Joint variable threshold M-QAM and ARQ for Nakagami-m fading channel with feedback delay

In this paper, we develop a cross-layer combining of adaptive M-ary quadrature amplitude modulation (M-QAM) and automatic repeat request (ARQ) protocol, which adapts the threshold of rate-region boundaries to the variation of feedback delay over the Nakagami-m fading (NMF) channels. We derive a threshold adaptation scheme to reduce the effect of the feedback delay on bit error rate (BER). Numerical results reveal that MQAM with threshold adaptation is more reliable to the feedback delay than M-QAM with fixed thresholds. When we combine the proposed scheme with ARQ, the enhanced BER can lower the probability of packet loss and reduce the number of packet retransmissions.     

Power adaptation for BPSK signaling with average and peak power constraints in Rayleigh fading channels

We consider power adaptation strategies for binary phase-shift keying signals in Rayleigh fading channels under the assumption that channel state information is provided at both the transmitter and the receiver. We first derive a closed-form expression for the optimal power adaptation that minimizes average bit-error rate (BER) subject to average and peak transmission power constraints. Then, we analyze the average BER for channel inversion power adaptation with the same constraints. Our results show that the performance difference between the optimal power adaptation and the channel inversion becomes negligibly small as available average transmission power increases and/or peak-to-average power ratio decreases. We also find that an optimal peak-to-average power ratio exists that minimizes the average BER in the channel inversion scheme.     

Effect of channel estimation error on M-QAM BER performance inRayleigh fading

We determine the bit-error rate (BER) of multilevel quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates, Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables, our exact BER expression has a particularly simple form that involves just a few finite-range integrals. This approach can be used to compute the BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1-dB degradation in average signal-to-noise ratio and combined amplitude-phase estimation error leads to 2.5-dB degradation for the parameters we consider     

Practical Multiuser Diversity With Outdated Channel Feedback

Inspired by the information theoretic results concerning multiuser diversity, we address practical issues in implementing multiuser diversity in a multiple access wireless setting. Considering a channel-assigning strategy that assigns the channel only to the user with the best instantaneous SNR [3], our emphasis is on the effects of channel feedback delay in downlink transmissions. A finite set of M-ary quadrature amplitude modulation (M-QAM) constellations is adopted and a constant transmit power is assumed in this practical multiuser adaptive modulation scheme. Based on the closed-form expressions for average bit error rate (BER) and average data rate, we illustrate the impact of channel feedback delay on the achievable multiuser diversity gain with the number of users. Simple and accurate asymptotic approximations are also provided in the limit of large numbers of users. Focusing on different applications, we propose two optimization criteria for the switching thresholds, based on either an average BER, or an outage probability constraint. Two novel constant power, variable rate M-QAM schemes that are less sensitive to feedback delay are proposed using the optimal switching thresholds, which are derived to maximize the average data rate subject to these two constraints, respectively. To obtain a certain degree of fairness among the users, we also consider a fair channel-assigning strategy that assigns the channel to only the user with the greatest normalized SNR.     

Variable-rate variable-power MQAM for fading channels

We propose a variable-rate and variable-power MQAM modulation scheme for high-speed data transmission over fading channels. We first review results for the Shannon capacity of fading channels with channel side information, where capacity is achieved using adaptive transmission techniques. We then derive the spectral efficiency of our proposed modulation. We show that there is a constant power gap between the spectral efficiency of our proposed technique and the channel capacity, and this gap is a simple function of the required bit-error rate (BER). In addition, using just five or six different signal constellations, we achieve within 1-2 dB of the maximum efficiency using unrestricted constellation sets. We compute the rate at which the transmitter needs to update its power and rate as a function of the channel Doppler frequency for these constellation sets. We also obtain the exact efficiency loss for smaller constellation sets, which may be required if the transmitter adaptation rate is constrained by hardware limitations. Our modulation scheme exhibits a 5-10-dB power gain relative to variable-power fixed-rate transmission, and up to 20 dB of gain relative to nonadaptive transmission. We also determine the effect of channel estimation error and delay on the BER performance of our adaptive scheme. We conclude with a discussion of coding techniques and the relationship between our proposed modulation and Shannon capacity     

Effect of channel-estimation error on QAM systems with antenna diversity

This paper studies the effect of channel estimation error and antenna diversity on multilevel quadrature amplitude modulation (M-QAM) systems over Rayleigh fading channels. Based on the characteristic function method, a general closed-form bit-error rate (BER) for M-QAM systems is presented. The effect of the inaccurate channel estimation on the performance for pilot-symbol-assisted modulation M-QAM systems with antenna diversity is investigated. Simulation results for M-QAM (M = 4, 16, 64, 256, etc.) show that the analytical method can accurately estimate the system performance. Moreover, numerical results show that with the antenna-diversity technique, the BER performance improves significantly, especially in perfect channel-estimation cases. It is also found that the channel-estimation error limits the benefit of antenna diversity. By increasing the length of the channel estimator and the amplitude of the pilot symbol, more accurate channel estimation can be achieved, so that the BER performance is improved.     

