We investigate information-theoretic limits and design of communication under receiver quantization. Unlike most existing studies that focus on low-resolution quantization, this work is more focused on the impact of weak nonlinear distortion due to resolution reduction from high to low. We consider a standard transceiver architecture, which includes an independent and identically distributed (i.i.d.) complex Gaussian codebook at the transmitter, and a symmetric quantizer cascaded with a nearest neighbor decoder at the receiver. Employing the generalized mutual information (GMI), an achievable rate under general quantization rules is obtained in an analytical form, which shows that the rate loss due to quantization is log (1 + γSNR), where SNR is the signal-to-noise ratio at the receiver front-end, and γ is determined by thresholds and levels of the quantizer. Based on this result, the performance under uniform receiver quantization is analyzed comprehensively. We show that the front-end gain control, which determines the loading factor (normalized one-sided quantization range) of quantization, has an increasing impact on performance as the resolution decreases. In particular, we prove that the unique loading factor that minimizes the mean square error (MSE) of the uniform quantizer also maximizes the GMI, and the corresponding irreducible rate loss is given by log (1 + mmse · SNR), where mmse is the minimum MSE normalized by the variance of quantizer input, and it is equal to the minimum of γ. A geometrical interpretation for the optimal uniform quantization at the receiver is further established. Moreover, by asymptotic analysis, we characterize the impact of biased gain control, showing how small rate losses decay to zero and providing approximations for the achievable rate under large bias. From asymptotic expressions of the optimal loading factor and mmse, approximations and several “per-bit rules” for performance are also provided. Finally we discuss more types of receiver quantization and show that the consistency between achievable rate maximization and MSE minimization does not hold in general.

We investigate performance limits and design of communication in the presence of uniform output quantization with moderate to high resolution. Under independent and identically distributed (i.i.d.) complex Gaussian codebook and nearest neighbor decoding rule, an achievable rate is derived in an analytical form by the generalized mutual information (GMI). The gain control before quantization is shown to be increasingly important as the resolution decreases, due to the fact that the loading factor (normalized one-sided quantization range) has increasing impact on performance. The impact of imperfect gain control in the high-resolution regime is characterized by two asymptotic results: 1) the rate loss due to overload distortion decays exponentially as the loading factor increases, and 2) the rate loss due to granular distortion decays quadratically as the step size vanishes. For a$2 K$-level uniform quantizer, we prove that the optimal loading factor that maximizes the achievable rate scales like$2 \sqrt{\ln (2 K)}$as the resolution increases. An asymptotically tight estimate of the optimal loading factor is further given, which is also highly accurate for finite resolutions.

Due to the high data rates, license-free operations and inherent security, visible light communication (VLC) is highly valued in Industrial Internet of Things (IIoT) applications. Short packet communication, which offers ultralow latency and efficient resource utilization, is suitable for the low-latency and massive connectivity demand of the IIoT system. It adopts finite blocklength codewords for data transmissions. In this article, we present a general framework of designing geometrically shaped constellations in short-packet VLC with peak and average intensity constraints for IIoT applications. By leveraging tools from large deviation theory, we first characterize the second-order asymptotics of the optimal constellation shaping region under aforementioned intensity constraints, which serves as a good performance metric for the best geometric shaping in finite blocklength. To further incorporate a sufficiently large coding gain and a nearly maximum shaping gain, we construct multidimensional constellations by the nested structure of Construction B lattices, where the constellation shaping is implemented by controlling the boundary of the embedded sublattice, i.e., a strategy called coarsely shaping and finely coding. Fast algorithms for constellation mapping and demodulation are presented as well. As an illustrative example, we present an energy-efficient 24-D constellation design based on the Leech lattice, whose superiority over existing constellation designs is verified by numerical results.

