Asymptotic Capacity Research Articles

Interference-Based Capacity Analysis for Vehicular Ad Hoc Networks

Although some scaling law-based studies have been conducted for describing the asymptotic capacity of Vehicular Ad Hoc Networks (VANETs), the obtained results are not easy to directly use for estimating the actual capacity of a communication link or the entire network. To overcome this drawback, an interference-based capacity analysis is carried out in this letter for the abstracted 1-dimensional VANETs scenario. For a reasonable and tractable modeling, the classic Car-Following model is applied to represent the dynamic change of the inter-vehicle distance, which strongly affects the power decay of both the signal and interference in the network. Based on that, a series of probability characteristics is derived for the worst-case interfering scenario, which finally leads to the stochastic characteristics for both the link and network capacity.

Asymptotic Capacity Lower Bound for an OFDM System With Lasso Compressed Sensing Channel Estimation for Bernoulli-Gaussian Channel

We analyze the asymptotic capacity of an OFDM system with pilot aided channel estimation over a Bernoulli-Gaussian sparse channel, with Lasso compressed sensing (CS) used for channel estimation. In the analysis, we utilize the CS asymptotic performance similarity when using Haar and DFT measurement matrices. We evaluate the mean square estimation error of an augmented Lasso estimator using the replica method results and then use it to obtain an asymptotic capacity lower bound for the OFDM system. For the considered system with equi-power pilot symbols, we optimize the average fraction of pilot subcarriers used for channel estimation and the pilot to data power ratio, given an average symbol power per subcarrier, and evaluate the asymptotic capacity bound increase due to CS.

Capacity of the Memoryless Additive Inverse Gaussian Noise Channel

The memoryless additive inverse Gaussian noise channel model describing communication based on the exchange of chemical molecules in a drifting liquid medium is investigated for the situation of simultaneously an average-delay and a peak-delay constraint. Analytical upper and lower bounds on its capacity in bits per molecule use are presented. These bounds are shown to be asymptotically tight, i.e., for the delay constraints tending to infinity with their ratio held constant (or for the drift velocity of the fluid tending to infinity), the asymptotic capacity is derived precisely. Moreover, characteristics of the capacity-achieving input distribution are derived that allow accurate numerical computation of capacity. The optimal input appears to be a mixed continuous and discrete distribution.

The Impact of Rate Adaptation on Capacity-Delay Tradeoffs in Mobile Ad Hoc Networks

In this paper, we focus on the asymptotic capacity and delay, and their tradeoffs in mobile ad hoc networks (MANETs). As we all know, some fixed rate communication models such as the protocol model and the physical model have been studied in the past. However, our work aims to investigate the impact of an adaptive rate communication model on capacity-delay tradeoffs in MANETs under classical mobility models. Specifically, we adopt a well-known adaptive rate model called the generalized physical model (GphyM). The mobility of nodes is characterized by two broad classes of practical mobility models and they are hybrid random walk models and discrete random direction models. The two models generalize many mobility models studied in the literature, including the random walk, i.i.d., Brownian, and random way point models. For each mobility model, we derive the optimal delay for the optimal per-session unicast capacity (that of constant order Θ(1)) under the generalized physical model, depending on the individual parameters of mobility models. In particular, we show that for the i.i.d. model, compared with those under the protocol and physical models, the adaptive feature of link rate under the generalized physical model results in a significant decrease in the optimal delay for the optimal capacity; more precisely, both the optimal capacity and optimal delay can be simultaneously achieved, while there is no improvement for the random way-point model.

Impact of Feedback and Side-Information on the Asymptotic Capacity of Single-Input Multiple-Output Fading Channels With Memory

An analytic expression for the asymptotic capacity of noncoherent single-input multiple-output regular fading channels with memory and with partial receiver side information is derived and is shown to remain unchanged by causal or acausal side information at the transmitter and by a noiseless feedback link. In particular, the corresponding fading numbers are identical. Furthermore, the asymptotic capacity of a single-input single-output nonregular Gaussian fading channel with memory is investigated, and it is shown that the prelog is unaffected by noiseless feedback.

Coding Schemes and Asymptotic Capacity for the Gaussian Broadcast and Interference Channels With Feedback

A coding scheme is proposed for the memoryless Gaussian broadcast channel with correlated noises and feedback. For all noise correlations other than ±1, the gap between the sum-rate that the scheme achieves and the full-cooperation bound vanishes as the signal-to-noise ratio tends to infinity. When the correlation coefficient is -1, the gains afforded by feedback are unbounded and the prelog is doubled. When the correlation coefficient is +1, we demonstrate a dichotomy that if the noise variances are equal, then feedback is useless, and otherwise, feedback affords unbounded rate gains and doubles the prelog. The unbounded feedback gains, however, require perfect (noiseless) feedback. When the feedback links are noisy, the feedback gains are bounded, unless the feedback noise decays to zero sufficiently fast with the signal-to-noise ratio. Extensions to more receivers are also discussed as is the memoryless Gaussian interference channel with feedback.

