Non-Symmetric Decompanding for Improved Performance of Companded OFDM Systems

Recent work in literature suggests the use of companding transforms to reduce the peak to average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) systems. However, previous performance evaluations assume the availability of infinite bandwidth. In bandlimited conditions, the performance deteriorates as a result of filtering out the out-of-band radiation (OBR). In this letter, we first study the effect of filtering on the performance of various companding techniques. We further propose a simple yet very effective method to overcome this performance degradation. The essential idea is to use companding and decompanding transforms which are not exact inverse of each other. Simulation results show that the proposed scheme significantly outperforms the previous schemes under more realistic channel conditions.     

Hybrid Zadoff‐Chu and multilateral piecewise exponential companding transform–based PAPR reduction technique in OFDM systems

The orthogonal frequency‐division multiplexing (OFDM) is a multicarrier modulation system that is used to transmit the large volume of data to the receiver. Reducing the peak‐to‐average power ratio (PAPR) in OFDM system is one of the demanding and crucial task in recent days. For this reason, various precoding and companding mechanisms are developed in the traditional works, but it remains with the limitations of increased complexity, reduced performance, and nonlinear distortion. The reduction of PAPR is achieved by minimizing the companding distortion with the enhancement of the bit error rate (BER) performance significantly. Then, in order to avoid clipping in OFDM, a multilateral piecewise exponential companding transform (MPECT) method has been utilized rather than using piecewise exponential companding transform (PEC) where PAPR is getting reduced. The OFDM is very sensitive to synchronizing error. To overcome this sensitivity, employ the Zadoff‐Chu sequence to carrier frequency offsets. Zadoff‐Chu matrix transform (ZCMT) has numerous merits among the other ODFM systems such as the improvement in the performance of the channels that are fading away and provides an ideal periodic autocorrelation and a constant magnitude periodic cross correlation. Both of these techniques provide improvement in the ODFM systems. To get more efficiency, this paper aims to develop a hybrid technique by integrating the ZCMT and MPECT techniques for reducing the PAPR in OFDM systems. Further, convolutional encoding is applied for better BER and PAPR. The simulation results of the proposed ZCMT‐MPECT technique are evaluated and compared with the conventional OFDM and other precoding methods.     

On the Nonlinear Companding Transform for Reduction in PAPR of MCM Signals

In this paper, we provide the design criteria of the nonlinear companding transforms for reduction in peak-to-average power ratio (PAPR) of multi-carrier modulation (MCM) signals, which can enable the original MCM signals to be transformed into the desirable distribution. As examples, some novel nonlinear companding transforms have been proposed to transform the amplitude or power of the original MCM signals into uniform distribution, which can effectively reduce the PAPR for different modulation formats and subcarrier sizes without any complexity increase and bandwidth expansion. It has been shown by computer simulations that the proposed schemes can significantly improve the performance of MCM systems including bit-error-rate and PAPR reduction.     

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.     

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。     

Linear Companding Transform for the Reduction of Peak-to-Average Power Ratio of OFDM Signals

A major drawback of orthogonal frequency-division multiplexing (OFDM) signals is their high peak-to-average power ratio (PAPR), which causes serious degradation in performance when a nonlinear power amplifier (PA) is used. Companding transform (CT) is a well-known method to reduce PAPR without restrictions on system parameters such as number of subcarriers, frame format and constellation type. Recently, a linear nonsymmetrical companding transform (LNST) that has better performance than logarithmic-based transforms such as $mu$-law companding was proposed. In this paper, a new linear companding transform (LCT) with more design flexibility than LNST is proposed. Computer simulations show that the proposed transform has a better PAPR reduction and bit error rate (BER) performance than LNST with better power spectral density (PSD).      

联合迭代滤波与压扩参数优化的OFDM信号峰平比抑制

针对现有基于压扩变换处理的信号峰平比抑制方法性能单一且参数固定等缺陷,提出一种联合迭代滤波与自适应压扩参数优化的OFDM信号峰平比抑制方案。该方案能够同时对信号的峰平比PAPR和接收端误码率BER性能进行联合优化,并在迭代过程中有效消除因信号幅度畸变所引起的带外频谱再生;所提信号压扩及解压扩函数形式简单,计算复杂度较小;推导并给出了该方案可获得的PAPR抑制增益和BER理论性能界。仿真结果表明,该方案可同时获得较好的信号PAPR抑制、误码率以及带外功率谱性能,并在迭代过程中对压扩参数进行自适应调整,能够有效提高算法的适用灵活性。     

Hybrid delta modulators for digital encoding at low bit rates

A performance comparison study of four HDM systems is presented. The four systems studied are hybrid companding delta modulation (HCDM), hybrid constant factor incremental DM (HCF1DM), song hybrid companding DM (SHCDM) and modified SHCDM (MSHCDM). The study was done at low bit rates with three different input signals. According to our results, the MSHCDM always performs better while the HCDM systems may not always be good. Further, for low frequency input signals the dynamic range of SHCDM and HCFIDM is much wider than that of HCDM. In a noisy channel, the results for HCDM at a bit rate of 24 kbs^-1 indicate that the values of SNR at an error rate of 0·001 and 0·01 are, respectively, 15 dB and 6 dB, whereas in the case of HCFIDM and SHCDM they are 16 dB and 10 dB.     

