Capacity evaluation for equal gain diversity schemes over Rayleigh fading channels

In this paper, closed-form expressions for the capacities per unit bandwidth for Rayleigh fading channels with equal gain combining (EGC) diversity case are derived for power and rate adaptation, constant transmit power, channel inversion with fixed rate, and truncated channel inversion adaptation policies. Channel inversion policies provide the highest capacity over the other adaptation policies with EGC diversity. The constant transmit power policy provides the lowest capacity as compared to the other policies.     

Capacity of correlative nakagami-m fading channels under adaptive transmission and maximal-ratio combining diversity technique

The study of channel capacity evaluation in conjunction with maximal ratio diversity-combining (MRC) is presented in this paper. Analysis of the capacity in correlative Nakagami-m fading channels is observed. Using the proposed fading model, the power and rate adaptation, constant transmit power, channel inversion with fixed rate and truncated channel inversion adaptation policies are analyzed. Our results show that the power and rate adaptation policy, being only slightly higher than capacity of constant transmit power policy, provides the highest capacity over the other adaptation policies. The results also show that truncated channel inversion adaptation policy is better alternative compared to complete channel inversion policy for all values of fading severity, diversity order and correlation coefficient.     

Spectrum Efficiency Evaluation with Diversity Combining for Fading and Branch Correlation Impairments

In this paper, closed-form expressions for capacities per unit bandwidth for fading channels with impairments due to Branch Correlation are derived for optimal power and rate adaptation, constant transmit power, channel inversion with fixed rate, and truncated channel inversion policies for maximal ratio combining diversity reception case. Closed-form expressions for system spectrum efficiency when employing different adaptation policies are derived. Analytical results show accurately that optimal power and rate adaptation policy provides the highest capacity over other adaptation policies. In the case of errors due to branch correlation, optimal power and rate adaptation policy provides the best results. All adaptation policies suffer no improvement in channel capacity as the branch correlation is increased. This fact is verified using various plots for different policies. With increase in branch correlation, capacity gains are significantly larger for optimal power and rate adaptation policy as compared to the other policies. The outage probability for branch correlation is also derived and analyzed using plots for the same.     

Spectrum Efficiency Evaluation for MRC Diversity Schemes Under Different Adaptation Policies Over Generalized Rayleigh Fading Channels

In this paper, closed-form expressions for the capacities per unit bandwidth for Generalized Rayleigh fading channels are derived for optimal power adaptation, constant transmit power, channel inversion with fixed rate, and truncated channel inversion adaptation policies. The closed-form solutions are derived for the single antenna reception (without diversity combining) and MRC diversity reception cases. Optimal power adaptation policy provides the highest capacity over the other adaptation policies both with and without diversity combining. Truncated channel inversion policy suffers a large capacity penalty relative to the optimal power adaptation policy as the number of degrees of freedom is increased. However, with increase in diversity, the capacity penalty for the truncated channel inversion policy decreases. Capacity gains are more prominent for channel inversion with fixed rate policy as compared to the other adaptation policies.

Spectral Efficiency Evaluation for MRC Diversity Schemes Over Generalized Rician Fading Channels

In this paper, closed-form expressions for the capacities per unit bandwidth for generalized Rician fading channels are derived for power and rate adaptation, constant transmit power, channel inversion with fixed rate, and truncated channel inversion adaptation policies. The closed-form solutions are derived for the single antenna reception (without diversity combining) and maximal-ratio combining (MRC) diversity cases. Truncated channel inversion adaptation policy is the best policy for the single antenna reception case, while the channel inversion with fixed rate policy is the best policy for the MRC diversity case. Constant transmit power policy provides the lowest spectral efficiency as compared to the other policies with and without diversity.     

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     

Ergodic capacity analysis of cooperative amplify‐and‐forward relay networks over generalized fading channels

This paper presents two new methods for evaluating the ergodic channel capacities of cooperative non‐regenerative multirelay networks in a myriad of fading environments and under three distinct source‐adaptive transmission policies: (i) optimal rate adaptation with a fixed transmit power; (ii) optimal joint power‐and‐rate adaptation; and (iii) truncated channel inversion with fixed rate. In contrast to the previous related works, our proposed unified analytical frameworks that are based on the moment generating function and/or the cumulative distribution function of end‐to‐end signal‐to‐noise ratio allow us to gain insights into how power assignment during different transmission phases, relay node placement, fade distributions, and dissimilar fading statistics across the distinct communication links impact the ergodic capacity, without imposing any restrictions on the channel fading parameters. Copyright © 2013 John Wiley & Sons, Ltd.     

