Closed‐form expressions for the average channel capacity of the α– μ fading model under different adaptive transmission protocols

In this paper,we consider a small‐scale multipath fading channel following the α– μ generalized fading model distribution.We first derive an expression for the amount of fading () for this channel model to show the generalization attribute of this fading model recently reported in the literature. Then, we derive closed‐form expressions for the average channel capacity considering this channel distribution under different adaptive transmission protocols, namely the simultaneous power and rate adaptation protocol, the optimal rate adaptation with fixed power protocol, and the channel inversion with fixed‐rate protocol. All the obtained expressions are in closed‐form and general expressions that can reduce to other channel capacity expressions that are well‐known and to some others that are not known for Rayleigh, Nakagami‐m, and Weibull, as special cases. The derived expressions in this paper are new and have not been previously reported in the literature. Copyright © 2012 John Wiley & Sons, Ltd.     

Channel capacity of adaptive transmission with maximal ratio combining in correlated Rayleigh fading

We derive closed-form expressions for the single-user capacity of maximal ratio combining diversity systems taking into account the effect of correlation between the different branches. We consider a Rayleigh fading channel with two kinds of correlation: 1) equal branch signal-to-noise ratios (SNRs) and the same correlation between any pair of branches and 2) unequal branch SNRs and arbitrary correlation between branches such that the eigenvalues of the branch covariance matrix are all distinct. Three adaptive transmission schemes are analyzed: 1) optimal simultaneous power and rate adaptation; 2) optimal rate adaptation with constant transmit power; and 3) channel inversion with fixed rate.     

A novel low‐complexity transmission power adaptation in MC‐CDMA systems with a‐MRC receiver over Nakagami‐m fading channels

In this paper, we propose a novel low‐complexity transmission power adaptation with good bit error rate (BER) performance for multicarrier code‐division multiple‐access (MC‐CDMA) systems over Nakagami‐m fading channels. We first propose a new receiver called ath‐order‐maximal‐ratio‐combining (a‐MRC) receiver with which the receiver power gain for the nth subcarrier is the ath (a?1) power of the corresponding channel gain. Incorporating the a‐MRC receiver, we then propose a new transmission power adaptation scheme where the transmission power is allocated over all the N subcarriers according to the subchannel gains and the transmitter adapts its power to maintain a constant signal‐to‐interference‐plus‐noise (SINR) at the receiver. The proposed scheme has a significant performance gain over the nonadaptive transmission scheme over both independent and correlated fading channels. Moreover, the proposed scheme keeps good BER performance while it is much simpler than the previous power control/adaptation schemes. Copyright © 2008 John Wiley & Sons, Ltd.     

Performance analysis of an opportunistic multi‐user cognitive network with multiple primary users

Consider a multi‐user underlay cognitive network where multiple cognitive users concurrently share the spectrum with a primary network with multiple users. The channel between the secondary network is assumed to have independent but not identical Nakagami‐m fading. The interference channel between the secondary users (SUs) and the primary users is assumed to have Rayleigh fading. A power allocation based on the instantaneous channel state information is derived when a peak interference power constraint is imposed on the secondary network in addition to the limited peak transmit power of each SU. The uplink scenario is considered where a single SU is selected for transmission. This opportunistic selection depends on the transmission channel power gain and the interference channel power gain as well as the power allocation policy adopted at the users. Exact closed form expressions for the moment‐generating function, outage performance, symbol error rate performance, and the ergodic capacity are derived. Numerical results corroborate the derived analytical results. The performance is also studied in the asymptotic regimes, and the generalized diversity gain of this scheduling scheme is derived. It is shown that when the interference channel is deeply faded and the peak transmit power constraint is relaxed, the scheduling scheme achieves full diversity and that increasing the number of primary users does not impact the diversity order. Copyright © 2014 John Wiley & Sons, Ltd.     

