel matrix realization, and any dimension of the MIMO system. In addition, two variants of the upper bound are proposed: one is useful to ensure the feasibility in the evaluation of the bound and the other to improve the bound’s performance in the low SNR regime. Finally, the upper bound is specialized for two practical transmitter configurations, either employing a single power amplifier for all transmitting antennas or a power amplifier for each antenna.

This paper considers a discrete time-Poisson noise channel which is used to model pulse-amplitude modulated optical communication with a direct-detection receiver. The goal of this paper is to obtain insights into the capacity and the structure of the capacity-achieving distribution for the channel under the amplitude constraint A and in the presence of dark current λ. Using recent theoretical progress on the structure of the capacity-achieving distribution, this paper develops a numerical algorithm, based on the gradient ascent and Blahut-Arimoto algorithms, for computing the capacity and the capacity-achieving distribution. The algorithm is used to perform extensive numerical simulations for various regimes of A and λ.

This paper studies secrecy-capacity of an n-dimensional Gaussian wiretap channel under the peak-power constraint. This work determines the largest peak-power constraint ${\overline {\text{R}} _n}$ such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the low amplitude regime. The asymptotic of ${\overline {\text{R}} _n}$ as n goes to infinity is completely characterized as a function of noise variance at both receivers. Moreover, the secrecy-capacity is also characterized in a form amenable for computation. Furthermore, several numerical examples are provided, such as the example of the secrecy-capacity achieving distribution outside of the low amplitude regime.

Upper bounds on the capacity of vector Gaussian channels affected by fading are derived under peak amplitude constraints at the input. The focus is on constraint regions that can be decomposed in a Cartesian product of sub-regions. This constraint models a transmitter configuration employing a number of power amplifiers less than or equal to the total number of transmitting antennas. In general, the power amplifiers feed distinct subsets of the transmitting antennas and partition the input in independent subspaces. Two upper bounds are derived: The first one is suitable for high signal-to-noise ratio (SNR) values and, as we prove, it is tight in this regime; The second upper bound is accurate at low SNR. Furthermore, the derived upper bounds are applied to the relevant case of amplitude constraints induced by employing a distinct power amplifier for each transmitting antenna.

The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented. Furthermore, it is provided an iterative algorithm to numerically evaluate both the information capacity and the optimal input distribution of such channel.

This work studies the secrecy-capacity of a scalar-Gaussian wiretap channel with an amplitude constraint on the input. It is known that for this channel, the secrecy-capacity-achieving distribution is discrete with finitely many points. This work improves such result by showing an upper bound of the order $\frac{A^{2}}{\sigma_{1}^{2}}$ where A is the amplitude constraint and $\sigma_{1}^{2}$ is the variance of the Gaussian noise over the legitimate channel.

This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper and lower bounds on the number of mass points. Concretely, an upper bound of order$\mathsf {A}\log ^{2}(\mathsf {A})$and a lower bound of order$\sqrt { \mathsf {A}}$are established where$\mathsf {A}$is the constraint on the input amplitude. In addition, along the way, we show several other properties of the capacity and capacity-achieving distribution. For example, it is shown that the capacity is equal to$- \log P_{Y^\star }(0)$where$P_{Y^\star }$is the optimal output distribution. Moreover, an upper bound on the values of the probability masses of the capacity-achieving distribution and a lower bound on the probability of the largest mass point are established. Furthermore, on the per-symbol basis, a nonvanishing lower bound on the probability of error for detecting the capacity-achieving distribution is established under the maximum a posteriori rule.

Absorbing sets (ASs) cause the error floor phenomenon in many low-density parity-check (LDPC) codes by entrapping iterative decoders. A recent simplified system model for practical min-sum (MS) LDPC decoding predicts that if all variable nodes in an AS have channel messages above a certain threshold, the AS cannot entrap the decoder. The threshold is an AS parameter that depends on its Tanner graph, and is the result of a nonlinear optimization. In this paper, we analyze the messages exchanged in the directed graph (digraph) of the AS during MS decoding while evaluating the AS threshold. By doing this, we unveil the meaning of the threshold value, which is the minimum channel message for which positive feedback loops in the digraph involve all the messages exchanged.

