Reduction of peak-to-average power ratio of OFDM system using acompanding technique

A companding technique is proposed to reduce the peak-to-average-power ratio of the orthogonal frequency division multiplexing (OFDM) signal in this paper. The probability density function of the amplitude of the OFDM signal is determined. Because of the Gaussian distribution of the OFDM signal, the companding technique can be quite effective, since a large OFDM signal only occurs infrequently. The peak-to-average power ratio of an OFDM system and the optimal companding coefficient are determined in this paper. The symbol error rate of the systems after the companding is derived. The performances of the system with and without the companding are also compared     

High-resolution source coding for non-difference distortionmeasures: multidimensional companding

Entropy-coded vector quantization is studied using high-resolution multidimensional companding over a class of nondifference distortion measures. For distortion measures which are “locally quadratic” a rigorous derivation of the asymptotic distortion and entropy-coded rate of multidimensional companders is given along with conditions for the optimal choice of the compressor function. This optimum compressor, when it exists, depends on the distortion measure but not on the source distribution. The rate-distortion performance of the companding scheme is studied using an asymptotic expression for the rate-distortion function which parallels the Shannon lower bound for difference distortion measures. It is proved that the high-resolution performance of the scheme is arbitrarily close to the rate-distortion limit for large quantizer dimensions if the compressor function and the lattice quantizer used in the companding scheme are optimal, extending an analogous statement for entropy-coded lattice quantization and MSE distortion. The companding approach is applied to obtain a high-resolution quantizing scheme for noisy sources     

Reduction of PAPR of OFDM Signals Using Nonlinear Companding Transform

In this paper, we propose and evaluate a novel nonlinear companding transform (NCT) scheme for peak-to-average power ratio (PAPR) reduction in orthogonal frequency division multiplexing (OFDM) systems. The key idea of the proposed scheme is to transform the original Gaussian-distributed OFDM signals into a specific statistics form, whose target probability density function is defined by a piecewise function with an inflexion point. By properly choosing the transform parameters, this scheme can enable more flexibility and freedom in the companding form so that a favorable tradeoff between PAPR reduction and bit error rate (BER) performance can be achieved. Moreover, compared to existing NCT techniques, this scheme dramatically decreases the impact of companding distortion on the BER performance to reach a given PAPR level. The analytical expressions regarding the achievable transform gain in PAPR, complementary cumulative density function, attenuation coefficient, and selection criteria of transform parameters are derived. Simulation results justify the significance and accuracy of the analytical expressions presented.     

A novel criterion for designing of nonlinear companding functions for peak-to-average power ratio reduction in multicarrier transmission systems

Nonlinear companding transform is a promising technique for the peak-to-average power ratio (PAPR) reduction in multicarrier transmission systems. However, conventional hard piecewise companding schemes often along with serious nonlinear distortion or complex companding parameters optimization embarrassment. In this paper, a novel designing criterion of nonlinear companding functions with more effective system performance is proposed. By transforming the Gaussian-distributed multicarrier signals into desirable statistics forms, we show that the smooth and differentiable concave probability distribution function of companded signals can obtain a better PAPR reduction and less out-of-band radiation as well as more simple companding parameters optimization than the traditional piecewise companding schemes. A detailed theoretical analysis and discussion is formulated, and then based on the analysis results, a novel trigonometric function companding scheme is presented and evaluated. Numerical results demonstrate that the companding schemes which consistent with the proposed criterion may significantly outperform conventional schemes by choosing the companding form and parameters appropriately.     

非线性自动压扩的开关电流电路行为级建模方法

提出了一种新的基于非线性压扩函数自动构造的开关电流电路行为级建模方法,从而简化电路的建模和仿真.与原有的建模方法相比,该方法不仅可以对模型的误差分布进行有效地调控,而且能够降低模型的误差.为了验证本文所提出的行为级建模方法,对几种开关电流电路进行了建模和模拟试验.     

