Tone reservation (TR) is a well-known and practical strategy to reduce peak-to-average power ratio (PAPR) in OFDM signals. In TR some unused or reserved subcarriers are used to accommodate a peak-cancelling signal that lowers the PAPR of the time domain OFDM signal. Several methods have been proposed to optimise the peak-cancelling signal, amongst which the so called active-set method has been shown to converge very quickly to a minimum PAPR solution for a real baseband signal with no additional power constraints. However, for a general complex baseband signal and/or when the peak-cancelling signal has to be power limited, there is no guarantee of optimality. Moreover, in the complex baseband model, the TR optimisation problem is a quadratically constrained quadratic program (QCQP), which has a prohibitive computational cost. In this paper we introduce a tree-search approach to designing the TR signal based on the sphere decoding/encoding principle. The method is proved to provide the minimum PAPR solution in the limit of fine lattice quantisation. Simulation results show a significant margin of improvement over the best known active-set method.

In wireless industry, the out-of-band (OOB) leakage power of transmit signals is widely used as a simple yet important metric to evaluate the interference to the signals communicated in adjacent frequency bands. A common way of measuring the OOB emission is via a spectrum analyzer (SA) that allows us to directly read the OOB level from the displayed trace of the signal spectra. Although this task, as such, is simple and there seems to be no potential for failure, we argue that deliberate consideration upon the detection mode of the SA should be made by looking into its intricate operation principle. Due to several internal signal processings for detection and visualization, the spectrum trace finally displayed on the monitor does not necessarily equal to the real power of the RF signal fed to the SA and varies depending on detection modes. In this paper, we demonstrate by simulation that the measurement using SAs can possibly underestimate the actual OOB leakage power unless a root mean square (RMS) detector is employed. Other type of detectors, such as peak and sample detectors, are subject to a non-trivial mismatch. The underlying reason for this is the difference of the envelope amplitude statistics inside and outside the channel, and this fact seems to have been given no particular attention so far.

In communication theory, the conventional role of precoding is to reshape a spectrally flat sequence of data symbols in favor of a particular inter-symbol interference (ISI) channel such that signal-to-noise power ratio (SNR) is maximized. In contrast, in this paper a novel precoding technique is devised to exploit a particular property of the information source rather than the channel. Specifically, we focus on the scenario where the source sequence has an inherent correlation that is known a priori, and design a precoding filter that attempts to reduce the average power of the resulting transmit symbol sequences. The proposed precoding technique is thus termed power-reductive precoding (PRP). This reduction of average transmit power accrues without changing the amplitude of the original sequence and thus can be treated as a system gain. An apparent drawback of this approach is the intentional ISI introduced by the precoding filter, which may lessen the minimum distance among legitimate sequences. Nevertheless, we show that even if the loss associated with the minimum distance penalty is properly taken into account, the achievable error rate versus SNR can be made superior to the case without precoding.

Trellis shaping (TS) is known as a flexible technique to generate transmit symbols constrained (or controlled) for a particular desired property of communication systems. In our recent results, an application of TS for peak-to-average power ratio (PAPR) reduction of single-carrier (SC) signals has been extensively studied, to show that even a highly fluctuating envelope can be reduced to a nearly constant level. In this paper, we first demonstrate that the performance of the proposed TS in terms of the bit error rate (BER) and PAPR reduction capability strongly depends on the bit labeling. We then propose a new bit labeling for high-order PSK constellation that can efficiently reduce PAPR while achieving BER performance comparable to that of the Gray labeling (GL).

Trellis shaping (TS) has found its application in the peak power control of band-limited single-carrier signals. Our recent work has demonstrated that a well-designed TS can control the symbol transitions such that the output signal has almost constant envelope, which significantly alleviates the linearity requirement of power amplifiers. Compared to transmission without constellation shaping, however, the TS involves signal constellation expansion exclusively for peak power control. Therefore, unlike trellis coded modulation (TCM) that increases the minimum Euclidean distances (MED), the TS decreases the MED, thus incurring the increase in signal-to-noise power ratio (SNR) required for achieving a certain error rate. In this letter, in order to overcome this drawback, we propose a serial concatenation of coding and shaping together with an effective decoding algorithm that utilizes the memory effect (i.e., error correcting capability) of the shaped symbols. The achievable performance of the proposed system is analyzed in terms of the average mutual information. The simulation results demonstrate that the iterative decoding of the proposed concatenated system with outer convolutional codes and inner trellis shaping offers a significant performance gain.

