Optimal Power Adaptation Research Articles

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.

Capacity of η – μ fading channels under different adaptive transmission techniques

An analysis for the Shannon channel capacity of digital receivers operating over η–μ fading channels is presented under four adaptive policies: constant power with optimal rate adaptation, optimal power and rate adaptation, channel inversion with fixed rate and truncated channel inversion with fixed rate. In this context, useful formulae for the average channel capacity for maximal-ratio combining receivers with not necessarily identically distributed branches are derived. The analysis also includes the performance of single-branch receivers. These expressions provide an effective tool to assess the spectral efficiency of the aforementioned adaptive transmission techniques over practical fading channels. Our newly derived expressions include several special cases that arise from the η–μ distribution, namely the Nakagami-m and the Hoyt distribution. Extensive numerical and computer simulation results are also presented that illustrate the proposed mathematical analysis.

Capacity of amplify-and-forward multi-hop relaying systems under adaptive transmission

The capacity of amplify-and-forward multi-hop relaying systems under different adaptive transmission schemes over Nakagami-m fading channels is considered. Accurate theoretical approximations for the capacity of these systems are derived in terms of the characteristic function of the reciprocal of the instantaneous received signal-to-noise ratio. An accurate theoretical approximation for the probability of outage is also obtained. The accuracy of the expressions obtained is verified by Monte Carlo simulation. It is shown that a system with optimal power and rate adaptation outperforms the system with truncated channel inversion adaptive technique. Systems employing optimal rate adaptation with constant power achieve almost the same capacity as those with optimal rate and power adaptation at large values of signal-to-noise ratio. However, the capacity performance of a system with the truncated channel inversion adaptive technique is better than the corresponding system employing optimal rate adaptation with constant power for small values of signal-to-noise ratio.

Effective capacity of delay-constrained cognitive radio in Nakagami fading channels

In this paper, we consider coexistence of secondary and primary users who share particular portions of the spectrum and propose a delay-constrained power and rate allocation scheme for the secondary user link. Secondary users are allowed to access the spectrum occupied by a primary user subject to satisfying interference-power limitations imposed by the primary user. Applying this limitation, we obtain the maximum arrival-rate supported by the secondary channel in Nakagami-m block-fading environment subject to satisfying a given statistical delay quality-of-service (QoS) constraint. In this respect, we derive the optimal rate and power adaptation policy that maximizes the effective capacity of the channel, and provide closed-form expressions for the power allocation and the effective capacity. In addition, we obtain closed-form expressions for the expenditure-power that is required at the secondary transmitter to achieve the above-mentioned capacity metric. Moreover, for comparison purposes, we consider two widely deployed power allocation strategies, namely, optimal power and rate allocation (opra) and channel inversion with fixed rate (cifr), and investigate the effective capacity of the channel under these power transmission techniques. Numerical simulations are conducted to corroborate our theoretical results.

Spectral efficiency of adaptive transmission and selection diversity on generalised fading channels

The spectral efficiency of L-branch selection diversity (SD) receiver with different adaptive transmission techniques operating over generalised-Gamma (GG) fading channels is studied. Novel expressions for important adaptive transmission techniques are obtained, namely optimal power and rate adaptation, optimal rate adaptation, channel inversion with fixed rate (CIFR) and truncated CIFR. Furthermore, simplified expressions for the capacities are obtained for SD reception in Nakagami-m as well as Weibull fading channels. The derived closed-from expressions extend previously published results to the GG fading model. Numerical results are given to demonstrate the usefulness of the theoretical approach.

Capacity of Correlated Generalized Gamma Fading With Dual-Branch Selection Diversity

The capacity of correlated generalized gamma (GG) fading channels with dual-branch selection diversity (SD) reception and channel side information (CSI) available at both the transmitter and the receiver is studied and analyzed. In particular, the capacity is evaluated under four adaptive transmission policies defined according to the operational CSI: 1) optimal power and rate adaptation (OPRA); 2) constant power with optimal rate adaptation (ORA); 3) channel inversion with fixed rate (CIFR); and 4) truncated CIFR (TIFR). Under these four adaptation policies, fast converging infinite series expressions for the capacity are derived and evaluated. Furthermore, for the simplifying cases of independent GG fading channels and/or single-channel reception (i.e., no diversity), closed-form expressions have been obtained. Previously published expressions are shown to be special cases of the derived expressions. Performance evaluation results obtained by means of numerical analysis clearly demonstrate the usefulness and accuracy of the analysis.

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.