Performance analysis of a variable‐gain amplify‐and‐forward relayed mixed RF‐FSO system

In this work, an amplify‐and‐forward variable‐gain relayed mixed RF‐FSO system is studied. The considered dual‐hop system consists of a radio frequency (RF) link followed by a free space optical (FSO) channel. The RF link is affected by short‐term multipath fading and long‐term shadowing effects and is assumed to follow the generalized‐K fading distribution that approximates accurately several important distributions often used to model communication channels. The FSO channel experiences fading caused by atmospheric turbulence that is modeled by the gamma‐gamma distribution characterizing moderate and strong turbulence conditions. The FSO channel also suffers path loss and pointing error induced misalignment fading. The performance of the considered system is analyzed under the collective influence of distribution shaping parameters, pointing errors that result in misalignment fading, atmospheric turbulence, and path loss. The moment‐generating function of the Signal power to noise power ratio measured end‐to‐end for this system is derived. The cumulative distribution function for the Signal power to noise power ratio present between the source and destination receiver is also evaluated. Further, we investigate the error and outage performance and the average channel capacity for this system. The analytical expressions in closed form for the outage probability, symbol and bit error rate considering different modulation schemes and channel capacity are also derived. The mathematical expressions obtained are also demonstrated by numerical plots.     

Capacity of Dual Branch MRC System Over Correlated Nakagami-<Emphasis Type="Italic">m</Emphasis> Fading Channels-A Review

Various papers on the channel capacity using different diversity combining techniques and/or adaptive transmission schemes are available to enhance channel capacity under fading environment without the necessity of increasing bandwidth and transmit powers. This paper provides the review on the channel capacity of MRC (Maximal ratio combining) over uncorrelated and correlated Nakagami-m fading channels with m = 1 (Rayleigh fading channel) under ORA (Optimum rate adaptation with constant transmit power), CIFR (Channel inversion with fixed rate) and OPRA (Optimum power and rate adaptation) schemes. We also highlight the effect of fade correlation on channel capacity and discuss the improvement of the system performance under the different adaptive techniques.     

On the capacity of Rayleigh fading cooperative systems under adaptive transmission

In this letter, the use of adaptive source transmission with amplify-and-forward relaying is proposed. Three different adaptive techniques are considered: (i) optimal simultaneous power and rate adaptation; (ii) constant power with optimal rate adaptation; (iii) channel inversion with fixed rate. The capacity upper bounds of these adaptive protocols are derived for the amplify-and-forward cooperative system over both independent and identically distributed (i.i.d.) Rayleigh fading and non-i.i.d. Rayleigh fading environments. The capacity analysis is based on an upper bound on the effective received signal-to-noise ratio (SNR). The tightness of the upper bound is validated by the use of a lower bound and by Monte Carlo simulation. It is shown that at high SNR the optimal simultaneous power and rate adaptation and the optimal rate adaptation with constant power provide roughly the same capacity. Channel inversion is shown to suffer from a deterioration in capacity relative to the other adaptive techniques.     

Quasi‐optimal power allocation based on ergodic capacity for wireless relay networks

Half‐duplex amplify‐and‐forward (AF) transmissions may result in insufficient use of degrees of freedom if they always use the cooperative mode regardless of the fading states. In this paper, we investigate the conditions under which cooperation offers better performance and the corresponding optimal power allocation during cooperation. Specifically, we first derive an expression of ergodic capacity and its upper bound for an AF cooperative communication system with n relay nodes. Secondly, we propose a novel quasi‐optimal power allocation (QOPA) scheme to maximize the upper bound of the derived ergodic capacity. For the QOPA scheme, the cooperative mode is only adopted when the channel gain of source‐to‐destination is worse than that of relay‐to‐destination. Moreover, we analyze the performance of the system with QOPA scheme when the relay moves, which is based on the random direction model, in a single‐relay wireless network. For a multi‐relay AF network, we compare the ergodic capacity and symbol error rate, corresponding to the proposed QOPA and equal power allocation schemes, respectively. Extensive simulations were conducted to validate analytical results, showing that both ergodic capacity and symbol error rate of the system with QOPA scheme are better than those of the system with equal power allocation scheme in a multi‐relay AF network. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance Evaluation of Generalized Selection Combiners Over Slow Fading with Estimation Errors

