Makoto Tanahashi

A multilevel coded modulation approach for hexagonal signal constellation

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.

On the distribution of instantaneous power in single-carrier signals

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).

Turbo decoding of concatenated channel coding and trellis shaping for peak power controlled single-carrier systems

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.

Trellis Shaping for Controlling Envelope of Single-Carrier High-Order QAM Signals

In this paper, trellis shaping (TS) is applied to dynamic range control of band-limited single-carrier high-order quadrature amplitude modulation (QAM) signals. With a newly designed shaping metric, we show that a signal with very low peak-to-average power ratio (PAR) can be achieved without significant loss of data rate. A specific example demonstrates that a band-limited transmission with spectral efficiency of 4.55 bit/s/Hz (including the redundancy due to the shaping) and PAR below 3 dB is achievable using a square 64-ary QAM constellation and a root raised-cosine filter with a roll-off factor 0.1. Furthermore, the proposed TS for high-order QAM can simultaneously reduce the average power and thus offers a shaping gain. The reduction of the PAR and average power can be flexibly controlled by adjusting a parameter associated with the shaping process.

A New Trellis Shaping Approach for Pulse-Shaped PSK Signals with Almost Constant Envelope

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.

A bit-labeling design for trellis-shaped single-carrier PSK with PAPR reduction

Band-limited single-carrier signals, even with a phase-shift keying (PSK) constellation, suffer from relatively high peak-to-average power ratio (PAPR) when a narrow pulse-shaping filter is used at the transmitter. In our recent work, an application of trellis shaping (TS) has been studied extensively for the purpose of reducing PAPR of band-limited single-carrier PSK signals, and it has been shown that a nearly constant envelope signal can be generated even with the use of nearly rectangular pulse-shaping filter. In this paper, we first demonstrate that the uncoded bit error rate (BER) and PAPR reduction capability of the TS considerably depend 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 Gray labeling. Finally, the BER of each constellation is theoretically analyzed and compared with the simulation results.

A new bit-labeling for trellis-shaped PSK with improved PAPR reduction capability

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).

Peak Power Reduction of Single-Carrier Signals Using Trellis Shaping with M and Stack Algorithms

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. I. INTRODUCTION In many wireless and mobile communication systems, band- width and power efficiencies are the two most important factors. In order to enhance bandwidth efficiency, the use of linear modulations such as pulse-shaped PSK and QAM is necessary, and even higher efficiency can be achieved by using a pulse shaping filter with a narrow roll-off band or by combining QAM with orthogonal frequency-division multiplexing (OFDM). The OFDM signals, however, tend to

On destructive superposition of shaping pulses in band-limited linear modulation systems

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.

Analysis and Efficient Computation of Instantaneous Power Distribution of Single-Carrier Signals

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.