Bhattacharyya bound, cutoff rate, and constellation design for thecompanding channel

In modern voiceband data communication, the received signal is subject to nonlinear quantization noise due to companding. Under certain conditions, this quantization noise may become dominant and cause serious degradation in performance. In this paper, we first calculate the Bhattacharyya bound on the error probability between two signal points, which we then use to obtain some insight into the effects of the companding channel. Next, we compute the cutoff rate, and then use these results to design new “optimal” signal constellations for the companding channel. The bound, cutoff rate, and new constellations are computed assuming a signal-dependent noncircular Gaussian channel transition density. In addition, we obtain “optimal” a priori probabilities for this channel     

降低OFDM系统峰均比的压扩算法对系统误码率的影响

讨论了降低OFDM系统峰均比所采用的基于数值变换的压缩扩张算法,给出了几种压扩函数,推导出了使用压扩变换后OFDM系统的误码率公式,由此分析了压扩算法对OFDM系统性能的影响。可以看出,该算法不仅能有效降低OFDM系统的峰均比,而且能降低系统的误码率。仿真结果表明,本文给出的公式较好地反映了使用该算法后OFDM系统的误码性能。     

Optimum Weighted PCM for Speech Signals

Weighted digital modulation schemes which provide bit error probabilities matched to the PCM bits with respect to their sensitivity to digital errors are analyzed. The channel is additive, white Gaussian. The PCM system has arbitrary code, companding law and input signal density function. Especially optimum weighted PSK/PCM and QAM/PCM are given for speech signals. The average channel signal to noise ratio is kept constant when schemes are compared. We obtain a channel signal to noise ratio gain in threshold extension of 2 dB for standard 8 bit PCM. The performance of suboptimum schemes, where the number of different bit error probability levels are smaller than the number of PCM bits are also studied. Two levels per 8 bit PCM word yield more than half of the achievable gain (in dB) and 4 levels is almost equal to optimum.     

Asymptotical performance of M-ary and binary signals overmultipath/multichannel Rayleigh and Rician fading

This paper presents a general framework for computing the asymptotic error probability (i.e., at high average SNRs) of M-ary and binary signaling schemes over Rician and Rayleigh fading diversity channels. A general theorem (Theorem 1) relates the asymptotic error rate of multipath and multichannel receivers (over AWGN, ISI free channels) to the multidimensional integral of the conditional error probability. Two other theorems are presented for the particular cases where the conditional error probability is a function of the sum of received SNRs (Theorem 2) or received amplitudes (Theorem 3). Theorems 2 and 3 are related for linear coherent systems, and closed form expressions are obtained for equal gain combining systems. Detection structures for typical diversity schemes (coherent/noncoherent maximal ratio and equal gain combining, and quadratic noncoherent combining) are considered. We analyze the asymptotic error rates of some M-ary signaling schemes (MPSK/MPAM with Kth order diversity and orthogonal signals with K=1 and with coherent and noncoherent detection). Binary signaling is also considered in our study     

Asymptotically optimal block quantization

In 1948 W. R. Bennett used a companding model for nonuniform quantization and proposed the formulaD : = : frac{1}{12N^{2}} : int : p(x) [ É(x) ]^{-2} dxfor the mean-square quantizing error whereNis the number of levels,p(x) is the probability density of the input, andE prime(x) is the slope of the compressor curve. The formula, an approximation based on the assumption that the number of levels is large and overload distortion is negligible, is a useful tool for analytical studies of quantization. This paper gives a heuristic argument generalizing Bennett's formula to block quantization where a vector of random variables is quantized. The approach is again based on the asymptotic situation whereN, the number of quantized output vectors, is very large. Using the resulting heuristic formula, an optimization is performed leading to an expression for the minimum quantizing noise attainable for any block quantizer of a given block sizek. The results are consistent with Zador's results and specialize to known results for the one- and two-dimensional cases and for the case of infinite block length(k rightarrow infty). The same heuristic approach also gives an alternate derivation of a bound of Elias for multidimensional quantization. Our approach leads to a rigorous method for obtaining upper bounds on the minimum distortion for block quantizers. In particular, fork = 3we give a tight upper bound that may in fact be exact. The idea of representing a block quantizer by a block "compressor" mapping followed with an optimal quantizer for uniformly distributed random vectors is also explored. It is not always possible to represent an optimal quantizer with this block companding model.     