End-to-end outage minimization in OFDM based linear relay networks

Multi-hop relaying is an economically efficient architecture for coverage extension and throughput enhancement in future wireless networks. OFDM, on the other hand, is a spectrally efficient physical layer modulation technique for broadband transmission. As a natural consequence of combining OFDM with multi-hop relaying, the allocation of per-hop subcarrier power and per-hop transmission time is crucial in optimizing the network performance. This paper is concerned with the end-to-end information outage in an OFDM based linear relay network. Our goal is to find an optimal power and time adaptation policy to minimize the outage probability under a long-term total power constraint. We solve the problem in two steps. First, for any given channel realization, we derive the minimum short-term power required to meet a target transmission rate. We show that it can be obtained through two nested bisection loops. To reduce computational complexity and signalling overhead, we also propose a sub-optimal algorithm. In the second step, we determine a power threshold to control the transmission on-off so that the long-term total power constraint is satisfied. Numerical examples are provided to illustrate the performance of the proposed power and time adaptation schemes with respect to other resource adaptation schemes.

On the communication over strong atmospheric turbulence channels by adaptive modulation and coding

The free-space optical (FSO) communications can provide any connectivity need at high-speed. However, an optical wave propagating through the atmosphere experiences the variation in amplitude and phase due to scintillation. To enable high-speed communication over strong atmospheric turbulence channels, we propose to transmit the encoded sequence over both FSO and wireless channels, feedback channel state information of both channels by RF-feedback, and adapt powers and rates so that total channel capacity is maximized. The optimum power adaptation policy maximizing total channel capacity is derived. We show significant spectral efficiency performance improvement by employing this approach. We further show that deep fades in the order 35 dB and above can be tolerated by proposed hybrid communication scheme.

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.

Spectral efficiency of maximum ratio combining (MRC) over slow fading with estimation errors

In this paper, we derive closed-form expressions for capacity statistics of the maximal ratio combining (MRC) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying flat Rayleigh fading that is also spatially independent. The combiner weights are assumed to be affected by Gaussian errors at the receiver. In particular, we derive the moment generating function (MGF), complementary cumulative distribution function (CDF) and the probability density function (PDF) of the capacity. Furthermore, we derive closed-form expressions for the system capacity when employing different adaptive transmission schemes such as (1) optimal power and rate adaptation (opra); (2) constant power with optimal rate adaptation (ora); and (3) channel inversion with fixed rate (cifr). Analytical results show accurately the impact of the channel estimation error on the achievable spectral efficiency.

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.

On the performance analysis of composite multipath/shadowing channels using the G-distribution

Composite multipath fading/shadowing environments are frequently encountered in different realistic scenarios. These channels are generally modeled as a mixture of Nakagami-m multipath fading and log-normal shadowing. The resulting composite probability density function (pdf) is not available in closed form, thereby making the performance evaluation of communication links in these channels cumbersome. In this paper, we propose to model composite channels by the G-distribution. This pdf arises when the log-normal shadowing is substituted by the inverse-Gaussian one. This substitution will prove to be very accurate for several shadowing conditions. In this paper we conduct a performance evaluation of single-user communication systems operating in a composite channel. Our study starts by deriving an analytical expression for the outage probability. Then, we derive the moment generating function of the G-distribution, hence facilitating the calculation of average bit error probabilities. We also derive analytical expressions for the channel capacity for three adaptive transmission techniques, namely, i) optimal rate adaptation with constant power, ii) optimal power and rate adaptation, and iii) channel inversion with fixed rate.

Spectral efficiency evaluation for selection combining diversity (SCD) scheme over slow fading

In this paper we derive closed-form expressions for the single-user capacity of selection combining diversity (SCD) 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 analysed: 1) optimal power and rate adaptation opra; 2) constant power with optimal rate adaptation ora; and 3) channel inversion with fixed rate cifr. Furthermore, we derive in this paper analytical results for capacity statistics including moment generating function (MGF), complementary cumulative distribution function (CDF) and probability density function (PDF). These statistics are valid for arbitrary number of receive antennas. Our numerical results show the effect of Gaussian channel estimation error on the achievable spectral efficiency.

Cross-Layer Rate and Power Adaptation Strategies for IR-HARQ Systems over Fading Channels with Memory: A SMDP-Based Approach

Incremental-redundancy hybrid automatic repeat- request (IR-HARQ) schemes are proposed in several wireless standards for increased throughput-efficiency and greater reliability. We investigate transmit power and modulation order adaptation strategies for the IR-HARQ schemes over correlated Rayleigh fading channels using semi-Markov decision process-based model. In order to jointly analyze physical layer and link layer, transmitter model incorporates a finite-size buffer that receives randomly varying traffic from a higher layer application. It is assumed that channel variations can be modeled with a first-order Markov chain. We show that the optimal transmission power and rate adaptation laws under buffering delay and packet overflow constraints can be obtained using the framework of semi-Markov decision process. We discuss three different adaptation models for the IR-HARQ schemes and compare their performances with the non-adaptive scheme. It is shown that unique optimal policy exists for each case and it can be computed using linear programming approach. This optimal policy is then applied for realistic channel fading and incoming traffic samples to evaluate its performance for both hard-decision and soft-decision decoding. Simulation results in general point out that substantial power savings can be achieved using adaptation and also if the transmission-delay requirements are relaxed.

