Trellis Shaping Research Articles

Gray mapping method of QAM constellation for trellis shaping

Gray mapping method of QAM constellation for trellis shaping

Coded Modulation and Shaping for Multivalued Physical Unclonable Functions

In this paper, a coded modulation scheme employing signal shaping is proposed and designed for use in multi-valued physical unclonable functions (PUFs). In the literature, usually binary PUFs are considered, where less than one bit of entropy is extracted from each fundamental building block (PUF node). This randomness in the hardware may then used for the derivation of cryptographic keys. Meanwhile, PUFs over higher-order alphabets, so-called multi-valued PUFs (MVPUFs) have been presented. Typically, symbols from a higher-order alphabet are extracted by suited quantization. In contrast, in this paper we propose a coded modulation scheme which directly works on the analog values provided by the PUF nodes. We establish an interpretation as digital transmission with randomness at the transmitter, and thereon calculate the respective capacities of bit levels for the Gaussian distributed reference PUF readout in additive Gaussian noise. In addition, the metric for optimum soft-decision decoding is derived. Thereby, the coded modulation scheme can be designed for the present situation. A helper data scheme adapted to the given situation is proposed and analyzed. Moreover, on top of the multilevel coding scheme, we employ signal shaping for the first time in the context of PUFs. In particular, trellis shaping is applied. By this, the coded modulation scheme can be perfectly matched to the PUF statistics. This is reflected by the results of conducted numerical simulations. High coding rates can be used, i.e., a large entropy per PUF node can be extracted, with very high reliabilities.

Trellis Shaping for Fiber Nonlinearity Mitigation in Coherent Optical OFDM Systems

In this article, trellis shaping technique is numerically and experimentally investigated to improve the performance of optical orthogonal frequency division multiplexing (OFDM) signal. Different from other constellation shaping techniques, trellis shaping can be designed to reduce the correlation value of OFDM data sequence and average power simultaneously in one OFDM symbol. It means that optical OFDM signals generated by trellis shaping can improve the performance under both linear and nonlinear channels. For comparison with trellis shaping technique, we also consider optimal Maxwell–Boltzmann (MB) shaping and uniform signaling techniques at spectral efficiency (SE) of 10 and 14 bits/4D-sym. Numerical simulations show that trellis shaping can provide certain shaping gain over uniform signaling under linear additive white Gaussian noise (AWGN) channel. The fiber transmission results indicate that OFDM signals with trellis shaping have higher effective signal-to-noise ratio (SNR) than those with MB shaping and uniform signaling. It means that trellis shaping technique has the ability to mitigate the fiber nonlinear noise. Considering both linear and nonlinear noise in the fiber link, trellis shaping can extend the transmission distance by $\sim$ 110 km and $\sim$ 200 km over MB shaping and uniform signaling at SE of 10 bits/4D-sym. At SE of 14 bits/4D-sym, trellis shaping provides similar performance as MB shaping but $\sim$ 120-km extension reach in comparison with uniform signaling. The performances of OFDM signals with trellis shaping, MB shaping and uniform signaling are also experimentally investigated in a four-channel wavelength division multiplexing (WDM) fiber transmission systems. The experimental results show that trellis shaping can also mitigate the nonlinear distortions induced by the clipping effects at the transmitter side. Compared with MB shaping, trellis shaping extends the transmission reach by $\sim$ 240 km and $\sim$ 90 km at SE of 10 and 14 bits/4D-sym, respectively.

PAPR Reduction of OFDM With Trellis Shaping Based on ${p}$ -Norm Minimization

We propose a new metric for trellis shaping (TS) that reduces the peak-to-average power ratio (PAPR) of orthogonal frequency-division multiplexing (OFDM) signals. The proposed metric is based on the ${p}$ -norm of the OFDM signal instantaneous power and generalization of the conventional time-domain metric based on the maximum peak power. Furthermore, we prove that the proposed metric with ${p} =$ 2 is equivalent to the conventional frequency-domain (FD) approach that minimizes the squared sidelobe of the autocorrelation function of transmit symbols. Simulation results demonstrate that the TS using the proposed metric with the optimized norm outperforms the conventional maximum peak power and FD approaches by 0.15 dB and 0.95 dB, respectively, in terms of the PAPR evaluated at $\mathrm {CCDF}={10}^ {-4}$ . On the other hand, the FD metric still performs best in terms of the achievable cubic metric.