The performance of multiple-input multiple-output (MIMO) integrated sensing and communication systems (ISAC) can be evaluated from the perspectives of information theory and estimation theory to provide more fundamental insights. In this paper, we study the relationship between mutual information (MI) and minimum mean square error (MMSE) by characterizing the Pareto boundary for a general ISAC scenario, a dual-functional BS simultaneously estimates the target response matrix while communicating with a user. First, optimization problems are formulated to achieve MI Pareto boundary and MMSE Pareto boundary, respectively. Then, we show that under the same maximum transmit power constraint and set of transmit filters, MI Pareto bounary can be transformed to MMSE Pareto boundary with optimized MSE-weights in ISAC with colored Gaussian noise. Subsequently, based on unified MI and MMSE performance, we propose Data-dependent alternate algorithm (DDA) to obtain the MI Pareto boundary with colored Gaussian noise. In order to reduce complexity, we propose Data-independent alternate algorithm (DIA) when noise degenerates into white Gaussian noise. Finally, simulation results show DDA almost achieves the MI Pareto boundary with colored Gaussian noise and DIA achieves almost the same performance as DDA with white Gaussian noise at a lower cost to implement.

In this paper, for a single-input multiple-output (SIMO) system aided by a passive reconfigurable intelligent surface (RIS), the joint transmission accomplished by the single transmit antenna and the RIS with multiple controllable reflective elements is considered. Relying on a general capacity upper bound derived by using a maximum-trace argument, we respectively characterize the capacity slope of low-signal-to-noise-ratio channels and the exact capacity of rank-one channels, in which the optimal configuration of the RIS is proved to be beamforming-only with carefully-chosen phase shifts. To exploit the potential of modulating extra information on the RIS, by leveraging a strategy named partially beamforming and partially information-carrying based on QR decomposition and successive interference cancellation, we propose a novel transceiver architecture with only a single RF front end at the transmitter, by which the considered channel can be regarded as a concatenation of a vector Gaussian channel and several phase-modulated channels. Especially, we investigate a class of vector Gaussian channels with a hypersphere input support constraint, and not only generalize the existing result to arbitrary-dimensional real spaces but also present its high-order capacity asymptotics, by which both capacities of hypersphere-constrained channels and achievable rates of the proposed transceiver with two different signaling schemes can be well-approximated. Information-theoretic analyses show that the transceiver architecture designed for the SIMO channel has a boosted multiplexing gain, rather than one for the conventionally-used optimized beamforming scheme. Numerical results verify our derived asymptotic results and show notable superiority of the proposed transceiver as compared with the beamforming and the receive spatial modulation schemes.

This paper investigates the sum-capacity of two-user optical intensity multiple access channels with a per-user peak- or average-intensity constraint. By leveraging tools on decomposition of random variables, we derive lower bounds on the sum-capacity. In the high signal-to-noise ratio (SNR) regime, they asymptotically match the sum-capacity. In particular, for the peak-intensity constrained channel, our result closes the high-SNR asymptotic sum-capacity gap in the existing works.

This paper investigates the sum-capacity of two-user optical intensity multiple access channels with per-user peak- or/and average-intensity constraints. By leveraging tools from the decomposition of certain distributions, we derive several lower bounds on the sum-capacity. In the high signal-to-noise ratio (SNR) regime, some bounds asymptotically match or approach the sum-capacity, thus closing or reducing the existing gaps to the high-SNR asymptotic sum-capacity. At moderate SNR, some bounds are also fairly close to the sum-capacity.

We consider performance enhancement of asymmetrically-clipped optical orthogonal frequency division multiplexing (ACO-OFDM) and related optical OFDM schemes, which are variations of OFDM in intensity-modulated optical wireless communications. Unlike most existing studies on specific designs of improved receivers, this paper investigates information theoretic limits of all possible receivers. For independent and identically distributed (IID) complex Gaussian inputs, we obtain an exact characterization of information rate of ACO-OFDM with improved receivers for all SNRs. It is proved that the high-SNR gain of improved receivers asymptotically achieve 1/4 bits per channel use, which is equivalent to 3 dB in electrical SNR or 1.5 dB in optical SNR; as the SNR decreases, the maximum achievable SNR gain of improved receivers decreases monotonically to a non-zero low-SNR limit, corresponding to an information rate gain of 36.3%. For practically used constellations, we derive an upper bound on the gain of improved receivers. Numerical results demonstrate that the upper bound can be approached to within 1 dB in optical SNR by combining existing improved receivers and coded modulation. We also show that our information theoretic analyses can be extended to Flip-OFDM and PAM-DMT. Our results imply that, for the considered schemes, improved receivers may reduce the gap to channel capacity significantly at low-to-moderate SNR.