Impact of Spatial Fading Correlation and Keyhole on the Capacity of MIMO Systems with Transmitter and Receiver CSI

This paper investigates the impact of spatial fading correlation and keyhole (pinhole) condition on the capacity of multiple-input multiple-output (MIMO) channels when instantaneous channel state information (CSI) is available at the transmitter and receiver sides. A separable correlation model is considered, whereby spatial fading correlation is accounted for at either or at both sides of the collocated MIMO wireless channel. Two extreme scenarios of a double scattering environment are analyzed: (i) an extremely rich scattering environment corresponding to a conventional semi-correlated Rayleigh fading channel and (ii) a double-correlated rank-deficient keyhole channel with a single degree of freedom. In the case of semi-correlated Rayleigh fading, the capacity expressions are derived for two types of correlation structures among the transmitting or the receiving antennas, namely, a constant correlation model and an arbitrary correlation model, the latter being induced by a full-rank Hermitian covariance matrix with non-repeating distinct eigenvalues. On the other hand, the capacity expressions pertaining to the double-correlated keyhole channel are derived given arbitrary Hermitian covariance matrices at the transmitter and the receiver. For all channel types and correlation structures, closed-form expressions for the capacity of the eigen-mode optimal power and rate adaptation policy as well as for the sub-optimal eigen-mode channel inversion and its truncated variant are derived. Monte Carlo simulations are also carried out thereby upholding our theoretical analysis.

Optimum Power and Rate Adaptation for MQAM in Rayleigh Flat Fading With Imperfect Channel Estimation

We derive an optimum power and rate adaptation for maximizing the spectral efficiency based on an imperfect channel estimate and subject to average power and instantaneous bit error rate (BER) constraints for multilevel quadrature amplitude modulation (MQAM) over Rayleigh flat-fading channels. The optimal solution is derived for continuous- and discrete-rate adaptation and is expressed in terms of a specific bounded function that is the solution of a nonlinear equation and cannot be expressed in a closed mathematical form. The optimum power adaptation for the continuous rate is shown to be a generalization of water pouring for that function. It is also shown that the conventional water-pouring (with bias) strategy for power adaptation in the continuous-rate condition is a suboptimum solution of the general optimization problem, and it tends to the optimal solution as the correlation coefficient between the true channel gain and its estimate tends to one. We also show that less than 1 dB power is lost by using discrete-rate MQAM with only six different signal constellations compared to the continuous-rate adaptation with an unconstrained constellation size.

On the capacity of generalized-k fading channels

This letter investigates the capacity of generalized-k fading channels. This very general model describes accurately composite multipath/shaodwing fading channels which are widely encountered in real-world environments. We derive closed-form expressions for three adaptive transmission techniques, namely, i) optimal rate adaptation with constant power, ii) optimal power and rate adaptation, and iii) channel inversion with fixed rate. The analytical expressions obtained match perfectly the results obtained by computer simulations. These expressions provide a good tool to assess the spectral efficiency of the aforementioned adaptive transmission techniques over composite channels.

Capacity of MIMO Rician fading channels with transmitter and receiver channel state information

This paper investigates the capacity of multiple- input multiple-output (MIMO) wireless communication systems when instantaneous channel state information (CSI) is available at both the transmitter and the receiver in a line-of-sight Rician fading environment. Specifically, an infinite series representation for the ergodic capacity of MIMO channels subject to uncorrected Rician fading (URiF) is derived, assuming both transmitter and receiver CSI. The ergodic capacity and its associated outage probability are expressed as a function of a cutoff value capturing the optimal power allocation scheme. Moreover, an equation for evaluating the cutoff value using standard numerical search techniques is derived, along with closed-form expressions for the capacity of the URiF MIMO channel when the so-called eigen-mode channel inversion technique and its truncated variant are implemented. We then provide numerical results showing the effects of Ricianness on the capacity of the eigen-mode optimal power and rate adaptation, and the sub-optimal channel inversion techniques and compare the achievable spectral efficiencies with and without channel knowledge at the transmitter thereby highlighting the capacity gains enabled by channel side information in a Rician fading environment.

Power and Rate Adaptation Based on Imperfect Channel Estimation over MIMO Fading Channels

We derive the optimum power and rate adaptation for maximizing the spectral efficiency of Multilevel Quadrature Amplitude Modulation (MQAM) over Multiple-Input Multiple-Output (MIMO) fading channels based on imperfect channel estimation. We use Pilot Symbol Assisted Modulation (PSAM)-based Minimum Mean Square Error (MMSE) channel estimator, and show that the optimum power adaptation on each sub-channel is a generalization of water-filling. We also show that the conventional water-filling (with bias) strategy for power adaptation is a suboptimum solution of the general optimization problem and it tends to the optimal solution as the correlation coefficients between eigenvalues of the true channel matrix and its estimate tend to one.