OFDM Link Performance with Companding for PAP Ratio 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 non-linear 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. Past studies for OFDM have explored used of companding to mitigate A/D and D/A conversion distortion (quantization noise) in the presence of noise amplification from the expansion transform at the receiver. We neglect the quantization noise, which decreases with increasing compression, and instead consider noise amplification and distortion from nonlinearities in the transmit amplifier. In the absence of companding, transmitter operation near saturation in the nonlinear region of operation maximizes the SNR at the receiver but also results in distortion that impacts overall link performance. As the transmit power is backed-off from saturation, amplifier distortion reduces, 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 optimal 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. Introduction Orthogonal Frequency Division Multiplexing (OFDM) is a firmly established air interface for fixed wireless, WLAN, and mobile wireless applications. Because OFDM is a multicarrier waveform, it may exhibit large peak-to-average power ratios (PAPR), which can result in saturation of the amplifier or alternatively encourage use of large back-offs that impact power efficiency and subsequently SNR at the receiver. Hence, methods to reduce PAPR are of interest, since they potentially can yield performance gains. Previous studies have considered PAPR reduction techniques, including This material is based upon work supported by The National Science Foundation under Grant No. 0121565. companding to reduce PAPR levels [4-9] for A/D and D/A conversion. However, these studies have not jointly considered the interplay between PAPR reduction techniques and non-linear amplification at the transmitter. This paper extends the body of knowledge from these previous works by investigating companding impacts on link performance in the presence of both high PAPR signals and nonlinear power amplification at the transmitter. To improve link performance with any given amplifier, one strategy is to increase the transmit power, shifting the operating point towards amplifier saturation. However, while this increases the signal power at the receive end of the link, high-PAPR signals undergo distortion in the nonlinear operating region of the amplifier [1]. The nonlinear amplifier distortion translates to spectral regrowth and to a subsequent increase in BER, potentially offsetting any performance gains derived from the increased received signal power level. Transmit powers can be decreased by backing-off the operating point from saturation to reduce the amplifier distortion, but this is done at the expense of reducing the signal-to-noise power ratio (SNR) at the receiver. In [2], for example, backoffs of 8 dB are considered for the IEEE802.16.3c standard. Clearly, there is a design tradeoff in defining a useful operating point, and this will depend upon the characteristics of the power amplifier. Armada and Garcia [3] have suggested a practical way of specifying the optimal operating point for OFDM in the presence of nonlinear amplifiers. Their heuristic approach involves setting the backoff such that the spectral regrowth shoulders are 20 dB below the in-band signal level. However, their analysis does not address PAPR reduction techniques. Such techniques may permit the transmitter to operate closer to saturation, without substantially increasing signal distortion caused by the non-linear amplifier. In this work, we explore a simple PAPR reduction approach based on mu-law companding. Companding is well-known in speech compression applications, and is generally utilized to limit the dynamic range of the signal. For OFDM signaling, companding is known to reduce the PAPR ratio [4-9]. Hence, it would potentially allow the transmitter to operate at a reduced backoff level (i.e., closer to saturation), thus resulting in a higher-power signal at the receiver. But studies have not addressed the impact of nonlinear amplification as the transmitter’s operating point moves towards saturation. There are some potential drawbacks to adopting signal compression techniques. One drawback is that signal compression results in spectral regrowth, a form of signal distortion similar to that occurs with signal limiting (e.g. such as with hard-limiters). Filtering could be applied following compression to contain the spectral regrowth, but at the expense of increasing the PAPR [10]. Another undesired effect of companding techniques, perhaps of greater concern, involves the requisite expansion of the compressed signal at the receiver, a process which amplifies receiver noise [4-8]. One of the first papers to deal with companding for PAPR reduction of OFDM signals was the work of Wang and his colleagues [4]. In their analysis, u-law companding was employed to reduce PAPR from OFDM signals to minimize A/D and D/A distortion, and to apparently reduce symbol error rates. In following correspondence letters, comments from Mattsson et al [5] noted that in Wang’s analysis, the noise power was constant, while the transmitted signal’s power was increased as it was expanded at the receiver. A more meaningful performance, they suggested, would involve a comparison between companded and uncompanded signals of equal power. A subsequent analysis by Wang reported that companding proved to be beneficial in high SNR cases (e.g., SNR>35 dB). However, these analyses did not directly incorporate impairments due to a nonlinear power amplifier. When such effects are included in an end-to-end systems model, we find that companding offers modest performance improvements, even at lower SNR. In [7], Wang et al also investigated OFDM systems with A-Law companding and determined optimal A-law companding coefficients for different OFDM FFT sizes. In later work, Huang et al [8,9] investigated companding transforms , which combined advantages of both clipping and companding. Compared with conventional companding techniques, the transform was found to reduce PAPR more effectively. In both of these studies, impairments due to nonlinear power amplifiers were not considered. Clearly, while the aforementioned studies have investigated the PAPR reduction capability of companding and the noise amplification problem as a function of various system design parameters (e.g., SNR, OFDM symbol length, and companding parameters), they have not considered the combined impact of these effects with nonlinear transmit amplifier distortion in the characterization of overall link performance. This latter problem is particularly important since it reflects the end-to-end performance and leads to more comprehensive analysis tradeoffs to help select operating parameters for given transmit amplifier saturation power, link range, and demodulation SNR requirements. Link performance depends not only on the transmit power (and hence the received SNR) and the companding parameters, but also on power amplifier distortion. Such interdependencies between PAPR reduction techniques, power amplification charactreristics, and noise amplification help to motivate this study, since an understanding of these provide a springboard for legitimizing the consideration of companding as a viable PAPR reduction technique. System Description The system that is analyzed in this work involves an OFDM air interface with system processing functions and impairments as illustrated in Figure 1. The transmitter section maps a random data bit sequence, btx, into a sequence of QAM symbols, Stx. The QAM symbols are partitioned into N-length blocks and modulated onto the subcarriers of an OFDM modulator via the inverse Fast Fourier Transform (IFFT). After guard interval insertion, the resulting OFDM signal is integrated into a frame that includes a preamble and training sequences for synchronization and channel estimation, respectively. Prior to transmission, the signal is companded with a mu-law compander, and then scaled for power normalization. The scaled, companded signal is then passed through the transmit amplifier, which distorts the signal according to non-linear PA models [9]. At the receiver, the signal is corrupted with additive white Gaussian noise. Processing within the receiver includes synchronization, channel estimation and compensation, ulaw expansion, and OFDM demodulation. The resulting QAM symbols are then compared with the transmitted QAM symbols to form an error metric for performance comparisons. Error metrics used in this study include the average symbol error distance, which is used in the simulations to identify performance trends, and bit error rates in hardware testing to corroborate the observed trends. The salient features of the signal and impairment models associated with this system are described in greater detail in the remainder of this section. QAM Mapper Data bits Tx Amp Compander TRANSMIT AWGN S/P GI Framing Scale