We evaluate capacity bounds for multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) fading channels subject to input amplitude constraints. We focus on two practical cases, in which the transmitter: (i) employs a single antenna amplifier, which induces a constraint on the norm of the input vector, and (ii) it employs multiple amplifiers, one per antenna, which leads to independent constraints on the amplitude of each input vector entry. For both cases, we evaluate the asymptotic capacity gap between upper and lower bounds at high signal-to-noise ratio.

An upper bound on the capacity of multiple-input multiple-output (MIMO) additive white Gaussian noise fading channels is derived under peak amplitude constraints. The tightness of the bound is investigated at high signal-to-noise ratio (SNR), for any arbitrary convex amplitude constraint region. Moreover, a numerical simulation of the bound for fading MIMO channels is analyzed, at any SNR level, for a practical transmitter configuration employing a single power amplifier for all transmitting antennas.

In this paper, we consider spatially coupled LDPC codes derived from protographs. In particular, we analyze the performance of the window decoder (WD), which allows reducing the complexity, the memory requirements, and the latency of the flood belief-propagation decoder. We show that the performance degradation of WD is due to the fact that it exploits a single decoding wave instead of two. This has effect both in the ideal case of infinite code length, where it may imply a threshold loss, and in the case of finite length, where it affects the slope of the BER curve in the waterfall region. We show how a forward-backward decoder can reduce such problems at the price of a limited increase of average complexity.

The discrete-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver, referred to as the Oversampled Wiener Phase Noise (OWPN) channel is studied. The capacity of this channel is characterized by three parameters: transmit power P, oversampling factor L, and the variance of the Wiener phase noise σ2. The capacity of this model is connected to the capacity of two related models: the Oversampled Non-Coherent (ONC) channel and the Additive White Gaussian Noise (AWGN) channel. More precisely, it is shown that (i) the capacity of the OWPN is close to the ONC channel when σ2> L while (ii) the capacity of the OWPN is close to that of the AWGN channel when σ2-1.

Multicore fibers (MCFs) are one of the main technological enablers for space-division multiplexing. In principle, MCFs could scale the fiber capacity by a factor equal to the number of cores, but in practice such increase is hindered by transmission impairments due to the inter-core crosstalk between adjacent lit cores. The entity of such crosstalk depends on the number of cores and on their disposition within the fiber cladding, and also on the baud rate and modulation format used for transmission. As first MCF applications are expected over point-to-point systems, in this paper we concentrate on the resource allocation over a single link. Specifically, we study the Baud rate, Modulation format, Core and Spectrum Assignment problem in a multicore flexi-grid link, considering distance-adaptive reaches for different baud rates, modulation formats, and crosstalk impairments. We show that the problem is NP-hard and provide two integer linear programs, as well as heuristic approaches to solve it over large/practical traffic instances. Our problem formulations incorporate modeling of the exact inter-core crosstalk contributions depending on the number of lit neighbor cores. Numerical results are provided in a high-spatial-efficiency 19-core fiber considering different transmission impairment conditions.

Emerging memory technologies (like PCM, MRAM and 3D XPoint) can make data storage as fast as the rest of the system. But to cope with the reliability targets of storage applications, error correcting codes (ECCs) able to correct many errors might be needed anyway. Hierarchical codes, ECCs enabling two levels of correction, can be good candidates to satisfy these reliability targets, without impacting (on average) the low-latency characteristics of these technologies. In particular, an Ultra-Fast (UF) ECC can be used as first trial as long as it is able to flag its failures with high probability and low latency. In this paper we design an UF-ECC able to produce a check for incorrect decoding with probability lower than the typical target uncorrectable bit-error rate (UBER) of storage applications (e.g. 1e-15) and with a latency comparable with the UF-ECC correction process.