抑制LOFDM系统PAPR非线性压扩变换算法

针对网格正交频分复用(LOFDM,lattice OFDM)系统具有较传统OFDM系统更高峰均功率比(PAPR,peak-to-average power ratio)的问题,在将传统非线性压扩变换应用于LOFDM系统的同时研究并分析了一种新的基于原信号统计分布特性的连续可导非线性压扩算法。该算法从原信号的渐进高斯分布特性出发并对原信号的幅度分布函数进行截断逼近,在保持平均功率不变的条件下,将压扩后的信号限制在与原信号分布特性一致的特定范围内,使压扩后的信号在保持其原有分布特性的同时,能更大程度改善系统PAPR和误比特(BER,biterror ratio)性能。理论分析和仿真实验表明,所提出的算法性能要显著优于传统非线性压扩算法。     

OFDM link performance with companding for PAPR reduction in the presence of non-linear amplification

Use of companding for peak-to-average-power ratio (PAPR) control is explored for a link involving a nonlinear transmit power amplifier with orthogonal frequency division multiplexing (OFDM). Specifically, the objective of the study was to determine if companding using u-law compression/expansion at the transmitter/receiver, respectively, provides end-to-end performance gains relative to a system without companding. We consider the use of companding to ameliorate the impact of nonlinearities in the transmit amplifier. In the absence of companding, transmitter operation near saturation raises the signal level at the receiver but, because of the nonlinearities in the amplifier response, also results in distortion that impacts overall link performance. As the transmit power is backed-off from saturation, amplifier distortion is reduced, but error components due to lower SNR at the receiver become more significant. When companding is introduced in the system, the system is able to operate closer to saturation without substantial transmit distortion. However, requisite expansion of the compressed signal at the receiver yields noise amplification which can counteract any of the performance gains that would otherwise accrue from the increased SNR at the receiver. At issue is whether or not operating conditions exist (e.g., backoff, SNR, amplifier linearity model, etc) for which companding enhances the end-to-end performance relative to the link performance without companding. System simulation models were employed using Rapp's nonlinear power amplification models, where average symbol distance errors were used as performance metrics. We found that companding can provide very modest performance gains in comparison to systems that do not employ companding. Performance trends were corroborated in a hardware testbed with an amplifier chain, where average bit error rates were experimentally determined.     

A low‐complexity companding technique using Padé approximation for PAPR reduction of an OFDM system

Orthogonal Frequency Division Multiplexing (OFDM) systems have become the most promising wireless communication systems in the recent years. For OFDM systems, there is one major drawback, which is the high peak‐to‐average power ratio (PAPR). Companding techniques have been frequently proposed to reduce PAPR. Exponential companding technique offers efficient PAPR reduction with a low bit error rate (BER). However, the exponential companding technique is difficult to implement. This paper utilizes the Padé approximation to simplify the exponential companding technique. The simulation results demonstrate that the proposed companding technique offers the same performance results as those of the exponential companding technique, while Additive White Gaussian Noise (AWGN) or multipath fading channel is considered. Further, the hardware implementation results show that the complexity of the proposed companding technique is less than that of the exponential companding technique. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance enhancement of SC-FDMA systems using a companding technique

In this paper, a companding technique is proposed to effectively reduce the peak-to-average power ratio (PAPR) in single-carrier frequency division multiple access (SC-FDMA) systems. By companding the samples with large amplitudes, while enhancing those with small amplitudes, a significant reduction in the PAPR can be achieved. The performance of the proposed SC-FDMA with companding system is studied and compared with that of the standard SC-FDMA system. Simulation results show that the SC-FDMA with companding system has a lower PAPR when compared with the conventional SC-FDMA system, while the complexity of the system slightly increases. Results also reveal that the companding coefficient must be chosen carefully in order to limit the PAPR without introducing degradations into the bit error rate performance.     

Probability of error of some adaptive pattern-recognition machines

A simple taught pattern-recognition machine for detecting an unknown, fixed, randomly occurring pattern is derived using a Bayes' approach, and its probability of error is analyzed. It is shown that with probability one, the machine converges to the optimal detector (a matched filter) for the unknown pattern, that the asymptotic decision function statistics are Gaussian, and that for an important class of problems, the central-limit theorem can be invoked to calculate the approximate probability of error at any stage of convergence. An untaught adaptive pattern-recognition machine may be made from the taught machine by using its own output instead of a teacher, and the asymptotic probability of error of this device is derived. It is shown that it does not converge to a matched filter for the unknown pattern, but that in any practical case it performs almost as well. Finally, the results of an experimental simulation of both machines are presented as curves of the relative frequency of error vs. time, and are compared with the values calculated by theory.     

