A deterministic algorithm that achieves the PMEPR of c log n for multicarrier signals

Multicarrier signals often exhibit large peak to mean envelope power ratios (PMEPR) which can be problematic in practice. In this paper, we study adjusting the sign of each subcarrier in order to reduce the PMEPR of a multicarrier signal with n subcarriers. Considering that any randomly chosen codeword has PMEPR of log n with probability one and for large values of n [1], randomly choosing signs should lead to the PMEPR of log n in the probability sense. Based on the derandomization algorithm suggested in [2], we propose a deterministic and efficient algorithm to design signs such that the PMEPR of the resulting codeword is less than c log n for any n where c is a constant independent of n. By using a symmetric q-ary constellation, this algorithm in fact constructs a code with rate 1 - logq 2, PMEPR of c log n, and with simple encoding and decoding. We then present simulation results for our algorithm

Existence of codes with constant PMEPR and related design

Recently, several coding methods have been proposed to reduce the high peak-to-mean envelope ratio (PMEPR) of multicarrier signals. It has also been shown that with probability one, the PMEPR of any random codeword chosen from a symmetric quadrature amplitude modulation/phase shift keying (QAM/PSK) constellation is logn for large n, where n is the number of subcarriers. Therefore, the question is how much reduction beyond logn can one asymptotically achieve with coding, and what is the price in terms of the rate loss? In this paper, by optimally choosing the sign of each subcarrier, we prove the existence of q-ary codes of constant PMEPR for sufficiently large n and with a rate loss of at most log/sub q/2. We also obtain a Varsharmov-Gilbert-type upper bound on the rate of a code, given its minimum Hamming distance with constant PMEPR, for large n. Since ours is an existence result, we also study the problem of designing signs for PMEPR reduction. Motivated by a derandomization algorithm suggested by Spencer, we propose a deterministic and efficient algorithm to design signs such that the PMEPR of the resulting codeword is less than clogn for any n, where c is a constant independent of n. For symmetric q-ary constellations, this algorithm constructs a code with rate 1-log/sub q/2 and with PMEPR of clogn with simple encoding and decoding. Simulation results for our algorithm are presented

Peak to average power reduction using amplitude and sign adjustment

In this paper, we propose a method to reduce the peak to mean envelope power ratio (PMEPR) of multicarrier signals by modifying the constellation. For MPSK constellations, we minimize the maximum of the multicarrier signal over the sign and amplitude of each subcarrier. In order to find an efficient solution to the aforementioned non-convex optimization problem, we present a suboptimal solution by first optimizing over the signs using the result of [1], and then optimizing over the amplitudes given the signs. We prove that the minimization of the maximum of a multicarrier signal over the amplitude of each subcarrier can be written as a convex optimization problem with linear matrix inequality constraints. We also generalize the idea to other constellations such as 16QAM. Simulation results show that by an average power increase of 0.21 db and not sending information over the sign of each subcarrier, PMEPR can be decreased by 5.1 db for a system with 128 subcarriers

Amplitude and Sign Adjustment for Peak-to-Average-Power Reduction

In this letter, we propose a method to reduce the peak-to-mean-envelope-power ratio (PMEPR) of multicarrier signals by modifying the constellation. For$M$-ary phase-shift keying constellations, we minimize the maximum of the multicarrier signal over the sign and amplitude of each subcarrier. In order to find an efficient solution to the aforementioned nonconvex optimization problem, we present a suboptimal solution by first optimizing over the signs, and then optimizing over the amplitudes given the signs. We prove that the minimization of the maximum of a continuous multicarrier signal over the amplitude of each subcarrier can be written as a convex optimization problem with linear matrix inequality constraints. We also generalize the idea to other constellations such as 16-quadrature amplitude modulation. Simulation results show that by an average power increase of 0.21 dB, and not sending information over the sign of each subcarrier, PMEPR can be decreased by 5.1 dB for a system with 128 subcarriers

A Generalized Construction of OFDM M-QAM Sequences With Low Peak-to-Average Power Ratio

A construction of $2^{2n}$-QAM sequences is given and an upper bound of the peak-to-mean envelope power ratio (PMEPR) is determined. Some former works can be viewed as special cases of this construction.Comment: published by Advances in Mathematics of Communication

Peak Power Reduction of OFDM Signals with Sign Adjustment

It has recently been shown that significant reduction in the peak to mean envelope power (PMEPR) can be obtained by altering the sign of each subcarrier in a multicarrier system with n subcarriers. However, finding the best sign not only requires a search over 2n possible signs but also may lead to a substantial rate loss for small size constellations. In this paper, we first propose a greedy algorithm to choose the signs based on p-norm minimization and prove that the resulting PMEPR is guaranteed to be less than c log n where c is a constant independent of n for any n. This approach has lower complexity in each iteration compared to the derandomization approach of while achieving similar PMEPR reduction. We further improve the performance of the proposed algorithm by enlarging the search space using pruning. Simulation results show that PMEPR of a multicarrier signal with 128 subcarriers can be reduced to within 1.6 dB of the PMEPR of a single carrier system. In the second part of the paper, we address the rate loss by proposing a block coding scheme in which only one sign vector is chosen for K different modulating vectors. The sign vector can be computed using the greedy algorithm in n iterations. We show that the multi-symbol encoding approach can reduce the rate loss by a factor of K while achieving the PMEPR of c logKn, i.e., only logarithmic growth in K. Simulation results show that the rate loss can be made smaller than %10 at the cost of only 1 db increase in the resulting PMEPR for a system with 128 subcarriers

On the average power of multiple subcarrier intensity modulated optical signals: Nehari's problem and coding bounds

Multiple subcarrier modulation (MSM) is an attractive technique for optical wireless communication for high speed applications. The main disadvantage of this scheme is its low average power efficiency which is an analogous problem to the high peak to mean envelope power ratio (PMEPR) of multicarrier signals. In this paper, we consider the achievable average power reduction of MSM signals by using optimized reserved carriers and coding methods. Based on Nehari’s result we present a lower bound for the maximum average power of the signal after adding the reserved carriers. It is shown that the mean value of the average required power behaves very close to √2n log log n for a BPSK constellation where n is the number of subcarriers. We then consider finding the optimum values for the carriers and the effect of having finite bandwidth for reserved carriers. In the next section, mainly based on recent coding results for the PMEPR of multicarrier signals, we show the existence of very high rate codes with average power of O(√n log n) for large values of n, and furthermore the existence of codes with non-vanishing to zero rate and average power of O(√n) asymptotically