Ali Behravan

PAPR and other measures for OFDM systems with nonlinearity

In this paper, we discuss the effects of nonlinearity on the performance in transmission of OFDM signals. Furthermore, we study measures related to nonlinearities, such as PAPR (peak-to-average-power-ratio), with respect to their ability to correctly predict the effect of a nonlinearity in an OFDM system. We also propose new measures for signal distortion in nonlinear systems. The performance of the measures are studied using several examples.

Evaluation of Performance Improvement Capabilities of PAPR-reducing Methods

One of the major drawbacks of multicarrier modulation is the large envelope fluctuations which either require an inefficient use of high power amplifiers or decrease the system performance. Peak-to-average power ratio (PAPR) is a very well known measure of the envelope fluctuations and has become the cost function used to evaluate and design multicarrier systems. Several PAPR-reducing techniques have been proposed with the aim to alleviate back-off specifications or increase the system performance. Besides the fact that these techniques have varying PAPR-reduction capabilities, power, bandwidth and complexity requirements, it is interesting to notice that the performance of a system employing these techniques has not been fully analyzed. In this paper we, first, develop a theoretical framework for both PAPR and the distortion introduced by a nonlinearity, and then simulate an OFDM system employing several well known PAPR-reducing techniques from the literature. By means of the theoretical analysis and the simulation results we will show the relation between PAPR and the performance of OFDM systems when a clipping device is present and we will evaluate the real performance improvement capabilities of the PAPR-reducing methods. The agreement between the theoretical and the simulation results demonstrate the validity of the analysis.

On Cubic Metric Reduction in OFDM Systems by Tone Reservation

One of the major drawbacks of multicarrier modulation is the large envelope fluctuations which either requires an inefficient use of high power amplifiers (HPAs) or decreases the system performance. Peak-to-average power ratio (PAPR) is the best known measure of the envelope fluctuations and is widely employed to design multicarrier systems. However, recently, another metric known as cubic metric (CM), is being considered in several multicarrier systems since it can predict HPA power de-rating more accurately. In this paper tone reservation (TR) technique, originally used for PAPR-reduction, is reformulated to reduce CM. We first simplify CM to define the objective function, denoted as objective CM (OCM). Then we demonstrate that OCM is convex and formulate TR for CM-reduction as an unconstrained convex optimization problem. The solution to this problem is found by means of an iterative algorithm which approaches the optimal solution with few steps. In this paper a low-complexity suboptimal algorithm capable of approaching the optimum with sufficient accuracy is also proposed. Simulation results show that for similar computational complexity, the performance of CM-reduction is superior to that of PAPR-reduction both in terms of bit error rate and out-of-band leakage.

Tone reservation to reduce the envelope fluctuations of multicarrier signals

In this paper we propose a method for reducing nonlinearity distortion by limiting the envelope fluctuations of an OFDM signal. The method is based on tone reservation, and the free tones are assigned in a way to limit the variations of the instantaneous power of the time domain signal. The problem is shown to be convex, and by adding an equality constraint, zero constellation error is guaranteed. We present an iterative solution for this problem, and show that the globally optimal point can be approached by only a few iterations. Both in-band and out-of-band distortions are reduced at the expense of a small increase in bandwidth of the signal. The corrected signal is less sensitive to nonlinearities, and therefore the distortion is reduced for all input backoff values.

Some Statistical Properties of Multicarrier Signals and Related Measures

In this paper we study some statistical properties of a multicarrier signals using the order statistics. Analytical expressions for the probability density function of different order statistics of a sampled OFDM system is presented. We then find the amount of power which is clipped from each order of the signal when the signal is passed through a clipping nonlinearity. This is used to represent the relevance of peak-to-average power ratio (PAPR) to evaluate the effect of nonlinearity on the performance of a multicarrier system. The agreements between the theoretical results and the simulated ones demonstrate the validity of the analysis. We will also study different metrics for the signal envelope variations in terms of the sensitivity of each metric to amplitude nonlinearities. In the end the performance of an OFDM system with selected mapping based on different metrics is evaluated and compared with each other

Constrained Clipping for Peak Power Reduction of Multicarrier Systems by Tone Reservation

In this paper we introduce a new method to limit the peak factor of a multicarrier signal based on tone reservation. A peak-reducing signal is computed by clipping the original OFDM symbol. The peak-reducing signal is forced to have the constraints of tone reservation, so that when added to the original signal, the peak factor is reduced without increasing the BER and the out-of-band radiation. The proposed method has low computational complexity requirements and is fast-converging. Moreover, simulation results show that it has higher PAPR-reduction capabilities than other PAPR-reducing methods based on TR in the literature.

Peak Reduction of Multi-Carrier Systems by Controlled Spectral Outgrowth

One of the major drawbacks with multi-carrier (MC) modulations is the large peak-to-average power ratio (PAPR) of the transmitted signal which significantly reduces the power amplifier efficiency and the system performance. Several PAPR reducing methods which do not decrease the system performance have been proposed. In this paper, we present a new low complexity PAPR reduction technique based on the controlled spectral outgrowth (CSO) of the nearby subcarriers which neither requires the transmission of additional information nor reduces the system performance and is independent of the mapping scheme. The proposed method can be easily combined with most of the methods in the literature to provide a further peak reduction in any MC or MC spread spectrum (MC-SS) system. An analog PAPR reduction about 2.5 dB at 10-4 symbol clip probability and a power increase about 0.12 dB are obtained for a 256-subcarrier of OFDM transmission

Baseband compensation techniques for bandpass nonlinearities [RF front-ends]

In this paper, we present and compare several methods of compensating the nonlinearity of the RF front-end of a wireless system. Two baseband compensation techniques, namely predistortion and postdistortion (equalization) of the baseband signal are discussed and the problems associated with each one is addressed. Furthermore, a combination of a predistorter and a nonlinear equalizer, and also predistortion of an oversampled baseband signal, are analyzed. It is shown that under realistic conditions, with a frequently saturated amplifier, and ISI channel, the latter two methods are able to compensate for the nonlinearity to a good extent, while the first two methods can only operate under certain assumptions for channel conditions and nonlinearity type.

A model for bandpass nonlinearities based on harmonic measurements

This paper presents a model for a bandpass nonlinearity, which is based on measurements on several harmonics of the output. The model has a quadrature structure, with a memoryless nonlinearity and a filter in each branch. The structure can describe AM/AM as well as AM/PM conversions. The parameters of the nonlinearity and the filter are jointly optimized to fit the measurements. Analytic expressions for the parameters of the model are found by means of the MMSE optimization. The method is applied to find a model for a 60 GHz solid-state power amplifier based on a set of measurements of different harmonics of the output.

MAP Detection of Nonlinearly Distorted OFDM Signals

This paper presents the maximum a posteriori (MAP) detector for a multicarrier system with nonlinearity at the transmitter front-end. The analysis is based on block detection of multicarrier symbols. Since implementation of the MAP detector for a system with a large number of subcarriers is far too complex, a sub-optimum algorithm that can be implemented with acceptable complexity is also presented. It will be shown that when the nonlinearity distortion dominates the channel noise, without knowledge of the nonlinearity, the proposed detector outperforms the conventional ML detector