In this paper we derive closed-form expressions for the single-user adaptive capacity of generalized selection combining (GSC) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying spatially independent flat Rayleigh fading channel. The complex channel estimate and the actual channel are modelled as jointly Gaussian random variables with a correlation that depends on the estimation quality. Three adaptive transmission schemes are analyzed: (1) optimal power and rate adaptation; and (2) constant power with optimal rate adaptation, and (3) channel inversion with fixed rate. In addition to deriving an exact expression for the capacity of the aforementioned adaptive schemes, we analyze the impact of channel estimation error on the capacity statistics and the symbol error rate for GSC systems. The capacity statistics derived in this paper are the moment generating function, complementary cumulative distribution function and probability density function for arbitrary number of receive antennas. Moreover, exact closed-form expressions for M-PAM/PSK/QAM employing GSC are derived. As expected, the channel estimation error has a significant impact on the system performance.     

Maximizing the data transmission rate of a cooperative relay system in an underwater acoustic channel

In this paper, we investigate the problem of maximizing the data transmission rate of a cooperative relay system in an underwater acoustic communication channel. With amplify‐and‐forward relaying and adaptive source transmission, we present optimal transmit signal power adaptation policies that maximize the data transmission rate, considering both frequency and time domains. The analysis takes into account a physical model of acoustic path loss and ambient noise power spectral density. Typical characteristics of underwater channel such as frequency‐dependent fading and time variations are also considered. Capacity bounds for channel state information (CSI) only at the receiver and CSI at both transmitter and receiver are presented. To maximize the data rate, we use the notion of an optimal bandwidth which corresponds to efficient allocation of signal power across the transmission bandwidth. Under the constraint of an average transmit power, the optimal transmit power adaptation policy is found to be ‘water‐pouring’ in frequency‐time domain, while the transmit power adaptation policy with a total power constraint is ‘water‐pouring’ in frequency domain. Results show that both frequency domain and frequency‐time domain power adaptation schemes provide much greater improvement in average data rate over that of the constant power case. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive orthogonal frequency division multiplexing channel capacity employing diversity in cellular fading environments with symmetric scattering distributions

Gaussian and hyperbolic angle‐of‐arrival probability density functions are used to derive channel capacity of orthogonal frequency division multiplexing transmission employing diversity techniques and adaptive policies in cellular wireless fading environments. The intercarrier interference (ICI) power is quantified and given as a function of Doppler shift f_d, symbol duration T_s, frequency correction ζ and propagation ratio τ. Two scattering distributions, which have been shown to closely fit experimental empirical data, are examined in this paper: (i) Gaussian and (ii) hyperbolic. A new signal‐to‐interference‐and‐noise ratio probability density function is derived as a function of the ICI power using diversity techniques and adaptive policies. From that, effects of f_dT_s, ζ and τ on channel capacity can be discussed. The main contribution of this work is to model ICI as a function of f_d and symbol duration T_s. Two diversity techniques are considered: (i) maximal ratio combining and (ii) selective combining. Three adaptive policies are studied: (i) optimal rate adaptation, (ii) optimal rate and power adaptation and (iii) channel inversion with fixed rate. Closed‐form expressions and bounds on various channel capacity with orthogonal frequency division multiplexing transmission under different scenarios are derived. Copyright © 2012 John Wiley & Sons, Ltd.     