A New Trellis Shaping Design for Peak Power Reduction of SC-FDMA Signals With High-Order QAM

Single-carrier frequency-division multiple-access (SC-FDMA) has been adopted as the uplink radio access scheme of the fourth-generation mobile wireless communication system because of its signal with lower peak-to-average power ratio (PAPR) compared to multicarrier based signals. However, when it is combined with high-order quadrature amplitude modulation (QAM) for higher bandwidth efficiency, the SC-FDMA signal also exhibits relatively high PAPR, and thus, the resulting efficiency of power amplifier (PA) will be considerably reduced. Since PA is a dominant source of power consumption at the transmitter, further reduction of PAPR should be necessary in view of future green cellular systems. In this paper, we propose a new trellis shaping (TS) design for peak power reduction of SC-FDMA signals. We first observe that the direct application of the TS developed for peak power reduction of conventional single-carrier signals tends to incur high peaks at the edges of each SC-FDMA signal due to their circularly periodic structure. We tackle this problem by introducing a novel modification of TS such that the symbols at one edge can be controlled by those located at the other edge. It is shown that the SC-FDMA signal with the proposed TS is able to significantly improve the PA efficiency. We demonstrate its effectiveness by investigating system level performances, such as the achievable PA efficiency and resulting power spectral density, as well as its symbol error rate (SER) over additive white Gaussian noise channels with frequency-selective Rayleigh fading in the presence of PA nonlinearity.

Trellis-Assisted Constellation Subset Selection for PAPR Reduction of OFDM Signals

In this paper, we propose a new peak-to-average power ratio (PAPR) reduction technique, which is referred to as trellis-assisted constellation subset selection ( TACSS , or TAX for short), for orthogonal frequency-division multiplexing (OFDM) signals. We control the signal transition by judiciously selecting the appropriate constellation subset for PAPR reduction with the controlling bits that are subject to the trellis-based constraint imposed by a bank of memories. A novel constellation design suitable for the proposed system is also introduced. A major property offered by the proposed approach is that the controlling bits and the information bits are perfectly separable at the receiver, which leads to a simple implementation of its soft-in–soft-out (SISO) decoder for coded OFDM systems. Through the performance analysis of PAPR reduction capability, power amplifier (PA) efficiency, average mutual information (AMI), and bit error rate (BER), the achievable tradeoff relationship between the transmitter and receiver performances of the proposed system is addressed. Furthermore, performance comparisons of the proposed scheme with other major PAPR reduction schemes such as trellis shaping, discrete Fourier transform (DFT) precoding, and clipping and filtering demonstrate its practical advantage in a high-spectral-efficiency regime.

A Trellis Shaping for Peak and Average Power Reduction of BICM-OFDM Signals

One of the major drawbacks of orthogonal frequency-division multiplexing (OFDM) systems is their high peak-to-average power ratio (PAPR) signals, and trellis shaping (TS) is a promising approach for reducing both peak power and average power of OFDM signals. In practice, OFDM should be employed with coded modulation for improving reliability, and bit-interleaved coded modulation (BICM) has been often combined with OFDM to gain robustness against severe fading channels. In this work, we propose a new BICM-OFDM system concatenated with TS for achieving good error performance. To this end, a novel soft-in-soft-out decoder for TS is developed. Optimization of the shaping convolutional code in terms of transmitter performance is also discussed. The effectiveness of our system is demonstrated through the analysis in terms of average mutual information as well as frame error rate (FER) over an additive white Gaussian noise channel. Furthermore, the FER is evaluated over a frequency-selective Rayleigh fading channel and compared with the theoretical outage probability. The simulation results reveal that our system can achieve good frequency diversity effect over such a fading channel while enjoying much lower PAPR.