Asymptotic capacity analysis in multipoint-to-point cognitive radio networks with an arbitrary peak power

In this paper, we investigate the capacity of a multipoint-to-point cognitive radio network. In existing works, the asymptotic capacity is only obtained in the high peak power region at secondary transmitter (ST) or obtained without considering the interference from primary transmitter (PT) for easy analysis. Here, we analyze the asymptotic capacity by considering an arbitrary peak power at the ST and the interference from the PT based on extreme value theory. Simulation results show that our approximated capacity is well-matched to the exact capacity. Furthermore, the scaling law of our capacity is found to be double logarithm of the number of secondary users.

Error-Correction in Flash Memories via Codes in the Ulam Metric

<?Pub Dtl=""?> We consider rank modulation codes for flash memories that allow for handling arbitrary charge-drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked elements, the proposed translocation rank codes account for more general forms of errors that arise in storage systems. Translocations represent a natural extension of the notion of adjacent transpositions and as such may be analyzed using related concepts in combinatorics and rank modulation coding. Our results include derivation of the asymptotic capacity of translocation rank codes, construction techniques for asymptotically good codes, as well as simple decoding methods for one class of constructed codes. As part of our exposition, we also highlight the close connections between the new code family and permutations with short common subsequences, deletion and insertion error-correcting codes for permutations, and permutation codes in the Hamming distance.

On capacity gain of antenna subset selection for multiple antenna multicasting

AbstractIn this letter, we consider the transmit antenna subset selection scheme in multicast channels where the antenna subset is selected to maximise the minimum signal‐to‐noise power ratio among the associated users. Using an asymptotic analysis, the average capacity is derived for the large number of users asymptote under the assumption that the antennas are divided into non‐overlapping subsets, and each of them is independent, identical, spatially uncorrelated, and Rayleigh distributed. The numerical results demonstrate that the asymptotic average capacity is close to the exact capacity when signal‐to‐noise power ratio is not large or the number of users is large. Using this result, we compare the asymptotic average capacity of the selection scheme with that of the open‐loop multiple antenna multicasting scheme, in which only one antenna subset is employed, and its number of antennas is the same as that of the antenna subset of the selection scheme. Specifically, it is shown that the asymptotic capacity gain over the open‐loop scheme is significant when the number of antennas in each antenna subset is small. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Capacity of Hybrid Wireless Mesh Networks with Random APs

In conventional Wireless Mesh Networks (WMNs), multihop relays are performed in the backbone comprising of interconnected Mesh Routers (MRs) and this causes capacity degradation. This paper proposes a hybrid WMN architecture that the backbone is able to utilize random connections to Access Points (APs) of Wireless Local Area Network (WLAN). In such a proposed hierarchal architecture, capacity enhancement can be achieved by letting the traffic take advantage of the wired connections through APs. Theoretical analysis has been conducted for the asymptotic capacity of three-tier hybrid WMN, where per-MR capacity in the backbone is first derived and per-MC capacity is then obtained. Besides related to the number of MR cells as a conventional WMN, the analytical results reveal that the asymptotic capacity of a hybrid WMN is also strongly affected by the number of cells having AP connections, the ratio of access link bandwidth to backbone link bandwidth, etc. Appropriate configuration of the network can drastically improve the network capacity in our proposed network architecture. It also shows that the traffic balance among the MRs with AP access is very important to have a tighter asymptotic capacity bound. The results and conclusions justify the perspective of having such a hybrid WMN utilizing widely deployed WLANs.

Throughput Maximization in Poisson Fading Channels with Limited Feedback

A shot-noise limited single-user single-input single-output (SISO) Poisson fading channel with partial channel state information (CSI) at the transmitter and perfect CSI at the receiver is considered. We address an optimal transmit power allocation problem that maximizes the ergodic capacity of the SISO Poisson fading channel subject to peak and average power constraints with only quantized CSI available at the transmitter, acquired via a no-delay and error-free feedback link with finite-rate from the receiver to the transmitter. Due to the non-convexity of the proposed optimization problem, a globally optimum solution is difficult to obtain. However, we manage to obtain a locally optimal quantized power allocation (QPA) scheme by solving its dual Lagrangian optimization problem. We develop two efficient optimal QPA algorithms for solving the dual optimization problem and show that both of these algorithms converge to the globally optimal solution of the dual problem. A low-complexity near-optimal QPA algorithm is also derived for the case of large number of feedback bits. The results are then extended to the high peak signal-to-noise ratio (SNR) regime and an explicit expression for the approximate asymptotic ergodic capacity behavior in the high SNR regime with high rate quantization (as the number of feedback bits goes to infinity) is also provided. It is seen via numerical simulations that this asymptotic capacity expression correctly approaches the capacity of the corresponding full CSI case as the number of feedback bits becomes large. Finally, the effectiveness of the derived algorithms is examined through numerical simulations.