Spectrum Efficiency of Weibull Fading Channels for Various Adaptation Policies with and Without Diversity Combining

In this paper, closed-form expressions for the capacities per unit bandwidth (spectrum efficiency) of Weibull fading channels are derived and plotted for (a) Switch and Stay Combining diversity case and (b) no diversity case for adaptation policies like: (i) Optimal Power and Rate Adaptation policy, (ii) Optimal Rate Adaptation with constant transmit power policy, (iii) Channel Inversion with Fixed Rate policy, and (iv) Truncated Channel Inversion policy. In addition, spectrum efficiency expressions for asymptotic approximations, upper bounds, approximations for low and high SNR cases are derived for the cases with and without diversity. The probability density function of capacity, and the complementary cumulative distribution function of capacity are derived and plotted from the moment generating function for the cases with and without diversity. Optimal power and rate adaptation policy provides the highest capacity and optimal rate adaptation with constant transmit power policy provides the highest capacity penalty over other policies for the no diversity and SSC diversity cases. Numerical results for spectrum efficiency are plotted for all adaptation policies with and without diversity.     

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.     

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.     

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.     

Capacity Analysis of Opportunistic Cooperative Networks under Adaptive Transmission over Rayleigh Fading Channels

In this paper, opportunistic cooperative amplify-and-forward networks in conjunction with three different adaptive policies, namely optimal simultaneous power and rate adaptation (OPRA), constant power with optimal rate adaptation (OPA) and truncated channel inversion with fixed rate (TIFR), are investigated and compared in terms of Rayleigh channel capacity where the source adapts its rate and/or power level according to channel conditions while the best relay simply amplifies and then forwards the received signals. Furthermore, the effect of diversity combining on the network is studied by investigating two cases of maximal ratio combining (MRC) and selection combining (SC) equipped at the destination. To this end, the mathematically tractable form of the upper and lower bound of the end-to-end effective signal-to-noise ratio (SNR) is provided and then used to derive the closed-form expression of the Shannon capacity. Our results are verified through comparison with Monte Carlo simulations in some representative scenarios where we also illustrate that, among them, for an arbitrary number of cooperative relays, OPRA slightly outperforms ORA, which, in turn, outperforms TIFR.     

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.     

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.     

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.     

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.     

Joint Optimization Of “Transmission Rate” and “Outer-Loop SNR Target” Adaptation Over Fading Channels

Joint optimization of signal-to-noise ratio (SNR) target and transmission rate adaptation is examined for multilevel quadrature amplitude modulation (MQAM) over flat-fading channels, to maximize the spectral efficiency subject to an average transmit power constraint. We propose an adaptive transmission scheme in which the outer-loop SNR target and data rate are adapted to bit-error rate (BER), where total or truncated channel-inversion strategies are exploited for the (fast) inner-loop power control. We obtain the optimal solutions for both continuous and discrete rate adaptation, and consider cases where diversity combining is performed in the receiver. We show that by using this BER-based adaptive scheme, spectral efficiency can be improved compared with optimal SNR-based variable-rate variable-power MQAM. We also show that for continuous rate adaptation, the optimal SNR target monotonically increases with BER, while it descends within a BER range with constant rate     

Transmit power adaptation for multiuser OFDM systems

In this paper, we develop a transmit power adaptation method that maximizes the total data rate of multiuser orthogonal frequency division multiplexing (OFDM) systems in a downlink transmission. We generally formulate the data rate maximization problem by allowing that a subcarrier could be shared by multiple users. The transmit power adaptation scheme is derived by solving the maximization problem via two steps: subcarrier assignment for users and power allocation for subcarriers. We have found that the data rate of a multiuser OFDM system is maximized when each subcarrier is assigned to only one user with the best channel gain for that subcarrier and the transmit power is distributed over the subcarriers by the water-filling policy. In order to reduce the computational complexity in calculating water-filling level in the proposed transmit power adaptation method, we also propose a simple method where users with the best channel gain for each subcarrier are selected and then the transmit power is equally distributed among the subcarriers. Results show that the total data rate for the proposed transmit power adaptation methods significantly increases with the number of users owing to the multiuser diversity effects and is greater than that for the conventional frequency-division multiple access (FDMA)-like transmit power adaptation schemes. Furthermore, we have found that the total data rate of the multiuser OFDM system with the proposed transmit power adaptation methods becomes even higher than the capacity of the AWGN channel when the number of users is large enough.     

Optimizing the transmit power for slow fading channels

We consider the design of power-adaptive systems for minimizing the average bit-error rate over flat fading channels. Channel state information, obtained through estimation at the receiver, is sent to the transmitter over a feedback channel, where it is used to optimally adapt the transmit power. We consider finite-state optimal policies to reflect the limitations of the feedback channel. We develop an iterative algorithm that determines the optimal finite-state power control policy given the probability density function (PDF) of the fading. Next, we present a discretized formulation of the problem and obtain a suboptimal solution via standard dynamic programming techniques. The discretization of the problem enables us to obtain a suboptimal policy for arbitrary fading channels for which the analytic expression of the fading probability density function is not available. Simulation results are used to draw conclusions regarding the effects of limited feedback channel capacity, delay and number of states on the bit-error rate performance of the proposed policies under slow and moderate fading conditions