In this paper, we study the capacity and degree-of-freedom (DoF) scaling for the continuous-time amplitude limited AWGN channels in radio frequency (RF) and intensity modulated optical communication (OC) channels. More precisely, we study how the capacity varies in terms of the OFDM block transmission time $T$, bandwidth $W$, amplitude $A$, and the noise spectral density $N_0$. We first find suitable discrete encoding spaces for both cases, and prove that they are convex sets that have a semi-definite programming (SDP) representation. Using tools from convex geometry, we find lower and upper bounds on the volume of these encoding sets, which we exploit to drive pretty sharp lower and upper bounds on the capacity. We also study a practical Tone-Reservation (TR) encoding algorithm and prove that its performance can be characterized by the statistical width of an appropriate convex set. Recently, it has been observed that in high-dimensional estimation problems under constraints such as those arisen in Compressed Sensing (CS) statistical width plays a crucial role. We discuss some of the implications of the resulting statistical width on the performance of the TR. We also provide numerical simulations to validate these observations.
Multi-user Orthogonal Frequency Division Multiplexing (OFDM) and Multiple Output Multiple Output (MIMO) have been widely adopted to enhance the system throughput and combat the detrimental effects of wireless channels. Recently, interference alignment was proposed to exploit interference to enable concurrent transmissions of multiple signals. In this paper, we investigate how to combine these techniques to further enhance the system throughput. We first reveal the unique characteristics and challenges brought about by using interference alignment in diagonal channels. We then derive a performa…
Integrated sensing and communication (ISAC) has emerged as a key technology for future communication systems. In this paper, we provide a general framework to reveal the fundamental tradeoff between sensing and communication in OFDM systems, where a unified ISAC waveform is exploited to perform both tasks. In particular, we define the Capacity-Bayesian Cramer Rao Bound (BCRB) region in the asymptotically case when the number of subcarriers is large. Specifically, we show that the asymptotically optimal input distribution that achieves the Pareto boundary point of the Capacity-BCRB region is Ga…
In this work, the delay limited capacity (DLC) of orthogonal frequency division multiplexing (OFDM) systems is investigated. The analysis is organized into two parts. In the first part, the impact of system parameters on the OFDM DLC is analyzed in a general setting. The main results are that under weak assumptions the maximum achievable single user DLC is almost independent of the distribution of the path attenuations in the low signal-to-noise (SNR) region but depends strongly on the delay spread. In the high SNR region the roles are exchanged. Here, the impact of delay spread is negligible …
The analysis of the channel capacity in the absence of prior channel knowledge (noncoherent channel) has gained increasing interest in recent years, but it is still unknown for the general case. In this paper we derive bounds on the capacity of the noncoherent, underspread complex Gaussian, orthogonal frequency division multiplexing (OFDM), wide sense stationary channel with uncorrelated scattering (WSSUS), under a peak power constraint or a constraint on the second and fourth moments of the transmitted signal. These bounds are characterized only by the system signal-to-noise ratio (SNR) and b…
We present a comparative study of the influence of dispersion induced phase noise for CO-OFDM systems using Tx channel multiplexing and Rx matched filter (analogue hardware based); and FFT multiplexing/IFFT demultiplexing techniques (software based). An RF carrier pilot tone is used to mitigate the phase noise influence. From the analysis, it appears that the phase noise influence for the two OFDM implementations is very similar. The software based system provides a method for a rigorous evaluation of the phase noise variance caused by Common Phase Error (CPE) and Inter-Carrier Interference (I…
This contribution investigates the Degrees-of-Freedom region of a two-user frequency correlated Multiple-Input-Single-Output (MISO) Broadcast Channel (BC) with imperfect Channel State Information at the transmitter (CSIT). We assume that the system consists of an arbitrary number of subbands, denoted as $L$. Besides, the CSIT state varies across users and subbands. A tight outer-bound is found as a function of the minimum average CSIT quality between the two users. Based on the CSIT states across the subbands, the DoF region is interpreted as a weighted sum of the optimal DoF regions in the sc…