Asymptotic capacity of opportunistic scheduling over gamma–gamma (generalised-K) composite fading channels

The performance analysis of different transmission schemes in emerging wireless communication systems such as outdoor distributed antenna architectures and relay networks requires the adoption of joint multipath fading and shadowing channel models, since the geographically distributed ports experience different small-scale and large-scale fading conditions. In this study, extreme value theory is utilised to quantify the ergodic capacity of multiuser diversity (opportunistic scheduling) over shadowed Nakagami (gamma–gamma) fading channels. The distribution of the maximum extreme for a sequence of independent and identically distributed gamma–gamma random variables is shown to belong to the domain of attraction of the Gumbel distribution and subsequently the effect of independent shadowing on the ergodic capacity of opportunistic scheduling for large number of users is revealed.

A Unified Framework for the Ergodic Capacity of Spectrum Sharing Cognitive Radio Systems

We consider a spectrum sharing communication scenario in which a primary and a secondary users are communicating, simultaneously, with their respective destinations using the same frequency carrier. Both optimal power profile and ergodic capacity are derived for fading channels, under an average transmit power and an instantaneous interference outage constraints. Unlike previous studies, we assume that the secondary user has a noisy version of the cross link and the secondary link Channel State Information (CSI). After deriving the capacity in this case, we provide an ergodic capacity generalization, through a unified expression, that encompasses several previously studied spectrum sharing settings. In addition, we provide an asymptotic capacity analysis at high and low signal-to-noise ratio (SNR). Numerical results, applied for independent Rayleigh fading channels, show that at low SNR regime, only the secondary channel estimation matters with no effect of the cross link on the capacity; whereas at high SNR regime, the capacity is rather driven by the cross link CSI. Furthermore, a practical on-off power allocation scheme is proposed and is shown, through numerical results, to achieve the full capacity at high and low SNR

Capacity analysis of multicast transmission schemes in a spectrum-sharing scenario

In this study, the authors consider the asymptotic capacity of wireless multicast and unicast transmission schemes in a spectrum-sharing system. In these schemes, a secondary access point (SAP) utilises the licensed spectrum of an active primary user (PU) to send a common information to multiple secondary users simultaneously, as long as the interference power inflicted on the PU is less than a predefined threshold. At the SAP, interference channel-state information between the SAP and the PU is used to calculate the maximum allowable SAP transmit power to limit the interference. The authors derive the average capacity of these schemes based on extreme value theory. From the derived asymptotic capacities, the insights to the capacity behaviour can be drawn.

Throughput capacity analysis of large multi-channel, multi-interface random wireless mesh networks

This paper studies the asymptotic throughput capacity of a random infrastructure wireless mesh network (RndInfWMN). Generally an infrastructure wireless mesh network (InfWMN) comprises mesh clients, routers, gateways and has hierarchical structures. An InfWMN can be divided into two categories, which are arbitrary InfWMN (ArbInfWMN) and random InfWMN (RndInfWMN). In an ArbInfWMN, the locations of the WMRs are arbitrary while in an RndInfWMN, WMRs are distributed randomly. The latter is more interesting when randomly distributed WLANs are desired to be connected through a wired network of gateways. There are some analytical research on the asymptotic capacity of ArbInfWMN where the number of interfaces per-infrastructure node, m, is at the same order of the number of available channels for the network, c, i.e. cm=θ(1). In our previous research, we investigated the asymptotic throughput capacity of ArbInfWMNs for a more general case in which cm=O(1). However, to date, analytical facility has been limited by the absence of analysis in RndInfWMNs, especially for the general case in which cm=O(1). In this paper, we carry out an original analysis of the asymptotic per-client throughput capacity of multi-channel multi-interface RndInfWMNs for the case in which cm=O(1). Our analysis shows that by identifying cm in different scaling regimes, the asymptotic per-client throughput capacity of multi-channel multi-interface RndInfWMNs exhibits different bounds, depending on the ratio between c and m.