This paper investigates the capacity of general multiple-input single-output (MISO) optical intensity channels (OICs) under per-antenna peak- and average-intensity constraints. We first consider the MISO equal-cost constrained OIC (EC-OIC), where, apart from the peak-intensity constraint, average intensities of inputs areequal toarbitrarily preassigned constants. The second model of our interest is the MISO bounded-cost constrained OIC (BC-OIC), where, as compared with the EC-OIC, average intensities of inputs areno larger thanarbitrarily preassigned constants. By leveraging tools from quantile functions, stop-loss transform and convex ordering of nonnegative random variables, we prove two decomposition theorems for bounded and nonnegative random variables, based on which we equivalently transform both the EC-OIC and the BC-OIC into respective single-input single-output channels under a peak-intensity and several stop-loss mean constraints. Capacity lower and upper bounds for both channels are established, based on which the asymptotic capacity at high and low signal-to-noise-ratio are determined.

We investigate and elaborate upon a folklore in wireless communication systems that, when the nonlinearity at a transmitter is sufficiently weak so that the resulting spectral leakage is at a sufficiently low level, the capacity of the channel (including the transmitter) should be sufficiently close to the ideal channel capacity without transmitter nonlinearity. The context for this study is that effective predistortion techniques have been widely applied to linearize the transmitter nonlinearity in modern wireless communication systems, so as to render the electromagnetic radiation pattern to satisfy stringent spectral regrowth requirements. Based on the quasi-memoryless/memory polynomial model for the transmitter nonlinearity, via an information-theoretic approach, our study affirmatively validates the folklore, and more importantly, characterizes a quantitative relationship between the spectral leakage level and the capacity loss. Specifically, we prove that as the adjacent channel power ratio (ACPR) asymptotically vanishes, the capacity loss is upper bounded by a term that is proportional to the ACPR. We also establish a converse result, and further extend our results to spatial beamforming.

We consider performance enhancement of asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM), which is a variation of OFDM in intensity modulated optical wireless communications. To improve the conventional ACO-OFDM receiver that utilizes only odd-indexed subcarriers, several specific designs have been proposed in the literature. Unlike these studies, this paper investigates information theoretic limits of all possible improved receivers. More specifically, we prove that the maximum achievable information rate of ACO-OFDM is the sum of (i) the information rate of the conventional receiver, and (ii) a single-letter conditional mutual information expression corresponding to the maximum achievable gain of improved receivers. Asymptotic analysis shows that the high-signal-to-noise-ratio (high-SNR) limit of the maximum achievable gain of arbitrary improved receivers is 3 dB in (electrical) SNR, corresponding to an information rate gain of exactly 1/4 bits per channel use. We also show that the low-SNR limit of the maximum achievable gain of improved receivers is approximately 1.35 dB in SNR. Numerical evaluation of finite-SNR gains demonstrate that improved ACO-OFDM receivers may reduce the gap to capacity significantly, especially at low-to-moderate SNR.