Capacity of Rayleigh fading channels under different adaptivetransmission and diversity-combining techniques

We study the Shannon capacity of adaptive transmission techniques in conjunction with diversity-combining. This capacity provides an upper bound on spectral efficiency using these techniques. We obtain closed-form solutions for the Rayleigh fading channel capacity under three adaptive policies: optimal power and rate adaptation, constant power with optimal rate adaptation, and channel inversion with fixed rate. Optimal power and rate adaptation yields a small increase in capacity over just rate adaptation, and this increase diminishes as the average received carrier-to-noise ratio (CNR) or the number of diversity branches increases. Channel inversion suffers the largest capacity penalty relative to the optimal technique, however, the penalty diminishes with increased diversity. Although diversity yields large capacity gains for all the techniques, the gain is most pronounced with channel inversion. For example, the capacity using channel inversion with two-branch diversity exceeds that of a single-branch system using optimal rate and power adaptation. Since channel inversion is the least complex scheme to implement, there is a tradeoff between complexity and capacity for the various adaptation methods and diversity-combining techniques     

A New Closed-Form Expressions of Channel Capacity with MRC,EGC and SC Over Lognormal Fading Channel

In this work, we derive the closed-form expressions of channel capacity with maximal ratio combining, equal gain combining and selection combining schemes under different transmission policies such as optimal power and rate adaptation, optimal rate adaptation, channel inversion with fixed rate (CIFR) and truncated CIFR. Various approximations to the intractable integrals have been proposed using methods such as Holtzman and Gauss–Hermite approximations and simpler expressions are suggested. Moreover, as an application, the channel capacity of lognormally distributed fading channel in the interference-limited environment is discussed. The obtained closed-form expressions have been validated with the exact numerical results.

     

Spectral efficiency of dual diversity selection combining schemes under correlated Nakagami-0.5 fading with unequal average received SNR

The spectral efficiency results for different adaptive transmission schemes over correlated diversity branches with unequal average signal to noise ratio (SNR) obtained so far in literature are not applicable for Nakagami-0.5 fading channels. In this paper, we investigate the effect of fade correlation and level of imbalance in the branch average received SNR on the spectral efficiency of Nakagami-0.5 fading channels in conjunction with dual-branch selection combining (SC). This paper derived the expressions for the spectral efficiency over correlated Nakagami-0.5 fading channels with unequal average received SNR. This spectral efficiency is evaluated under different adaptive transmission schemes using dual-branch SC diversity scheme. The corresponding expressions for Nakagami-0.5 fading are considered to be the expressions under worst fading conditions. Finally, numerical results are provided to illustrate the spectral efficiency degradation due to channel correlation and unequal average received SNR between the different combined branches under different adaptive transmission schemes. It has been observed that optimal simultaneous power and rate adaptation (OPRA) scheme provides improved spectral efficiency as compared to truncated channel inversion with fixed rate (TIFR) and optimal rate adaptation with constant transmit power (ORA) schemes under worst case fading scenario. It is very interesting to observe that TIFR scheme is always a better choice over ORA scheme under correlated Nakagami-0.5 fading channels with unequal average received SNR.     

End‐to‐end performance of transmit antenna selection and generalized selection combining in dual‐hop amplify‐and‐forward relay network in the presence of feedback errors

In this paper, end‐to‐end performance of transmit antenna selection (TAS) and generalized selection combining (GSC) is studied in a dual‐hop amplify‐and‐forward relay network over flat Rayleigh fading channels. In the system, source and destination equipped with multiple antennas, communicate by the help of single relay equipped with single antenna. Source‐destination link is not available. TAS is used for transmission at the source, and GSC is used for reception at the destination. By considering the relay location and the presence of error in feedback channel from the relay to the source, we derive closed‐form outage probability, moment generating function and moments of end‐to‐end signal‐to‐noise ratio, and closed‐form symbol error probability (SEP) expressions for channel state information (CSI)‐based and fixed relay gains. The diversity order and array gain of the network are obtained for both CSI‐based and fixed relay gains by deriving asymptotical outage probability and SEP expressions. The analytical results are validated by the Monte Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Capacity of Orthogonalized Weibull MIMO Channels Under Different Adaptive Transmission Techniques

Space-time block codes (STBCs) are known to orthogonalize the multiple input multiple out (MIMO) wireless channels. In this paper, we study the capacity of STBCs over Weibull MIMO channels under three adaptive transmission techniques: optimal power and rate adaptation, optimal rate adaptation with constant transmit power and channel inversion with fixed rate, and obtain closed-form expressions for the corresponding capacity. This capacity provides an upper bound on spectral efficiency using these techniques and avoids Monte Carlo simulations. Moreover, we also examine the effects of the fading severity on the concerned quantities. The figures show that our theoretical results of channel capacity line up exactly with the simulations.     