Average Mutual Information Analysis of Multiple Input and Multiple Output System with Multihop Relaying in Wireless Communication System

Problem statement: Multiple Input and Multiple Output (MIMO) system with Multihop relaying techhnique is significant and active areas of wireless communication. In a rich scattering environment MIMO antenna system provides better channel capacity and data rates than single antenna systems. To provide high throughput, reliable transmission and broad coverage, wireless relaying techniques are essential in a variety of applications. In a cellular environment a relay can be used to overcome shadowing effect due to obstacles and multihop relaying can improve the throughput for mobiles suffering from poor signal to interference, noise ratio at the edge of a cell and reduce cell size to increase spectral efficiency. Approach: This study analyzes average mutual information of the Ricean channel for single hop Multiple Input Multiple Output (MIMO) system for different antenna configuation and dependence of capacity on the Rice factor for cellular system. The asymptotic capacity of multiuser two-hop MIMO system with Regularization Block Diagonalization (RBD) precoding techniques for Indepenent Identically Distributed (IID) channal and realistic Mobile to Mobile fading channel model was examined. In this realistic model, Non-Line-Sight (NLOS) propagation conditions are assumed from source mobile station to mobile relay and also from mobile relay to destination station. A non regenerative Amplify and Forward (AF) relay is used to optimize the capacity between the source and destination and also the evaluation was made for multiuser multi-hop relay system with correlated fading channel model using RBD precoding matrix. Results: The simulation results for average mutual information of single hop MIMO relay system for different antenna configuration with ricean channel model, ergodic sum mutual information for two hop relay system with RBD precoding technique and mutual information results for multiuser multihop relay system with correlated channel model was presented. Conclusion/Recommendations: Cellular systems generally operated at a fairly low SINR which can be increased on each hop by adding relays. Multiuser two hop relay system with RBD precoding for realistic mobile to mobile fading channel model is simulated and compared with IID channel model. Multiuser Multi-hop relay with optimal precoding and RBD precoding technique results were analyzed for correlated fading channel and found that capacity offered by RBD precoding scheme is better than other relaying systems.

Algorithmic superactivation of asymptotic quantum capacity of zero-capacity quantum channels

The superactivation of zero-capacity quantum channels makes it possible to use two zero-capacity quantum channels with a positive joint capacity for their output. Currently, we have no theoretical background to describe all possible combinations of superactive zero-capacity channels; hence, there may be many other possible combinations. In practice, to discover such superactive zero-capacity channel-pairs, we must analyze an extremely large set of possible quantum states, channel models, and channel probabilities. There is still no extremely efficient algorithmic tool for this purpose. This paper shows an efficient algorithmical method of finding such combinations. Our method can be a very valuable tool for improving the results of fault-tolerant quantum computation and possible communication techniques over very noisy quantum channels.

On the Capacity of Nakagami-m Fading Channels with Full Channel State Information at Low SNR

The capacity of flat Rayleigh fading channels with full channel state information (CSI) at the transmitter and at the receiver at asymptotically low SNR has been recently shown to scale essentially as SNR log(1/SNR). In this paper, we investigate the Nakagami-m fading channel capacity with full CSI, and show that the capacity of this channel scales essentially as Ω/m SNR log (1/SNR), where m is the Nakagami-m fading parameter and where Ω is the channel mean-square. We also show that one-bit CSI at the transmitter is enough to achieve this asymptotic capacity using an On-Off power control scheme. Our framework may be seen as a generalization of previous works as it captures the Rayleigh fading channel as a special case by taking m = 1.

Asymptotic Capacity Analysis for Adaptive Transmission Schemes Under General Fading Distributions

Asymptotic comparisons of ergodic channel capacity at high and low signal-to-noise ratios (SNRs) are provided for several adaptive transmission schemes over fading channels with general distributions, including optimal power and rate adaptation, rate adaptation only, channel inversion and its variants. Analysis of the high-SNR pre-log constants of the ergodic capacity reveals the existence of constant capacity difference gaps among the schemes with a pre-log constant of ?1. Closed-form expressions for these high-SNR capacity difference gaps are derived, which are proportional to the SNR loss between these schemes in dB scale. The largest one of these gaps is found to be between the optimal power and rate adaptation scheme and the channel inversion scheme. Based on these expressions it is shown that the presence of space diversity or multi-user diversity makes channel inversion arbitrarily close to achieving optimal capacity at high SNR with sufficiently large number of antennas or users. A low-SNR analysis also reveals that the presence of fading provably always improves capacity at sufficiently low SNR, compared to the additive white Gaussian noise (AWGN) case. Numerical results are shown to corroborate our analytical results.

Capacity Results of an Optical Intensity Channel With Input-Dependent Gaussian Noise

This paper investigates a channel model describing optical communication based on intensity modulation. It is assumed that the main distortion is caused by additive Gaussian noise, however, with a noise variance depending on the current signal strength. Both the high-power and low-power asymptotic capacities under simultaneously both a peak-power and an average-power constraint are derived. The high-power results are based on a new firm (nonasymptotic) lower bound and a new asymptotic upper bound. The upper bound relies on a dual expression for channel capacity and the notion of capacity-achieving input distributions that escape to infinity. The lower bound is based on a new lower bound on the differential entropy of the channel output in terms of the differential entropy of the channel input. The low-power results make use of a theorem by Prelov and van der Meulen.