The capacity of a Multiple-Input Multiple-Output (MIMO) channel in which the antenna outputs are processed by an analog linear combining network and quantized by a set of threshold quantizers is studied. The linear combining weights and quantization thresholds are selected from a set of possible configurations as a function of the channel matrix. The possible configurations of the combining network model specific analog receiver architectures, such as single antenna selection, sign quantization of the antenna outputs or linear processing of the outputs. An interesting connection between the capacity of this channel and a constrained sphere packing problem in which unit spheres are packed in a hyperplane arrangement is shown. From a high-level perspective, this follows from the fact that each threshold quantizer can be viewed as a hyperplane partitioning the transmitter signal space. Accordingly, the output of the set of quantizers corresponds to the possible regions induced by the hyperplane arrangement corresponding to the channel realization and receiver configuration. This connection provides a number of important insights into the design of quantization architectures for MIMO receivers; for instance, it shows that for a given number of quantizers, choosing configurations which induce a larger number of partitions can lead to higher rates1.

The degrees of freedom of a class of discrete-time non-coherent channels with oversampling, termed the Oversampled Non-Coherent (ONC) channel, are shown. The ONC channel is obtained from the classic continuous-time AWGN channel by considering the scenario in which the channel output is also corrupted by phase noise (PN) and processed by a multi-sample receiver. The continuous-time PN process has high variability which results in receiver output samples affected by a discrete-time PN process iid uniformly distributed over the unit circle. The ONC channel models the non-coherent detection scenario in which oversampling is employed for phase recovery but the PN process has such a high variance that its samples appear independent and uniformly distributed despite the oversampling. As such, the assumption of independent and uniformly distributed discrete PN is a limiting assumption that, generally speaking, well approximates the scenario in which the PN coherence time is much smaller than the oversampling time. In this paper, we obtain the generalized degrees of freedom for the case in which the oversampling factor L grows with the transmit power P as Pα. Perhaps surprisingly, we show that no degree of freedom for reliable information transfer is available for L > P2. We conjecture that the same capacity asymptotic holds for other PN channels with oversampling, such as the oversampled Wiener PN channel, when the noise variance grows to infinity faster than the sampling rate.

The behavior of exponential backoff (EB) has challenged researchers ever since its introduction, but only approximate and partial results have been produced up to this date. This paper presents accurate results about the effect of protocol parameters on throughput and delay, assuming queues in saturation. Among the manifold results, we first introduce a simple model that provides close-form results for the approximated model known as “decoupling assumption.” Since the latter fails to provide well approximated results in many cases, we also introduce a Markovian model able to trade the precision of the results with complexity even with an infinite number of users, enabling us to get definite throughput results, such as 0.3706 with binary EB, and 0.4303 with an optimized base. Analytical considerations allow to derive the tail of the access-delay distribution, found to be slowly decreasing and with no variance as the number of users goes to infinity. Taking into account the overall performance, preliminary results seem to indicate that the exponential base b=1.35 is more appealing than the standard value b=2.

The capacity of the discrete-time channel affected by both additive Gaussian noise and Wiener phase noise is studied. Novel inner and outer bounds are presented, which differ of at most 7.36 bit-per-channel-use for all channel parameters. The capacity of this model can be subdivided in three regimes: (i) for large values of the frequency noise variance, the channel behaves similarly to a channel with circularly uniform iid phase noise; (ii) when the frequency noise variance is small, the effect of the additive noise dominates over that of the phase noise, while (iii) for intermediate values of the frequency noise variance, the transmission rate over the phase modulation channel has to be reduced due to the presence of phase noise.

The Slotted-Aloha protocol has been widely studied in the past forty-five years. Nonetheless, when the Exponential Backoff (EB) is used to stabilize its behavior, the characterization of stability conditions have eluded all efforts. Here we prove that the EB with geometric law i ↦ b−i−i0, with queues in saturation, is ergodic if and only if b > 1 and the initial offset is i0> 1, for any number of users. If i0= 0 the system is transient, and null recurrent for 00≤ 1, where some intermediate behavior is possible, since not all backoff indexes are unstable.