In this paper, we consider two-way orthogonal frequency division multiplexing (OFDM) relay channels, where the direct link between the two terminal nodes is too weak to be used for data transmission. The widely known per-subcarrier decode-and-forward (DF) relay strategy, treats each subcarrier as a separate channel, and performs independent channel coding over each subcarrier. We show that this per-subcarrier DF relay strategy is only a suboptimal DF relay strategy, and present a multi-subcarrier DF relay strategy which utilizes cross-subcarrier channel coding to achieve a larger rate region. …
This paper investigates the impacts of Inter-Channel Interference (ICI) effects on a shallow underwater acoustic (UWA) orthogonal frequency-division multiplexing (OFDM) communication system. Considering both the turbulence of the water surface and the roughness of the bottom, a stochastic geometry-based channel model utilized for a wide-band transmission scenario has been exploited to derive a simulation model. Since the system bandwidth and the sub-carrier spacing is very limited in the range of a few kHz, the channel capacity of a UWA system is severely suffered by the ICI effect. For furthe…
In this paper, we propose a power allocation strategy for the adaptive orthogonal frequency-division multiplexing (OFDM) index modulation (IM) in cooperative networks. The allocation strategy is based on the Karush-Kuhn-Tucker (KKT) conditions, and aims at maximizing the average network capacity according to the instantaneous channel state information (CSI). As the transmit power at source and relay is constrained separately, we can thus formulate an optimization problem by allocating power to active subcarriers. Compared to the conventional uniform power allocation strategy, the proposed dyna…
In this paper, resource allocation for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) downlink networks with large numbers of base station antennas is studied. Assuming perfect channel state information at the transmitter, the resource allocation algorithm design is modeled as a non-convex optimization problem which takes into account the joint power consumption of the power amplifiers, antenna unit, and signal processing circuit unit. Subsequently, by exploiting the law of large numbers and dual decomposition, an efficient suboptimal iterative resource a…
Capacity is the eternal pursuit for communication systems due to the overwhelming demand of bandwidth hungry applications. As the backbone infrastructure of modern communication networks, the optical fiber transmission system undergoes a significant capacity growth over decades by exploiting available physical dimensions (time, frequency, quadrature, polarization and space) of the optical carrier for multiplexing. For each dimension, stringent orthogonality must be guaranteed for perfect separation of independent multiplexed signals. To catch up with the ever-increasing capacity requirement, i…
With the increase of physical antenna and subcarrier numbers in MIMO-OFDM systems, channel side information feedback amount and signal precoding complexity overburden will consume much more system resource, even become intolerable. To solve this problem, previous works mainly focused on fixed subcarrier grouping size and precoded MIMO signals in the same group with unitary channel state information (CSI). It could reduce the system overburden, but such a process would lead to system capacity loss due to the channel mismatch in precoding procedure. In this paper, we consider a MIMOOFDM system o…
The minimum average signal-to-noise ratio (SNR) per bit required for error-free transmission over a fading channel is derived, and is shown to be equal to that of the additive white Gaussian noise (AWGN) channel, which is $-1.6$ dB. Discrete-time algorithms are presented for timing and carrier synchronization, as well as channel estimation, for turbo coded multiple input multiple output (MIMO) orthogonal frequency division multiplexed (OFDM) systems. Simulation results show that it is possible to achieve a bit error rate of $10^{-5}$ at an average SNR per bit of 5.5 dB, using two transmit and …
We present a study of the influence of dispersion induced phase noise for CO-OFDM systems using FFT multiplexing/IFFT demultiplexing techniques (software based). The software based system provides a method for a rigorous evaluation of the phase noise variance caused by Common Phase Error (CPE) and Inter-Carrier Interference (ICI) including - for the first time to our knowledge - in explicit form the effect of equalization enhanced phase noise (EEPN). This, in turns, leads to an analytic BER specification. Numerical results focus on a CO-OFDM system with 10-25 GS/s QPSK channel modulation. A wo…
Interference alignment allows multiple users to share the same frequency and time resource in a wireless communications system. At present, two performance bounds, in terms of degree of freedom, have been proposed. One is for infinite-dimension extension and the other is for MIMO systems. This paper provides an understanding of the MIMO bound by examining its proofs and shows that it does not apply to a more practical case: MIMO-OFDM. Several approaches are proposed in searching for DoF bounds for systems such as finite-dimension time extension and MIMO-OFDM systems.