We investigate design and performance of communications over the bandlimited Gaussian channel with one-bit output quantization. A transceiver structure is proposed, which generates the channel input using a finite set of time-limited and approximately bandlimited waveforms, and performs oversampling on the channel output by an integrate-and-dump filter preceding the one-bit quantizer. The waveform set is constructed based on a specific bandlimited random process with certain zero-crossing properties which can be utilized to convey information. In the presence of the additive white Gaussian noise, a discrete memoryless channel model of our transceiver is derived. Consequently, we determine a closed-form expression for the high signal-to-noise-ratio (SNR) asymptotic information rate of the transceiver, which can be achieved by independent and identically distributed input symbols. By evaluating the fractional power containment bandwidth, we further show that at high SNR, the achievable spectral efficiency grows roughly logarithmically with the oversampling factor, coinciding with a notable result in the absence of noise (Shamai, 1994). Moreover, the error performance of our transceiver is evaluated by low density parity check coded modulation. Numerical results demonstrate that reliable communication at rates exceeding one bit per Nyquist interval can be achieved at moderate SNR.

This paper provides new inner and outer bounds on the capacity region of the optical intensity multiple access channel (OIMAC) with a per-user average- or peak-power constraint. For the average-power constrained OIMAC, our bounds at high power are asymptotically tight, thereby characterizing the asymptotic capacity region. The bounds are extended to the$K$-user OIMAC with an average-power constraint without loss of asymptotic optimality. For the peak-power constrained OIMAC, at high power, we bound the asymptotic capacity region to within 0.09 bits, and determine the asymptotic capacity region in the symmetric case. At moderate power, for both types of constraints, the capacity regions are bounded to within fairly small gaps.

We revisit Shannon'S problem of bounding the capacity of bandlimited Gaussian channel (BLGC) with peak power constraint, and extend the problem to the peak-to-average-power-ratio (PAPR) constrained case. By lower bounding the achievable information rate of pulse amplitude modulation with independent and identically distributed input under a PAPR constraint, we obtain a general capacity lower bound with respect to the shaping pulse. We then evaluate and optimize the lower bound by employing some parametric pulses, thereby improving the best existing result. Following Shannon'S approach, capacity upper bound for PAPR constrained BLGC is also obtained. By combining our upper and lower bounds, the capacity of PAPR constrained BLGC is bounded to within a finite gap which tends to zero as the PAPR constraint tends to infinity. Using the same approach, we also improve existing capacity lower bounds for bandlimited optical intensity channel at high SNR.

In this paper, we consider the detection of faster-than-Nyquist (FTN) signaling. By noticing that the whitening filter for FTN signaling cannot be directly derived when the symbol rate exceeds the signal bandwidth, we propose a new reduced-complexity M-algorithm BCJR (M-BCJR) algorithm based on the Ungerboeck observation model. By taking some “future” symbols into account, the proposed algorithm is able to select the M best states in the maximum a posteriori sense. We further simplify the above algorithm by choosing the key path from each possible state, which successfully reduces the complexity while maintaining a good bit error rate performance. Simulation results show that, with the use of the proposed methods, great gains can be obtained in terms of spectral efficiency (up to 186%) or signal-to-noise ratio (up to 4.5 dB) compared with the Nyquist signaling.

We study the information rates of unipolar orthogonal frequency division multiplexing (OFDM) in discrete-time optical intensity channels (OIC) with Gaussian noise under average optical power constraint. Several single-, double-, and multi-component unipolar OFDM schemes are considered under the assumption that independent and identically distributed. Gaussian or complex Gaussian codebook ensemble and nearest neighbor decoding (minimum Euclidean distance decoding) are used. We obtain an array of information rate result. These results validate existing signal-to-noise-and-distortion-ratio-based rate analysis, establish the equivalence of information rates of certain schemes, and demonstrate the evident benefits of using component-multiplexing at high signal-to-noise-ratio (SNR). For double- and multi-component schemes, the component power allocation strategies that maximize the information rates are investigated. In particular, by utilizing a power allocation strategy, we prove that several multi-component schemes approach the high SNR capacity of the discrete-time Gaussian OIC under average power constraint to within 0.07 bits.