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 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.     

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.     

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.     

低复杂度OFDM信号峰均功率比压缩技术

本文提出了一种用于减小OFDM信号峰均功率比(Peak-to-Average Power Ratio,PAPR)的压缩扩张变换技术.该技术能够以相对较低的计算复杂度大大降低OFDM信号的PAPR.作为应用实例,本文分析了线性压缩扩张、非线性对称压缩扩张和非线性准对称压缩扩张的PAPR改善幅度、计算复杂度、及其用于OFDM系统时对系统误比特率(BER)的改善等方面的性能.实验仿真表明,与采用传统的限幅滤波方法相比,本文提出的技术可以获得较明显的性能增益.     

A New PAPR Reduction Scheme for OFDM Systems Based on Gamma Correction

Orthogonal frequency division multiplexing (OFDM) is perhaps the most spectrally efficient method discovered so far for communication systems and yet have an excellent immunity against multipath fading and inter-symbol interference. One of the major drawbacks of OFDM systems is their high peak-to-average power ratio (PAPR), which degrades system performance when nonlinear high power amplifiers (HPA) are employed. In this article, a new companding technique based on gamma correction (GC) function is proposed and analyzed. Through extensive computer simulations, it is shown that the proposed technique outperforms the previously suggested A-law and μ-law companding methods for PAPR reduction. A thorough investigation of GCC companding is presented in terms of computational complexity (CC), complementary cumulative distribution function (CCDF), power spectral density (PSD), and bit-error-rate (BER). It is also shown that the proposed method is independent of modulation schemes and can be applied to any number of subcarriers.     

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.     

Pre‐filtering technique for MAI cancellation in MC‐CDMA systems

Multicarrier code division multiple access (MC‐CDMA), is a promising multiplexing technique for future communication systems. In this study, we employ the well‐known Walsh‐Hadamard spreading codes for synchronous downlink transmission of MC‐CDMA systems. The spreading codes allow that the frequency diversity to be efficiently exploited. However, multipath propagation may cause orthogonality among users is distorted, and this distortion produces multiple access interference (MAI). To eliminate this effect, we propose a pre‐filtering‐based MC‐CDMA system which uses a pre‐filtering technique at the transmitter and an equal gain combining (EGC) scheme at the receivers, respectively. Our proposed pre‐filtering technique transforms the transmitted signals so that the MAI can be eliminated, and the EGC scheme weights the signals received from all subcarriers so that channel distortions can be compensated. Furthermore, the proposed technique can calculate the transmitted power over all subcarriers to satisfy the required quality of service of each user and archive MAI‐free. In this paper, performance in terms of bit error rate is analyzed; in comparison with the EGC, orthogonal restoring combining, and maximal ratio combining schemes at receiver, respectively. Copyright © 2011 John Wiley & Sons, Ltd.     

Digital Companding Techniques

This paper deals with the requirements for the design of digital companding techniques in either delta or pulse-code modulation. Both delta and pulse-code modulation convert analogue signals into binary signals and in both these systems the dynamic range is normally small. By the use of companding, the dynamic range can be extended. Since both delta and pulse-code modulation are digital methods, they are well suited to the use of digital companding techniques. The binary transmitted signal normally contains a measure of the system performance. By observing certain patterns in this binary signal and using the occurrence or nonoccurrence of these patterns to change the gain of the modulator and demodulator, syllabic companding can be obtained. The selection of the binary pattern and the rate of change of gain of the modulator and demodulator, determines both the point at which the companding operates and the attack and decay times. The ratio of the largest to the smallest value of the gain determines the dynamic range. By the use of digital circuitry, the gain can be controlled with sufficient accuracy over a large dynamic range. The paper deals with the principles involved in selecting the binary patterns to control the gain of the modulator and as examples a delta modulation system and a pulse-code modulation system with companding ratios of 60 dB are discussed.     

Hybrid Companding Delta Modulation with Variable-Rate Sampling

Hybrid companding delta modulation (HCDM) is known to be superior in performance to other instantaneous or syllabic companding delta modulation systems [1]. To improve its performance or to reduce the bit rate further in coding speech, we propose to use a variable-rate sampling scheme in the HCDM system. The proposed system employs several different sampling rates but transmits the output binary signal at a fixed rate using a buffer. By using the variable-rate scheme, one can improve its performance by 3 to 4 dB in signal-to-quantization noise ratio (SQNR) over the fixedrate HCDM. Detailed algorithm and computer simulation results are presented. Buffer behavior and its control are also discussed. In addition, it is shown that the performance gain of a DM system with variable-rate sampling depends on the degree of variation of the input signal.     

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 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