The discrete-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. A novel outer bound on the capacity with an average input power constraint is derived as a function of the oversampling factor. This outer bound yields the degrees of freedom for the scenario in which the oversampling factor grows with the transmit power P as Pα. The result shows, perhaps surprisingly, that the largest pre-log that can be attained with phase modulation at high signal-to-noise ratio is at most 1/4.

The capacity of a discrete-time, multi-input multi-output (MIMO) channel with output quantization is investigated for different receiver architectures. A general framework for low-resolution quantization is proposed in which the antenna outputs are processed by analog combiners and sign quantizers are used for analog-to-digital conversion. The configuration of the analog combiners is chosen as a function of the channel realization so that the transmission rate can be maximized over the set of available configurations. To exemplify the proposed approach, four analog receiver architectures are considered: (a) sign quantization of the antenna outputs, (b) single antenna selection, (c) multiple antenna selection, and (d) linear processing of the antenna outputs. In each scenario, capacity is investigated as a function of the transmit power, the number of transmit/receive antennas and sign quantizers. In particular, it is shown that architecture (a) is sufficient to approach the optimal high signal-to-noise ratio (SNR) performance for a MIMO receiver in which the number of receive antennas is larger than the number of sign quantizers. Numerical evaluations of the average performance are presented for the case in which the channel gains are i.i.d. Gaussian distributed.

The stability and throughput of the Slotted Aloha protocol have been studied at length, yielding results that depend on the environment and channel assumptions, in many cases indicating e-1 as the S-Aloha capacity. When users can detect only their own collisions, and the number of users N goes to infinity, no definite capacity result exists. Approximated models have been introduced to study the exponential back-off mechanism, which seem to indicate an asymptotic capacity of ln(2)/2 when binary back-off is used, and again e-1 when the exponential base is optimized. Here we introduce a more accurate and flexible model that shows that past results miss their mark. In fact, we prove that with binary back-off the capacity is practically 0.370, slightly greater than e-1; furthermore, and more important, we prove that using 1.35 as exponential back-off base, the capacity reaches 0.4303 with an infinite number of users, and up to 0.496 with N = 2 users.

The equivalence of peeling decoding (PD) and Belief Propagation (BP) for low-density parity-check (LDPC) codes over the binary erasure channel is analyzed. Modifying the scheduling for PD, it is shown that exactly the same variable nodes (VNs) are resolved in every iteration than with BP. The decrease of erased VNs during the decoding process is analyzed instead of resolvable equations: This quantity can also be derived with density evolution, resulting in a drastic decrease in complexity. Finally, a scaling law using this quantity is established for spatially coupled LDPC codes.

A continuous-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. A lower bound to the capacity with an average input power constraint is derived, and a high signal-to-noise ratio (SNR) analysis is performed. The proposed lower bound suggests that the capacity pre-log depends on the oversampling factor, and amplitude and phase modulation do not equally contribute to capacity at high SNR.

A discrete-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver is studied. An upper bound to the capacity with an average input power constraint is derived, and a high signal-to-noise ratio (SNR) analysis is performed. If the oversampling factor grows as SNRαfor 0 ≤ α ≤ 1, then the capacity pre-log is at most (1 + α)/2 at high SNR.

A continuous-time model for the additive white Gaussian noise (AWGN) channel in the presence of white (memoryless) phase noise is proposed and discussed. It is shown that for linear modulation the output of the baud-sampled filter matched to the shaping waveform represents a sufficient statistic. The analysis shows that the phase noise channel has the same information rate as an AWGN channel but with a penalty on the average signal-to-noise ratio, the amount of penalty depending on the phase noise statistic.

In dynamic-frame Aloha, subsequent frame lengths must be optimally chosen to maximize throughput. When the initial population size N is known, numerical evaluations show that the maximum efficiency is achieved by setting the frame length equal to the backlog size at each subsequent frame; however, to the best of our knowledge, a formal proof of this result is still missing, and is provided here. As byproduct, we also prove that the asymptotic efficiency in the optimal case is e-1, provide tight upper and lower bounds for the length of the entire transmission period, and show that its asymptotic behavior is ~ne-ζ ln(n) with ζ =-0.5/\ln (1-e-1).