A structure of faster‐than‐Nyquist (FTN) signaling combined with superposition coded modulation (SCM) is considered. The so‐called FTN‐SCM structure is able to achieve the constrained capacity of FTN signaling and only requires a low detection complexity. By deriving a new observation model suitable for FTN‐SCM, we offer the power allocation based on a proper detection method. Simulation results show that, at any given spectral efficiency, the bit error rate (BER) curve of FTN‐SCM lies clearly outside the minimum signal‐to‐noise ratio (SNR) boundary of orthogonal signaling with a larger alphabet. The achieved data rates are also close to the maximum data rates of the certain shaping pulse.

We determine the lower and upper bounds on the capacity of bandlimited optical intensity channels (BLOIC) with white Gaussian noise. Three types of input power constraints are considered: 1) only an average power constraint; 2) only a peak power constraint; and 3) an average and a peak power constraint. Capacity lower bounds are derived by a two-step process including: 1) for each type of constraint, designing admissible pulse amplitude modulated input waveform ensembles and 2) lower bounding the maximum achievable information rates of the designed input ensembles. Capacity upper bounds are derived by exercising constraint relaxations and utilizing known results on discrete-time optical intensity channels. We obtain degrees-of-freedom-optimal (DOF-optimal) lower bounds which have the same pre-log factor as the upper bounds, thereby characterizing the high SNR capacity of BLOIC to within a finite gap. We further derive intersymbol-interference-free (ISI-free) signaling-based lower bounds, which perform well for all practical SNR values. In particular, the ISI-free signaling-based lower bounds outperform the DOF-optimal lower bound when the SNR is below 10 dB.

A novel time domain approach is introduced for the downlink pilot design of multiantenna OFDM systems. Zero correlation zone sequence sets are used to construct the pilot sequences so that the intra-and inter-cell interferences between pilots are cancelled. The pilot sequences are superimposed on the time domain data signals directly and keep interference-free because of the special frequency domain property of sequences. The overhead of pilots can adapt the number of the transmit antennas. Analysis, typical design example and numerical results demonstrate that a good performance-to-complexity tradeoff and lower pilot overhead compared to traditional frequency domain approaches can be obtained by the proposed approach.

We extend the concept of faster-than-Nyquist (FTN) signaling to linear digital modulation using arbitrary modulation pulses, called generalized faster-than-Nyquist signaling (GFTN). A universal definition of nominal bandwidth is given so that “how fast” can be measured for GFTN like FTN using T-orthogonal pulses. The capacities and their asymptotic behaviors are compared between GFTN and Nyquist signaling. We show that the gain of GFTN increases unboundedly with SNR. In high SNR regime the power gain is considerable. Our extension from FTN to GFTN gives more freedom on the design of pulses to achieve good performance and acceptable detection complexity.

This paper analyzes the performance of a novel time domain pilot scheme using least square channel estimation in convolutional multiplexed multicarrier (CMM) systems. To reduce decoding complexity and achieve higher spectral efficiency, data symbols are encoded through serial concatenated structure of convolutional multiplexing technique, while simultaneously pilot sequences are generated and multiplexed with orthogonal frequency division multiplexing (OFDM) symbols in time domain. The least square channel estimation is implemented in time domain and data symbols are detected with iterative decoding. The pilot sequences are generated based on complementary codes, whose periodic auto-correlation function (ACF) and cross-correlation function (CCF) are perfect, and there are no multiple access interference (MAI) and inter-symbol interference (ISI) when the maximum time delay is less than length of zero correlation zone (ZCZ) of the pilot sequences. The time domain pilot scheme is turned out to have high estimation accuracy with low calculation complexity. Mean square estimation (MSE) results are verified to be independent of unknown data symbols and insensitive to the power fraction for pilots. Combined with iterative detecting, bit error rate (BER) and frame error rate (FER) performance of proposed scheme can match with ideal channel estimation scenario whose channel impulse response (CIR) is known by the receiver. Besides, data transmission scheme with interference cancellation (IC) can retrieve half of the spectral efficiency loss than scheme without IC and only sacrifices tolerable estimation accuracy.