Orthogonal space-time block coded rate-adaptive modulation with outdated feedback

Abstract-Channel state information (CSI) at the transmitter can be used to adapt transmission rate or antenna gains in multi-antenna systems. We propose a rate-adaptive M-QAM scheme equipped with orthogonal space-time block coding with simple outdated, finite-rate feedback over independent flat fading channels. We obtain closed-form expressions for the average BER and throughput for our scheme, and analyze the effects of possibly delayed feedback on the performance gains. We derive optimal switching thresholds maximizing the average throughput under average and outage BER constraints with outdated feedback. Our numerical results illustrate the immunity of our optimal thresholds to delayed feedback.     

Threshold-Based Substream Selection for Closed-Loop Spatial Multiplexing

We propose a low-complexity closed-loop spatial multiplexing method with limited feedback over multi-input-multi-output (MIMO) fading channels. The transmit adaptation is simply performed by selecting transmit antennas (or substreams) by comparing their signal-to-noise ratios to a given threshold with a fixed nonadaptive constellation and fixed transmit power per substream. We analyze the performance of the proposed system by deriving closed-form expressions for spectral efficiency, average transmit power, and bit error rate (BER). Depending on practical system design constraints, the threshold is chosen to maximize the spectral efficiency (or minimize the average BER) subject to average transmit power and average BER (or spectral efficiency) constraints, respectively. We present numerical and Monte Carlo simulation results that validate our analysis. Compared to open-loop spatial multiplexing and other approaches that select the best antenna subset in spatial multiplexing, the numerical results illustrate that the proposed technique obtains significant power gains for the same BER and spectral efficiency. We also provide numerical results that show improvement over rate-adaptive orthogonal space-time block coding, which requires highly complex constellation adaptation. We analyze the impact of feedback delay using analytical and Monte Carlo approaches. The proposed approach is arguably the simplest possible adaptive spatial multiplexing system from an implementation point of view. However, our approach and analysis can be extended to other systems using multiple constellations and power levels.     

On the Performance of the MIMO Zero-Forcing Receiver in the Presence of Channel Estimation Error

By employing spatial multiplexing, multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. Zero-forcing (ZF) detection is a simple and effective technique for retrieving multiple transmitted data streams at the receiver. However the detection requires knowledge of the channel state information (CSI) and in practice accurate CSI may not be available. In this letter, we investigate the effect of channel estimation error on the performance of MIMO ZF receivers in uncorrelated Rayleigh flat fading channels. By modeling the estimation error as independent complex Gaussian random variables, tight approximations for both the post-processing SNR distribution and bit error rate (BER) for MIMO ZF receivers with M-QAM and M-PSK modulated signals are derived in closed-form. Numerical results demonstrate the tightness of our analysis     

Variable rate and variable power MQAM system based on bayesian bit error rate and channel estimation techniques

The impact of inaccurate channel state information at the transmitter for a variable rate variable power multilevel quadrature amplitude modulation (VRVP-MQAM) system over a Rayleigh flat-fading channel is investigated. A system model is proposed with rate and power adaptation based on the estimates of instantaneous signal-to-noise ratio (SNR) and bit error rate (BER). A pilot symbol assisted modulation scheme is used for SNR estimation. The BER estimator is derived using a maximum a posteriori approach and a simplified closed-form solution is obtained as a function of only the second order statistical characterization of the channel state imperfection. Based on the proposed system model, rate and power adaptation is derived for the optimization of spectral efficiency subject to an average power constraint and an instantaneous BER requirement. The performance of the VRVP-MQAM system under imperfect channel state information (CSI) is evaluated. We show that the proposed VRVP-MQAM system that employs optimal solutions based on the statistical characterization of CSI imperfection achieves a higher spectral efficiency as compared to an ideal CSI assumption based method.     

An adaptive modulation scheme for simultaneous voice and datatransmission over fading channels

We propose a new adaptive modulation technique for simultaneous voice and data transmission over fading channels and study its performance. The proposed scheme takes advantage of the time-varying nature of fading to dynamically allocate the transmitted power between the inphase (I) and quadrature (Q) channels. It uses fixed-rate binary phase shift keying (BPSK) modulation on the Q channel for voice, and variable-rate M-ary amplitude modulation (M-AM) on the I channel for data. For favorable channel conditions, most of the power is allocated to high rate data transmission on the I channel. The remaining power is used to support the variable-power voice transmission on the Q channel. As the channel degrades, the modulation gradually reduces its data throughput and reallocates most of its available power to ensure a continuous and satisfactory voice transmission. The scheme is intended to provide a high average spectral efficiency for data communications while meeting the stringent delay requirements imposed by voice. We present closed-form expressions as well as numerical and simulation results for the outage probability, average allocated power, achievable spectral efficiency, and average bit error rate (BER) for both voice and data transmission over Nakagami-m fading channels. We also discuss the features and advantages of the proposed scheme. For example, in Rayleigh fading with an average signal-to-noise ratio (SNR) of 20 dB, our scheme is able to transmit about 2 bits/s/Hz of data at an average BER of 10 ^-5 while sending about 1 bit/s/Hz of voice at an average BER of 10^-2     

