Peak-to-Average Power Ratio ( PAR ) Reduction in OFDM Based on Lattice Decoding

A new method for PAR reduction in OFDM is introduced. It is based on periodically extending the signal constellations (modulo-congruent points) in each carrier and the application of a lattice decoder to find the best representative in each carrier. Main advantages of this scheme are that no side information has to be communicated to the receiver and, without changing operation, any (square) signal constellation can be used. Numerical simulations cover the performance of PAR reduction in OFDM based on lattice decoding. I. I NTRODUCTION AND PAR REDUCTION Main point in orthogonal frequency-division multiplexing (OFDM) systems is the transmission of a data stream by modulating a (usually large) number of carriers individually. Due to the superposition of the individual signal components, the OFDM transmit signal is almost Gaussian distributed and hence exhibits a large peak-to-average power ratio (PAR) [4]. This fact significantly complicates implementation of the r adio frequency (RF) frontend since amplifiers operating linearly over a wide amplitude range have to be used. Nonlinear distortion and clipping of the RF signal lead to a loss in error performance and—even more undesirable—out-of-band radiation. A. PAR Reduction Techniques Over the last decade, a variety of methods for peak-toaverage power ratio reduction have been developed. Even though they are all based on introducing some new degree of freedom (implicitly or explicitely adding redundancy), very different approaches are present in literature. This includes, e.g. (the following list is not exhaustive, cf. also [12]) • redundant signal representations, i.e., the design of multiple transmit signals which represent the same data, and from which the “best” representation is selected, in particular selected mapping (SLM) and partial transmit sequences (PTS) [19], [6], [2] • (soft) clipping, i.e., the transmit signal (preferably the discrete-time symbols prior to pulse shaping) is passed through a nonlinear, memoryless device, e.g., [20], [3] • redundant coding techniques (possibly combined with channel coding), i.e., algebraic code constructions adopted to code over the frequency-domain symbols, e.g., [15], [22] • tone reservation, i.e., some carriers are omitted from data transmission and are selected via an algorithmic search (sometimes in an iterative way between frequency and time domain), e.g., [24], [17] • constellation expansion, i.e., the signal set is warped such that edge points are allowed to have (any) amplitude larger than the original one, e.g., [16] • (trellis) shaping over frequency, e.g, [13]. B. Contribution of the Paper In this paper, we introduce a new method for PAR reduction in OFDM. It is based on i) multiple signal representation by periodically extending the signal constellations (modulocongruent points, as it is common in precoding schemes [10]), ii) application of (modified) lattice decoding, i.e., a principle adopted from MIMO communications. The main advantages of this type of PAR reduction schemes is that no side information has to be communicated to the receiver. Simple modulo reduction is sufficient to eliminate the multiple signal representation and to recover the initial signal points. Moreover, the scheme can operate regardless of the signal constellation actually used per tone. Hence it is very flexible to use. In Section II, PAR reduction based on lattice decoding is introduced. The scheme is assessed via numerical simulations in Section III and some conclusions are drawn. II. PAR REDUCTION BASED ONLATTICE DECODING Recently, in multiple-input/multiple-output (MIMO) communication, detection and transmission techniques based on lattice decoding have become very popular, e.g., [8], [26], [18], [7] to cite only a few. Using regular QAM constellations, the (noise-less) channel output is drawn from a regular set of points. This set forms the mathematical structure of alattice (to be precise, usually a translate of a lattice), and is defined by the column vectors of the channel matrix. In turn, ignoring the boundary region of the constellation, the decoding problem is equivalent to finding the lattice point closest (in terms of Euclidean distance) to the received distorted and noisy signal point. Lattice decoding is preferably implemented by the socalled sphere decoder [29], [1] which limits the search space significantly and makes lattice decoding applicable in practice. Basically, sphere decoding is a revival of sequential decoding [28], [14] with the restriction to a finite number of dimensions, i.e., finite sequences. Besides receiver side equalization/detection techniques, in some situations transmitter side pre-processing, often denoted asprecoding is of interest. Basically, transmitter side techniques are justified from receiver side techniques via the so calleduplink-downlink duality [27] and obtained by flipping the respective structure. In MIMO communications, linear pre-equalization (dual to linear equalization) and Tomlinson-Harashima-type precoding (dual to decisionfeedback equalization) are well known. Recently, the dual to maximum-likelihood detection (approximated by lattice decoding) has been proposed and is called vector precoding (VP) [21]. Here, a lattice decoder operates at the transmitter and “decodes” for the “best” (with respect to some criteria of optimality) transmit sequence. An almost identical procedure for controlling average power and/or peak power—but operating over time and hence with the need of some suboptimal decoding procedure (joint precoding/signal shaping for channels with intersymbol interference)— was introduced in [9], [11]. The main principle of vector precoding is subsequently used for PAR reduction in OFDM.