This paper considers the distribution of the mutual information of frequency-selective spatially-uncorrelated Rayleigh fading MIMO channels. Results are presented for OFDM-based spatial multiplexing. New exact closed-form expressions are derived for the variance of the mutual information. In contrast to previous results, our new expressions apply for systems with both arbitrary numbers of antennas and arbitrary-length channels. Simplified expressions are also presented for high and low SNR regimes. The analytical variance results are used to provide accurate analytical approximations for the d…
It is well known that CS can boost massive random access protocols. Usually, the protocols operate in some overloaded regime where the sparsity can be exploited. In this paper, we consider a different approach by taking an orthogonal FFT base, subdivide its image into appropriate sub-channels and let each subchannel take only a fraction of the load. To show that this approach can actually achieve the full capacity we provide i) new concentration inequalities, and ii) devise a sparsity capture effect, i.e where the sub-division can be driven such that the activity in each each sub-channel is sp…
Interference alignment (IA) has been shown to achieve the maximum achievable degrees of freedom in the interference channel. This results in sum rate scaling linearly with the number of users in the high signal-to-noise-ratio (SNR) regime. Linear scaling is achieved by precoding transmitted signals to align interference subspaces at the receivers, given channel knowledge of all transmit-receive pairs, effectively reducing the number of discernible interferers. The theory of IA was derived under assumptions about the richness of scattering in the propagation channel; practical channels do not g…
Orthogonal Time Frequency Space (OTFS) is a novel modulation scheme designed in the Doppler-delay domain to fully exploit time and frequency diversity of general time-varying channels. In this paper, we present a novel discrete-time analysis of OFDM-based OTFS transceiver with a concise and vectorized input-output relationship that clearly characterizes the contribution of each underlying signal processing block in such systems. When adopting cyclic prefix in the time domain, our analysis reveals that the proposed MIMO OTFS and OFDM systems have the same ergodic capacity despite the well-known…
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 multicomponent unipolar OFDM schemes are considered under the assumption that independent and identically distributed (i.i.d.) 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…
This paper proposes a novel and simple orthogonal faster than Nyquist (OFTN) data transmission and detection approach for a single input multiple output (SIMO) system. It is assumed that the signal having a bandwidth $B$ is transmitted through a wireless channel with $L$ multipath components. Under this assumption, the current paper provides a novel and simple OFTN transmission and symbol-by-symbol detection approach that exploits the multiplexing gain obtained by the multipath characteristic of wideband wireless channels. It is shown that the proposed design can achieve a higher transmission …
The demand for high-speed mobile wireless communications is rapidly growing. Orthogonal Frequency Division Multiplexing (OFDM) technology promises to be a key technique for achieving the high data capacity and spectral efficiency requirements for wireless communication systems in the near future. This paper investigates the performance of OFDM-based system over static and non-static or fading channels. In order to investigate this, a simulation model has been created and implemented using MATLAB. A comparison has also been made between the performances of coherent and differential modulation s…
Optimal power allocation for orthogonal frequency division multiplexing (OFDM) wiretap channels with Gaussian channel inputs has already been studied in some previous works from an information theoretical viewpoint. However, these results are not sufficient for practical system design. One reason is that discrete channel inputs, such as quadrature amplitude modulation (QAM) signals, instead of Gaussian channel inputs, are deployed in current practical wireless systems to maintain moderate peak transmission power and receiver complexity. In this paper, we investigate the power allocation and ar…
We explore the capacity and generalized degrees of freedom of the two-user Gaussian X channel, i.e. a generalization of the 2 user interference channel where there is an independent message from each transmitter to each receiver. There are three main results in this paper. First, we characterize the sum capacity of the deterministic X channel model under a symmetric setting. Second, we characterize the generalized degrees of freedom of the Gaussian X channel under a similar symmetric model. Third, we extend the noisy interference capacity characterization previously obtained for the interferen…
This paper gives the approximate capacity region of a two-user MIMO interference channel with limited receiver cooperation, where the gap between the inner and outer bounds is in terms of the total number of receive antennas at the two receivers and is independent of the actual channel values. The approximate capacity region is then used to find the degrees of freedom region. For the special case of symmetric interference channels, we also find the amount of receiver cooperation in terms of the backhaul capacity beyond which the degrees of freedom do not improve. Further, the generalized degre…
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 $P^α$. 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 $1/4$.