Effect of Channel Estimation Errors on M -QAM With MRC and EGC in Nakagami Fading Channels

We study the effect of imperfect channel estimation (ICE) on the error probability performance of M-level quadrature amplitude modulation ( M-QAM) with maximal-ratio combining and equal-gain combining diversity formats in Nakagami fading channels. We provide a novel formulation of the bit-error rate (BER) of M-QAM with ICE in terms of the signal constellation-dependent effective signal-to-noise ratios (SNRs) or amplitudes, which allows us to derive the general, accurate, and easy-to-evaluate BER formulas for square and rectangular diversity M-QAM with channel estimation errors. Our result shows that the performance loss caused by ICE may be manifested by the signal decision space distortion and a scaling of the effective SNR. Using our analytical result, we evaluate the performance of M-QAM with pilot-symbol assisted modulation and present some insightful findings     

Analysis and optimization of pilot symbol-assisted Rake receivers for DS-CDMA systems

The effect of imperfect channel estimation (CE) on the performance of pilot-symbol-assisted modulation (PSAM) and MRC Rake reception over time- or frequency-selective fading channels with either a uniform power delay profile (UPDP) or a nonuniform power delay profile (NPDP) is investigated. For time-selective channels, a Wiener filter or linear minimum mean square error (LMMSE) filter for CE is considered, and a closed-form asymptotic expression for the mean square error (MSE) when the number of pilots used for CE approaches infinity is derived. In high signal-to-noise ratio (SNR), the MSE becomes independent of the channel Doppler spectrum. A characteristic function method is used to derive new closed-form expressions for the bit error rate (BER) of Rake receivers in UPDP and NPDP channels. The results are extended to two-dimensional (2-D) Rake receivers. The pilot-symbol spacing and pilot-to-data power ratio are optimized by minimizing the BER. For UPDP channels, elegant results are obtained in the asymptotic case. Furthermore, robust spacing design criteria are derived for the maximum Doppler frequency.     

Degrees of freedom in adaptive modulation: a unified view

We examine adaptive modulation schemes for flat-fading channels where the data rate, transmit power, and instantaneous BER are varied to maximize spectral efficiency, subject to an average power and BER constraint. Both continuous-rate and discrete-rate adaptation are considered, as well as average and instantaneous BER constraints. We find the general form of power, BER and data rate adaptation that maximizes spectral efficiency for a large class of modulation techniques and fading distributions. The optimal adaptation of these parameters is to increase the power and data rate and decrease the BER as the channel quality improves. Surprisingly, little spectral efficiency is lost when the power or rate is constrained to be constant. Hence, the spectral efficiency of adaptive modulation is relatively insensitive to which degrees of freedom are adapted     

Exact BER for M-QAM with MRC and Imperfect Channel Estimation in Rician Fading Channels

In this paper, we study the effect of imperfect channel estimation (ICE) on the performance of M-level quadrature amplitude modulation (M-QAM) with maximum ratio combining (MRC) and pilot-symbol assisted modulation (PSAM) in generalized Rician fading channels. By expressing the bit error rate (BER) of MRC diversity M-QAM in terms of the distribution of new decision variables, we derive novel, exact, and easy-to-evaluate BER expressions for diversity M-QAM with channel estimation errors. Our results include versatile system and fading channel parameters (e.g., arbitrary spatial and temporal correlation patterns among the diversity branches), and are valid for arbitrary linear channel estimators and square and rectangular M -QAM with different constellation sizes. In addition, we evaluate the performance of minimum mean-squared error (MMSE)- and sinc-interpolator-based channel estimators with PSAM, and provide some new insights into the performance of M-QAM with PSAM in generalized fading channels     

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.     

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     

采用两条支路分集接收的相关瑞利衰落信道容量

本文研究采用两条支路最大比合并(MRC)或选择合并(SC)分集接收的相关瑞利衰落信道理论容量推导恒定发射功率自适应M进制正交幅度调制(M-QAM)的频谱效率,并将它们与独立同分布瑞利信道理论容量进行比较,其结果对收发信机之间无视距分量路径、接收机上分集天线之间的距离小于半个波长的无线通信系统设计具有指导作用.     

Model-based pilot and data power adaptation in psam with periodic delayed feedback

We consider the optimum design of pilot-symbolassisted modulation (PSAM) schemes with feedback. The received signal is periodically fed back to the transmitter through a noiseless delayed link and the time-varying channel is modeled as a Gauss-Markov process. We optimize a lower bound on the channel capacity which incorporates the PSAM parameters and Kalman-based channel estimation and prediction. The parameters available for the capacity optimization are the data power adaptation strategy, pilot spacing and pilot power ratio, subject to an average power constraint. Compared to the optimized open-loop PSAM (i.e., the case where no feedback is provided from the receiver), our results show that even in the presence of feedback delay, the optimized power adaptation provides higher information rates at low signal-to-noise ratios (SNR) in mediumrate fading channels. However, in fast fading channels, even the presence of modest feedback delay dissipates the advantages of power adaptation.     

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.