Cross-layer Adaptive Transmission: Optimal Strategies in Fading Channels

We consider cross-layer adaptive transmission for a single-user system with stochastic data traffic and a time- varying wireless channel. The objective is to vary the transmit power and rate according to the buffer and channel conditions so that the system throughput, defined as the long-term average rate of successful data transmission, is maximized, subject to an average transmit power constraint. When adaptation is subject to a fixed bit error rate (BER) requirement, maximizing the system throughput is equivalent to minimizing packet loss due to buffer overflow. When the BER requirement is relaxed, maximizing the system throughput is equivalent to minimizing total packet loss due to buffer overflow and transmission errors. In both cases, we obtain optimal transmission policies through dynamic programming. We identify an interesting structural property of these optimal policies, i.e., for certain correlated fading channel models, the optimal transmit power and rate can increase when the channel gain decreases toward outage. This is in sharp contrast to the water-filling structure of policies that maximize the rate of transmission over fading channels. Numerical results are provided to support the theoretical development.     

Outage and ergodic sum‐rate performance of cooperative MIMO‐NOMA with imperfect CSI and SIC

In this paper, we examine a half‐duplex cooperative multiple‐input multiple‐output non‐orthogonal multiple access system with imperfect channel state information (CSI) and successive interference cancelation. The base station (BS) and mobile users with multi‐antenna communicate by the assistance of a CSI based or fixed gain amplify‐and‐forward (AF) relay with a single antenna. The diversity schemes, transmit antenna selection, and maximal ratio combining are applied at the BS and mobile users, respectively. We study the system performance in terms of outage probability (OP) and ergodic sum‐rate. Accordingly, the exact OP expressions are first derived jointly for the CSI based and fixed gain AF relay cases in Nakagami‐m fading channels. Next, the corresponding lower and upper bound expressions of the OP are obtained. The high signal‐to‐noise ratio analyses are also carried out to demonstrate the error floor value resulted in the practical case and achievable diversity order and array gain in the ideal case. Moreover, the lower and upper bounds of the ergodic sum‐rate expressions are derived together for the CSI based and fixed gain AF relay cases. Finally, the Monte‐Carlo simulations are used to verify the correctness of the analytical results.     

Channel capacity of OFDM systems employing diversity in fading environments

This paper derives capacity of a fading channel with orthogonal frequency division multiplexing (OFDM) transmission employing diversity techniques and adaptive policies involving (i) power and rate, (ii) optimal rate and (iii) channel inversion with fixed rate. Two major diversity techniques are considered (i) maximal ratio combining (MRC) and (ii) selective combining (SC). Closed‐form expressions and/or bounds on various channel capacity with OFDM transmission under different scenarios are derived. Simulation results are given. Copyright © 2011 John Wiley & Sons, Ltd.     

Novel Closed-Form Expressions for Ergodic Capacity of MIMO-OSFBC-OFDM Systems Over Channel Adaptation Policies

In this work, closed-form expressions for capacities per unit bandwidth for MIMO-OFDM systems employing Orthogonal Space-Frequency Block Coding over multipath frequency-selective fading channels are derived for adaptation policies like optimal power and rate adaptation, optimal rate adaptation with constant transmit power, channel inversion with fixed rate, and truncated channel inversion polices. A Signal-to-Noise Ratio based user selection scheme is considered. Optimal power and rate adaptation policy provides the highest capacity over other adaptation policies. Capacity penalty is the highest for optimal rate adaptation with constant transmit power policy, while the performance of channel inversion with fixed rate policy and truncated channel inversion policy lie between that of OPRA and ORA policies.