In this paper, we study the effect of feedback on two-user MIMO interference channels. The capacity region of MIMO interference channels with feedback is characterized within a constant number of bits, where this constant is independent of the channel matrices. Further, it is shown that the capacity region of a MIMO interference channel with feedback and its reciprocal interference channel are within a constant number of bits. Finally, the generalized degrees of freedom region for the MIMO interference channel with feedback is characterized.
The study investigated the allocation of transmission power and bits for a point-to-point orthogonal frequency-division multiplexing channel assuming perfect channel information at the receiver, but imperfect channel information at the transmitter. Channel information was quantized at the receiver and was sent back to the transmitter via a finite-rate feedback channel. Based on limited feedback from the receiver, the corresponding transmitter adapted the power level and/or modulation across subcarriers. To reduce the amount of feedback, subcarriers were partitioned into different clusters and …
This paper considers Electromagnetic Compatibility (EMC) aspects in the context of Power Line Communication (PLC) systems. It offers a complete overview of both narrow band PLC and broad band PLC EMC norms. How to interpret and translate such norms and measurement procedures into typical constraints used by designers of communication systems, is discussed. In particular, the constraints to the modulated signal spectrum are considered and the ability of pulse shaped OFDM (PS-OFDM), used in most of the PLC standards as IEEE P1901 and P1901.2, to fulfill them is analyzed. In addition, aiming to i…
The operational capacity of Gaussian MIMO channels with memory was obtained by Brandenburg and Wyner in [9] under certain mild assumptions on the channel impulse response and its noise covariance matrix, which essentuially require channel memory to be not too strong. This channel was also considered by Tsybakov in [10] and its information capacity was obtained in some cases. It was further conjectured, based on numerical evidence, that these capacities are the same in all cases. This conjecture is proved here. An explicit closed-form expression for the optimal input power spectral density matr…
Interference alignment is a key technique for communication scenarios with multiple interfering links. In several such scenarios, interference alignment was used to characterize the degrees-of-freedom of the channel. However, these degrees-of-freedom capacity approximations are often too weak to make accurate predictions about the behavior of channel capacity at finite signal-to-noise ratios (SNRs). The aim of this paper is to significantly strengthen these results by showing that interference alignment can be used to characterize capacity to within a constant gap. We focus on real, time-invar…
Massive multiple-input multiple-output (MIMO) systems have attracted much attention lately due to the many advantages they provide over single-antenna systems. Owing to the many antennas, low-cost implementation and low power consumption per antenna are desired. To that end, massive MIMO structures with low-resolution analog-to-digital converters (ADC) have been investigated in many studies. However, the effect of a strong interferer in the adjacent band on quantized massive MIMO systems have not been examined yet. In this study, we analyze the performance of uplink massive MIMO with low-resol…
Wireless fading networks with multiple antennas are typically studied information-theoretically from two different perspectives - the outage characterization and the ergodic capacity characterization. A key parameter in the outage characterization of a network is the diversity, whereas a first-order indicator for the ergodic capacity is the degrees of freedom (DOF), which is the pre-log coefficient in the capacity expression. In this paper, we present max-flow min-cut type theorems for computing both the diversity and the degrees of freedom of arbitrary single-source single-sink multi-antenna …
It has been generally believed that the multiple-input multiple-output (MIMO) channel capacity grows linearly with the size of antenna arrays. In terms of degrees of freedom, linear transmit and receive arrays of length $L$ in a scattering environment of total angular spread $|Ω|$ asymptotically have $|Ω| L$ degrees of freedom. In this paper, it is claimed that the linear increase in degrees of freedom may not be attained when scattered electromagnetic fields in the underlying scattering environment are statistically correlated. After introducing a model of correlated scattering, which is refe…