Starting from the definition of mutual information, one promptly realizes that the probabilities inferred by Bayesian tracking can be used to compute the Shannon information between the state and the measurement of a dynamic system. In the Gaussian and linear case, the information rate can be evaluated from the probabilities computed by the Kalman filter. When the probability distributions inferred by Bayesian tracking are nontractable, one is forced to resort to approximated inference, which gives only an approximation to the wanted probabilities. We propose upper and lower bounds to the information rate between the hidden state and the measurement based on approximated inference. Application of these bounds to multiplicative communication channels is discussed, and experimental results for the discrete-time phase noise channel and for the Gauss-Markov fading channel are presented.

Numerical upper and lower bounds to the information rate transferred through the additive white Gaussian noise channel affected by discrete-time multiplicative autoregressive moving-average (ARMA) phase noise are proposed in the paper. The state space of the ARMA model being multidimensional, the problem cannot be approached by the conventional trellis-based methods that assume a first-order model for phase noise and quantization of the phase space, because the number of state of the trellis would be enormous. The proposed lower and upper bounds are based on particle filtering and Kalman filtering. Simulation results show that the upper and lower bounds are so close to each other that we can claim of having numerically computed the actual information rate of the multiplicative ARMA phase noise channel, at least in the cases studied in the paper. Moreover, the lower bound, which is virtually capacity-achieving, is obtained by demodulation of the incoming signal based on a Kalman filter aided by past data. Thus we can claim of having found the virtually optimal demodulator for the multiplicative phase noise channel, at least for the cases considered in the paper.

In this paper we focus on a single carrier pilot-assisted transmission scheme where one pilot symbol is periodically inserted in the transmitted sequence on a time-division multiplexing basis. A new equalization scheme, where the knowledge of pilot symbols is exploited by the equalizer to generate an estimate of the noise affecting the symbol to be detected, is introduced and analyzed. The criterion used to compute the equalizer coefficients is the minimization of the mean-square error (MSE). The main new result of our analysis is that the optimal pilot aided equalizer (PAE) can be decomposed as the cascade of an unconstrained minimum MSE (MMSE) linear equalizer (LE) and a data- aided noise estimation filter. This result completes and extends the noise-predictive view of decision feedback equalization to general data-aided equalization. The PAE is compared here to the MMSE- LE and to the MSE decision feedback equalizer on two frequency selective wireless channels.

The hybrid decision feedback equalizer (DFE) is a combined time-frequency domain implementation of the conventional time-domain DFE that is able to provide a good trade-off between performance and computational complexity in single carrier transmission over severely frequency-selective channels. In the hybrid DFE the implementation of the feedforward filter is done in the frequency domain, while the feedback filter (FBF) is implemented in the time-domain. The computation of the coefficients for the two filters is usually done in the same domain where they are implemented. A method for frequency-domain computation of the FBF is proposed in the paper. As is known, the key operation in the computation of the FBF is the spectral factorization. In the paper it is proposed to adopt the (cepstral) method for spectral factorization due to Kolmogoroff, which can be efficiently implemented by using the fast Fourier transform (FFT). The application of the method is considered for highly dispersive channels. By using simulations we show that for this type of channels the performance of the proposed method is virtually the same as that obtained by using time-domain approaches. The advantage of the proposed approach is that the efficient FFT gives a substantial reduction of complexity compared to time-domain methods.

The paper deals with carrier recovery based on pilot symbols in single-carrier systems. The system model considered in the paper includes the channel additive white noise and the phase noise that affects the local oscillators used for up/down-conversion. Wiener's method is used to determine the optimal filter in estimation of phase noise assuming that a sequence of equally spaced pilot symbols is available. Our analysis allows to capture the cyclostationary performance of the estimate, a phenomenon that is not considered in the previous literature. In the paper, closed-form formulas for the transfer function of the optimal filter and for the mean-square phase error are derived for the case where the phase noise is modelled as random phase walk. For this case, a suboptimal filter is proposed. Numerical results are presented to substantiate the analysis.