Peak-to-mean Envelope Power Ratio Reduction Research Articles

Low PMEPR OFDM Radar Waveform Design Using the Iterative Least Squares Algorithm

This letter considers waveform design of orthogonal frequency division multiplexing (OFDM) signal for radar applications, and aims at mitigating the envelope fluctuation in OFDM. A novel method is proposed to reduce the peak-to-mean envelope power ratio (PMEPR), which is commonly used to evaluate the fluctuation. The proposed method is based on the tone reservation approach, in which some bits or subcarriers of OFDM are allocated for decreasing PMEPR. We introduce the coefficient of variation of envelopes (CVE) as the cost function for waveform optimization, and develop an iterative least squares algorithm. Minimizing CVE leads to distinct PMEPR reduction, and it is guaranteed that the cost function monotonically decreases by applying the iterative algorithm. Simulations demonstrate that the envelope is significantly smoothed by the proposed method.

Peak Power Reduction of OFDM Systems Through Tone Injection via Parametric Minimum Cross-Entropy Method

It is well known that the major drawback of orthogonal frequency-division multiplexing (OFDM) is its high peak-to-mean envelope power ratio (PMEPR). One of the promising schemes proposed for alleviating the high PMEPR of OFDM signals is tone injection (TI). In this paper, we propose a novel low-complexity algorithm for PMEPR reduction using TI. This algorithm first formulates the TI scheme as a combinatorial optimization problem and then finds a near-optimal solution to this problem via parametric minimum cross-entropy (PMCE) method. We also demonstrate that by effectively exploiting TI schemes in conjunction with cross constellations, it is possible to reduce the peak power of the system by more than 2 dB compared with sign selection schemes over conventional quadrature-amplitude modulation (QAM) constellations. Simulation results show that our algorithm outperforms similar existing algorithms, including the cross-entropy (CE) TI algorithm, the greedy sign selection algorithm, and the derandomization sign selection algorithm, in terms of PMEPR. We also present a threshold-based PMCE algorithm for TI that results in significant complexity reduction. Numerical results show that to achieve a prescribed PMEPR threshold, this threshold-based PMCE algorithm requires less computational complexity than the CE TI algorithm.

A novel complementary sequence and PMEPR reduction in OFDM

This paper introduces a novel sequence called the "beta-complementary sequence" to encode orthogonal frequency-division multiplexing (OFDM) signals, with which one can substantially increase the code rate while maintaining a tight peak-to-mean envelope power ratio (PMEPR) of at most 2. Moreover, encoding schemes based on beta-complementary sequences provide very good tradeoff performance between PMEPR and code rate. This observation follows from an intrinsic property of the beta-complementary sequences considered. Furthermore, the distribution of code rate versus beta is determined, and numerical results based on these properties are presented. Finally, comparisons with the well-known Golay complementary sequences and the generalized Golay complementary sequences (called "G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> -complementary sequences" in this paper) are made.

On the peak-to-mean envelope power ratio of phase-shifted binary codes

The peak-to-mean envelope power ratio (PMEPR) of a code employed in orthogonal frequency-division multiplexing (OFDM) systems can be reduced by permuting its coordinates and by rotating each coordinate by a fixed phase shift. Motivated by some previous designs of phase shifts using suboptimal methods, the following question is considered in this paper. For a given binary code, how much PMEPR reduction can be achieved when the phase shifts are taken from a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sup> -ary phase-shift keying (2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sup> -PSK) constellation? A lower bound on the achievable PMEPR is established, which is related to the covering radius of the binary code. Generally speaking, the achievable region of the PMEPR shrinks as the covering radius of the binary code decreases. The bound is then applied to some well understood codes, including nonredundant BPSK signaling, BCH codes and their duals, Reed-Muller codes, and convolutional codes. It is demonstrated that most (presumably not optimal) phase-shift designs from the literature attain or approach our bound.

A Balancing Method for PMEPR Reduction in OFDM Signals

A relation is established between the strength of a binary code over the alphabet {+1,-1}, and its ability to reduce peak-to-mean envelope power ratio (PMEPR) in n-subcarrier (OFDM) signals. Based on this relation, a method is proposed to deterministically bound PMEPR of such signals using coordinate-wise multiplication by a balancing vector (BV) chosen from a code of given strength. A practical probabilistic scheme considering a small number of candidate codewords is devised. For this scheme, estimates on the PMEPR reduction achievable with arbitrary high probability are derived. In particular, the scheme provides for large n PMEPR of lnn+2.01lnlnn with (ln2)middot(log2n)2+1 bits of redundancy, the failure probability at most e-n, and testing n/(lnlnn) candidate BVs. Finally, several practical settings are considered. For example, for quaternary phase-shift keying, n=128, the scheme with 36 bits of redundancy (18 redundant subcarriers), by testing only 4 BVs provides over 2 dB PMEPR reduction, for any failure rate below 10-2.5

Maximal Diversity Algebraic Space–Time Codes With Low Peak-to-Mean Power Ratio

The design requirements for coding typically involves achieving the goals of good performance, high rates, and decoding complexity. In this paper, we introduce a further constraint on code design in that the code should also lead to values of the peak-to-mean envelope power ratio (PMEPR) for each antenna. Towards that end, we propose a new class of codes called the low PMEPR space-time (LPST) codes. The LPST codes are obtained using the properties of certain cyclotomic number fields. The LPST codes achieve a performance identical to that of the threaded algebraic (TAST) codes but at a much smaller PMEPR. With M antennas and a rate of one symbol per channel use, the LPST codes lead to a decrease in PMEPR by at least a factor of M relative to a Hadamard spread version of the TAST code. For rates beyond one symbol per channel use and up to a guaranteed amount, the LPST codes have provably smaller PMEPR than the corresponding TAST codes. Additionally, with the concept of punctured LPST codes proposed in this paper, significant performance improvement is obtained over the full diversity TAST schemes of comparable complexity. Numerical examples are provided to illustrate the advantage of the proposed codes in terms of PMEPR reduction and performance improvement for very high rate wireless communications.

Construction of non-square M-QAM sequences with low PMEPR for OFDM systems

The author considers the use of coding to reduce the peak-to-mean envelope power ratio (PMEPR) for orthogonal frequency division multiplexing (OFDM) systems. Most of the existing schemes that use coding for PMEPR reduction assume a PSK constellation. The author presents the construction of non-square M-QAM symbols from a combination of QPSK and BPSK signals when M=2n and n is an odd number. By using QPSK and BPSK Golay (or Golay-like) sequences, M-QAM sequences with low PMEPR are generated. An upper bound for the instantaneous envelope power of Golay-like M-QAM sequences was derived. After the mean envelope power for these sequences was computed, the general upper bound for one PMEPR of M-QAM sequences with non-square constellations was derived.