In this paper, we characterize the information-theoretic capacity scaling of wireless ad hoc networks with $n$ randomly distributed nodes. By using an exact channel model from Maxwell's equations, we successfully resolve the conflict in the literature between the linear capacity scaling by Özgür et al. and the degrees of freedom limit given as the ratio of the network diameter and the wavelength $λ$ by Franceschetti et al. In dense networks where the network area is fixed, the capacity scaling is given as the minimum of $n$ and the degrees of freedom limit $λ^{-1}$ to within an arbitrarily sma…
Consider a problem of forward error-correction for the additive white Gaussian noise (AWGN) channel. For finite blocklength codes the backoff from the channel capacity is inversely proportional to the square root of the blocklength. In this paper it is shown that codes achieving this tradeoff must necessarily have peak-to-average power ratio (PAPR) proportional to logarithm of the blocklength. This is extended to codes approaching capacity slower, and to PAPR measured at the output of an OFDM modulator. As a by-product the convergence of (Smith's) amplitude-constrained AWGN capacity to Shannon…
In modern communication systems, channel state information is of paramount importance to achieve capacity. It is then crucial to accurately estimate the channel. It is possible to perform SISO-OFDM channel estimation using sparse recovery techniques. However, this approach relies on the use of a physical wave propagation model to build a dictionary, which requires perfect knowledge of the system's parameters. In this paper, an unfolded neural network is used to lighten this constraint. Its architecture, based on a sparse recovery algorithm, allows SISO-OFDM channel estimation even if the syste…
A 3-user device-to-device (D2D) communications scenario is studied where each user wants to send and receive a message from each other user. This scenario resembles a 3-way communication channel. The capacity of this channel is unknown in general. In this paper, a sum-capacity upper bound that characterizes the degrees-of-freedom of the channel is derived by using genie-aided arguments. It is further shown that the derived upper bound is achievable within a gap of 2 bits, thus leading to an approximate sum-capacity characterization for the 3-way channel. As a by-product, interesting analogies …
Similar to the energy flowing process in traditional heat engines, information could be considered to flow in the communication systems with the form of energy and entropy. Combining the thermodynamic Carnot machine and the classical Shannon information theory, a generalized thermodynamic MIMO (multiple input multiple outputs) communication system is established to analyze the channel capacity using forward error correction codes. Based on the concepts of freedom and entropy in the communication system, the generalized channel capacity is proposed under the thermodynamic theory. Furthermore, t…
Analog-to-digital converters (ADCs) stand for a significant part of the total power consumption in a massive MIMO base station. One-bit ADCs are one way to reduce power consumption. This paper presents an analysis of the spectral efficiency of single-carrier and OFDM transmission in massive MIMO systems that use one-bit ADCs. A closed-form achievable rate, i.e., a lower bound on capacity, is derived for a wideband system with a large number of channel taps that employs low-complexity linear channel estimation and symbol detection. Quantization results in two types of error in the symbol detect…
In this paper, we consider a reconfigurable intelligence surface (RIS) aided uplink multiuser multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) system, where the receiver is assumed to conduct low-complexity iterative detection. We aim to minimize the total transmit power by jointly designing the precoder of the transmitter and the passive beamforming of the RIS. This problem can be tackled from the perspective of information theory. But this information-theoretic approach may involve prohibitively high complexity since the number of rate constraints that specif…
Degree of freedom (DoF) region provides an approximation of capacity region in high signal-to-noise ratio (SNR) regime, while sum DoF gives the scaling factor. In this correspondence, we analyse the DoF region and sum DoF for unicast layered multi-hop relay wireless networks with arbitrary number of source/destination/relay nodes, arbitrary number of hops and arbitrary number of antennas at each node. The result is valid for quite a few message topologies. We reveal the limitation on capacity of multi-hop network due to the concatenation structure and show the similarity with capacitor network…
We investigate the role of cooperation in wireless networks subject to a spatial degrees of freedom limitation. To address the worst case scenario, we consider a free-space line-of-sight type environment with no scattering and no fading. We identify three qualitatively different operating regimes that are determined by how the area of the network A, normalized with respect to the wavelength lambda, compares to the number of users n. In networks with sqrt{A}/lambda < sqrt{n}, the limitation in spatial degrees of freedom does not allow to achieve a capacity scaling better than sqrt{n} and this p…