In this paper, we present a new modulation code, named symbol insertion (SI), that simultaneously achieves both peak-to-average power ratio (PAPR) reduction and forward error correction for pulse-shaped single-carrier systems in a low-complexity manner. Based on the fact that PAPR highly depends on the successive phase patterns of discrete complex symbols, the proposed code controls phase shifts by inserting a redundant symbol between consecutive information-bearing symbols. At the receiver, by viewing the inserted symbols as parities, we exploit them for error correction. We show that, when the SI is used as an inner code of serially concatenated codes, its error rate performance is close to those of conventional capacity-approaching codes. The proposed system thus becomes favorable if the amount of PAPR reduction is taken into account. Furthermore, the SI with a rotationally invariant insertion scheme can accommodate itself to noncoherent detection.

This paper studies a statistical distribution of instantaneous power in pulse-shaped single-carrier (SC) modulation. Such knowledge is of significant importance to estimate several concerns associated with the non-linearity of power amplifiers, e.g., required back-off level or clipping distortion in amplified signals. However, existing works often rely on Monte-Carlo simulations, since analytical derivation of the statistical distribution of SC signals is a complex problem involving combined dependency of a constellation format and a pulse shape. In this paper, we tackle this problem and propose two new analytical methods based on the uniform distribution approximation of discrete signal points. The derived expressions can be easily evaluated and serve as tight upper bounds for high-order pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM).

This paper analyzes statistical distribution of instantaneous power in pulse-shaped single-carrier (SC) modulation. Such knowledge is of significant importance to estimate several concerns associated with the non-linearity of power amplifiers, e.g., required back-off level or clipping distortion in amplified signals. However, existing works often rely on Monte-Carlo simulations, since analytical derivation of the statistical distribution of SC signals is a complex problem involving combined dependency of a constellation format and a pulse shape. In this paper, we tackle this problem and propose a new efficient analytical method by using the approximation of infinite number constellation points. Tight upper bounds for high-order pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) can be calculated from the proposed method.

Single-carrier (SC) transmission is considered as a promising candidate for the uplink of the next generation cellular systems due to its relatively low peak-to-average power ratio (PAR) compared to multi-carrier systems such as orthogonal frequency division multiplexing (OFDM). In SC systems, bandwidth efficiency can be effectively enhanced by the use of waveform shaping filter with low roll-off factor. However, as a price, non- negligible increase of PAR is incurred in pulse-shaped signals even for phase shift keying (PSK) modulation. To balance both low PAR and high bandwidth efficiency, the authors have recently proposed a novel PAR reduction technique for SC-PSK based on trellis shaping (TS). In this paper, we evaluate its effectiveness and feasibility through implementation with field programmable gate array (FPGA) and testbed experiments with a sample RF power amplifier (PA).

We analyze pulse-shaped transmit signals with correlated input sequences in the framework of band-limited liner modulations. These signals are formed by superposition (convolution) of the shaping pulses and may have different amplitude statistics depending on the correlation properties of the input sequences. Hence, even if the sequences have a unit average power in discrete-time domain, the resulting transmit signals exhibit smaller (or larger) average power if there are many destructive (or constructive) superpositions produced by the correlated source. Since such a reduction of average transmit power does not change the amplitude of the underlying discrete-time sequence, one may expect the so-called shaping gain. We comprehensively analyze the shaping gain achieved by the correlation of the input sequences, and show that the use of a pulse shape, which convolves the sequence destructively, is capable of increasing the achievable information rate of the system.

The authors have recently proposed a novel trellis shaping (TS) approach for peak power reduction of single-carrier signals. In this paper, we propose the use of M algorithm as well as sequential decoding with stack algorithm for the purpose of complexity reduction. Our comparative studies with the Viterbi algorithm (VA) show that the TS with these low-complexity algorithms can still offer substantial peak power reduction capabilities that are comparable to the VA.