Exponential companding technique for PAPR reduction in OFDM systems

In this paper, a new nonlinear companding technique, called "exponential companding", is proposed to reduce the high Peak-to-Average Power Ratio (PAPR) of Orthogonal Frequency Division Multiplexing (OFDM) signals. Unlike the /spl mu/-law companding scheme, which enlarges only small signals so that increases the average power, the schemes based on exponential companding technique adjust both large and small signals and can keep the average power at the same level. By transforming the original OFDM signals into uniformly distributed signals (with a specific degree), the exponential companding schemes can effectively reduce PAPR for different modulation formats and sub-carrier sizes. Moreover, many PAPR reduction schemes, such as /spl mu/-law companding scheme, cause spectrum side-lobes generation, but the exponential companding schemes cause less spectrum side-lobes. Computer simulations, which consider a baseband OFDM system with Additive White Gaussian Noise (AWGN) channels and a Solid State Power Amplifier (SSPA), show that the proposed exponential companding schemes can offer better PAPR reduction, Bit Error Rate (BER), and phase error performance than the /spl mu/-law companding scheme.     

Companding with junction f.e.t.

As companding elements, field-effect transistors have advantages over p?n diodes; they have suitably shaped i/v characteristics which are controllable by gate bias. Tests show that a departure from linearity of compressor and expander in cascade can be corrected to have an error of less than 1%.     

S.O. Rice's contributions to Shannon theory

The contributions of S.O. Rice to Shannon's formulations in communication theory are discussed. In `Communication in the presence of noise-Probability of error for two encoding schemes' (see Bell Syst. Tech. J., vol.29, p.60-93, Jan. 1950) Rice considered two explicit construction schemes for choosing the transmitted signals of duration T and exhibited an exact formula for the probability of error in the decoded messages. Rice evaluated these unwieldy expressions and presented tables and curves showing the trade-off between rate, delay, and error probability. He obtained asymptotic expressions for the error probability for large delay, and showed that with his scheme for choosing the signals, Shannon's results could be obtained. He recognized from his numerical calculations that the error probability seemed to approach zero much more rapidly than this and that, in his asymptotics, he had evidently made approximations that might one day be improved     

IGCC for PAPR Reduction in OFDM Systems Over the Nonlinearity of SSPA and Wireless Fading Channels

High peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems seriously impacts power efficiency in radio frequency section due to the nonlinearity of high-power amplifiers. In this article, an improved gamma correction companding (IGCC) is proposed for PAPR reduction and investigated under multipath fading channels. It is shown that the proposed IGCC provides a significant PAPR reduction while improving power spectral levels and error performances when compared with the previous gamma correction companding. IGCC outperforms existing companding methods when a nonlinear solid-state power amplifier (SSPA) is considered. Additionally, with the introduction of \(\alpha , \beta , \gamma \), and \(\varDelta \) parameters, the improved companding can offer more flexibility in the PAPR reduction and therefore achieves a better trade-off among the PAPR gain, bit error rate (BER), and power spectral density (PSD) performance. Moreover, IGCC improves the BER and PSD performances by minimizing the nonlinear companding distortion. Further, IGCC improves signal-to-noise ratio (SNR) degradation (\(\varDelta _{\mathrm{SNR}}\)) and total degradation performances by 12.2 and 12.8 dB, respectively, considering an SSPA with input power back-off of 3.0 dB. Computer simulation reveals that the performances of IGCC are independent of the modulation schemes and works with arbitrary number of subcarriers (N), while it does not increase computational complexity when compared with the existing companding schemes used for PAPR reduction in OFDM systems.     

A comprehensive performance analysis of relay-aided CDMA communications over dissimilar fading channels

In this paper, bit error probability (BEP), outage probability (OP) and channel capacity (CC) of direct-sequence code-division multiple access systems with amplify-and-forward relaying are presented for different fading scenarios. In the first scenario, the source-destination link is assumed to experience Rayleigh fading while it is subject to Nakagami-m fading in the second scenario. The source-relay and relay-destination channels are considered to have Nakagami-m fading conditions in two scenarios. First, analytical expressions for the end-to-end probability density function (PDF) are derived by using the convolution integral. Then, BEP, OP and CC are obtained based on these PDFs in terms of infinite series. Truncation error analyses are presented for different parameter values in order to show that truncation error arising from the infinite series is negligible. Simple and easy-to-compute asymptotic expressions are also introduced for BEP and OP in order to simplify the performance analysis in high signal-to-noise ratio region. Simulation results are provided to show the accuracy of the proposed approximate and asymptotic expressions.