In this paper, we investigate the capacity of known interference channel, where the receiver knows the interference data but not the channel gain of the interference data. We first derive a tight upper bound for the capacity of this known-interference channel. After that, we obtain an achievable rate of the channel with a blind known interference cancellation (BKIC) scheme in closed form. We prove that the aforementioned upper bound in the high SNR regime can be approached by our achievable rate. Moreover, the achievable rate of our BKIC scheme is much larger than that of the traditional inter…
We consider the Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and private messages. We obtain the degrees of freedom (DoF) region of this channel. We first show that a parallel Gaussian broadcast channel with unmatched sub-channels can be constructed from any given Gaussian MIMO broadcast channel by using the generalized singular value decomposition (GSVD) and a relaxation on the power constraint for the channel input, in a way that the capacity region of the constructed parallel channel provides an outer bound for the capacity region of the original channel. The…
We derive the capacity of the state-dependent half-duplex relay channel without source-destination link. The output of the state-dependent half-duplex relay channel depends on the randomly varying channel states of the source-relay and relay-destination links, which are known causally at all three nodes. For this channel, we prove a converse and show the achievability of the capacity based on a buffer-aided relaying protocol with adaptive link selection. This protocol chooses in each times slot one codeword to be transmitted over either the source-relay or the relay-destination channel dependi…
In this work we design a receiver that iteratively passes soft information between the channel estimation and data decoding stages. The receiver incorporates sparsity-based parametric channel estimation. State-of-the-art sparsity-based iterative receivers simplify the channel estimation problem by restricting the multipath delays to a grid. Our receiver does not impose such a restriction. As a result it does not suffer from the leakage effect, which destroys sparsity. Communication at near capacity rates in high SNR requires a large modulation order. Due to the close proximity of modulation sy…
Recent investigations have shown that the sum secure degrees of freedom of the Gaussian wiretap channel with a helper is $\tfrac{1}{2}$. The achievable scheme for this result is based on the real interference alignment approach. While providing a good way to show degrees of freedom results, this technique has the disadvantage of relying on the Khintchine-Groshev theorem and is therefore limited to {\it almost all channel gains}. This means that there are infinitely many channel gains, where the scheme fails. Furthermore, the real interference alignment approach cannot be used to yield stronger…
In this paper, we study achievable degrees of freedom (DoF) of a multiple-input multiple-output (MIMO) multiway relay channel (mRC) where $K$ users, each equipped with $M$ antennas, exchange messages in a pairwise manner via a common $N$-antenna relay node. % A novel and systematic way of joint beamforming design at the users and at the relay is proposed to align signals for efficient implementation of physical-layer network coding (PNC). It is shown that, when the user number $K=3$, the proposed beamforming design can achieve the DoF capacity of the considered mRC for any $(M,N)$ setups. % Fo…
Intelligent reflecting surface (IRS) is a promising solution to enhance the wireless communication capacity both cost-effectively and energy-efficiently, by properly altering the signal propagation via tuning a large number of passive reflecting units. In this paper, we aim to characterize the fundamental capacity limit of IRS-aided point-to-point multiple-input multiple-output (MIMO) communication systems with multi-antenna transmitter and receiver in general, by jointly optimizing the IRS reflection coefficients and the MIMO transmit covariance matrix. First, we consider narrowband transmiss…
We consider the extra degree of freedom offered by the rotation of the reconfigurable intelligent surface (RIS) plane and investigate its potential in improving the performance of RIS-assisted wireless communication systems. By considering radiation pattern modeling at all involved nodes, we first derive the composite channel gain and present a closed-form upper bound for the system ergodic capacity over cascade Rician fading channels. Then, we reconstruct the composite channel gain by taking the rotations at the RIS plane, transmit antenna, and receive antenna into account, and extract the op…