In band-limited communications, the use of root-Nyquist pulse-shaping filters, such as root raised cosine (RRC), is a common premise to guarantee no inter-symbol interference (ISI) in the output from matched filtering. We have recently shown that, for correlated source symbols, some non-root-Nyquist filter is capable of increasing the mutual information of the resulting channel. In this paper, we show that performance improvement can also be achieved in terms of bit error rate.

In this paper, we propose a powerful trellis shaping for peak-to-average power ratio (PAR) reduction of pulse-shaped phase shift keying (PSK) systems. The proposed approach consists of 1) memory extension of trellis shaping encoder for capturing the full effect of pulse shaping filter impulse response, and 2) simple branch metrics that quantify envelope fluctuation of the filter output. Simulation results demonstrate that achieving near constant envelope is possible even if a pulse shaping filter with a roll-off factor as low as 0.1 is employed. Furthermore, due to the circular nature of the resulting signal trajectory, the proposed system also exhibits a robustness against sampling timing jitter at the receiver.

We propose a new coded modulation called hexagonal shell modulation (HSM). The HSM has a signal constellation composed of shell-like tiling of hexagons and thus has a lower peak-to-average power ratio (PAR) than a standard square quadrature amplitude modulation (QAM) with comparable bandwidth efficiency and minimum Euclidean distance. The main challenge is that HSM has a non-power-of-two number of constellation points, and thus assignment of binary information to HSM is not straightforward. We resolve this by applying a multilevel coded modulation (MLC) scheme where a ternary set partitioning combined with binary-input ternary-output (BITO) turbo codes is employed to fully exploit the property of the nonpower- of-two constellation points. Throughout this letter, we focus on an 18-ary HSM with the information rate of 3 bit/symbol as a specific example. It is shown that this system outperforms the standard square 16-QAM with the same rate when PAR is constrained.

We extend our trellis shaping approach of reducing peak-to-average power ratio (PAR) of single-carrier PSK systems to high-order quadrature amplitude modulations (QAMs). Simulation results show that, with only one-bit redundancy per transmitted symbol, significant PAR reduction can be achieved. For example, band-limited transmission with PAR below 3 dB can be achieved with a square 64-QAM after pulse shaping with a roll off factor of as low as 0.1. Furthermore, the newly developed shaping metric offers a capability of simultaneously reducing the average power. The reduction of the PAR and average power can be flexibly controlled by adjusting a parameter associated with the shaping metric.

In this paper, a simple modulation code called symbol insertion for band-limited single-carrier systems is proposed. This code can reduce the peak-to-average power ratio (PAR) with an inherent forward error correction (FEC) capability. The idea of the proposed code is as follows; since the PAR is largely proportional to the phase shifts of consecutive discrete symbols, we eliminate large phase shifts by inserting redundant symbols every after information symbols. Furthermore, exploiting the fact that the insertion process has a trellis structure, we employ the symbol insertion as a component code of concatenated codes. An 8-PSK example demonstrates not only that the PAR reduction performance is superior to conventional PAR reduction schemes, but also that the coding gain is as large as those of conventional capacity-approaching turbo and LDPC codes. Another advantage of the proposed system is simplicity of both coding and decoding processes.

The trellis shaping (TS) is an effective technique not only for average power reduction of high-order QAM signals, but also for peak power reduction of band-limited single-carrier PSK signals. Our recent work has demonstrated that signals with almost constant envelope can be generated. Compared to the unshaped PSK system, however, this shaping process introduces signal constellation expansion exclusively for peak power reduction and thus reduces the minimum Euclidean distance of the PSK signal constellation, rendering the overall system sensitive to channel noise. To overcome this drawback, this paper proposes a new decoding algorithm of the TS that exploits the Markov process property of the shaped symbols. This decoding algorithm can work alone, but becomes more effective when the shaping encoder is serially concatenated with a channel coding. The simulation results demonstrate that this serial concatenation together with an iterative decoding between shaping and coding can achieve a significant amount of coding gain.

In this paper, a novel peak power reduction scheme based on trellis shaping is proposed for single-carrier pulse- shaped phase shift keying (PSK) systems. The use of PSK generally results in relatively low signal dynamic range, but its peak-to-average power ratio tends to increase as the bandwidth of pulse shaping filter becomes narrower. The simulation results demonstrate that the proposed approach can generate signals with almost constant envelope, even with the existence of pulse- shaping filters operated with roll-off factors as low as 0.1.