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.

I. Introduction

One of the major disadvantages of orthogonal frequency division multiplexing (OFDM) is the large amplitude variations. In order to reduce the distortion caused by a high power amplifier (HPA) without setting it to large back-offs, the amplitude variations of the OFDM signal have to be decreased. Peak-to-average power ratio (PAPR) is widely being used to quantify the envelope fluctuations. In fact, many techniques can be found in the literature that limit the peak power of the signal [1], a problem that is usually referred to as PAPR-reduction. In some recent contributions, another metric of the envelope fluctuations, known as cubic metric (CM) [2], is being considered [3], [4]. The motivation for CM relies on the fact that the major distortion introduced by the nonlinear amplifier is caused by the third order intermodulation product. Recent studies on PAPR and CM suggest that, except for large back-offs, CM is more related to the amount of distortion introduced by a nonlinearity than PAPR [4]. Moreover, in the 3GPP, after analyzing certain OFDM-type signals that are considered to meet the long-term evolution (LTE) goals, it is shown that CM predicts HPA power de-rating more accurately than PAPR [5].