Peak and Average Power Reduction of OFDM Signals Based on Trellis Shaping with Controllable Region Expansion

Trellis shaping (TS) is an efficient and flexible signal controlling technique based on the trellis structure at the transmitter. It can be used for reducing both average power and peak-to-average power ratio (PAPR) of orthogonal frequency-division multiplexing (OFDM) signals. Most studies in the framework of TS have focused on the simple sign-bit shaping, which controls the signal transition with only a single controlling bit per quadrature amplitude modulation (QAM) symbol (or subcarrier). In this paper, we attempt to increase the number of the controlling bits so as to improve the PAPR reduction capability of OFDM signals. The resulting approach, which we refer to as a controllable region expansion, is a novel extension of the conventional TS where the number of the controlling bits per QAM is increased without imposing additional complexity. Through the investigation based on extensive computer simulations using a nonlinear power amplifier (PA) model, it is shown that the proposed extended TS can achieve a better trade-off compared to the conventional sign-bit TS in terms of PAPR reduction capability, PA efficiency, and resulting bit error rate (BER) performance.

WITHDRAWN: Peak power reduction of SC-FDMA signals based on trellis shaping

WITHDRAWN: Peak power reduction of SC-FDMA signals based on trellis shaping

Performance Comparison of Uncoded OFDM Systems with Trellis Shaping over Nonlinear Channels

Orthogonal frequency-division multiplexing (OFDM) can achieve remarkable performance in terms of spectral efficiency, but its power amplifier efficiency becomes poor because of its high peak-to-average power ratio (PAPR) nature of transmitted signals. Trellis shaping is an effective method to reduce peak and average power without signal distortion at the cost of transmitter complexity and its performance depends on the metric used for the trellis decoder. Several metrics, defined in either time or frequency domain, have been proposed in the literature. In many practical OFDM systems, however, slight nonlinearity is tolerable as long as the resulting distortion meets the system requirements such as bit error rate (BER) and spurious level of transmitted signals. In this paper, we make a thorough performance comparison of trellis-shaped uncoded OFDM systems with different metrics in terms of complexity, achievable PAPR, and resulting BER as well as power spectrum in a practical channel where the signal envelope is distorted by a power amplifier (PA). Our study shows that the metric designed in frequency domain is mostly favorable in such a scenario.

OFDM PAPR Reduction by Shifting Null Subcarriers Among Data Subcarriers

This proposed method reduces the peak-to-average power ratio (PAPR) of multi-carrier transmission, by exploiting null-subcarriers. Compared with the Partial Transmit Sequence Simulated Annealing (PTS-SA) method, the proposed method yields better PAPR reduction performance while consuming the same computation complexity and less channel side information (CSI). The proposed method also demonstrates better bit-error-rate (BER) performance and much lower computation complexity than Null-Switching when CSI is available. Meanwhile, our method is compatible with the current commercial systems and can incorporate with most other PAPR-reduction methods (such as partial transmit sequences, selective mapping, tone injection, trellis shaping).

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.

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 precoding for MIMO broadcast signaling

Channel inversion, and its minimum mean square error (MMSE) variation, are low complexity methods for space division multiple access (SDMA) in multiple input multiple output broadcast channel (MIMO-BC). As the channel matrix deviates from orthogonal, these methods result in a waste of transmit power. This paper proposes a trellis precoding method (across time and space) to improve the power efficiency. Adopting a 4-state trellis shaping method, the complexity of the proposed method, which is entirely at the transmitter side, is equivalent to the search in a trellis with 4N states where N is the number of transmit antennas. Numerical results are presented showing that the achievable gains, which depend on the channel realization, can be significantly higher than the traditional shaping gain which is limited to 1.53 dB.

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 novel PAPR reduction with trellis shaping for NC-OFDM in cognitive radio

In this paper, trellis shaping is applied to reducing the Peak-to-Average Power Ratio (PAPR) of NC-OFDM signals due to the fact that the total number of active subcarriers and their locations might change continuously in a dynamic spectrum access network. A new branch metric of trellis shaping is proposed which reduces the PAPR of OFDM signals through minimizing the variance of the power by VA decoder. The overall performance considerably depends on the type of signal mapping, and therefore a new type of 64QAM mapping method is designed. Simulation results show that this scheme significantly reduces the PAPR. Finally, a significant phenomenon is demonstrated that the PAPR of NC-OFDM signals in which the deactivated carriers is distributed in the Bernoulli distribution has better performance than that of OFDM signals.

Near constant envelope trellis shaping for PSK signaling

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.

On Trellis Shaping for PAR Reduction in OFDM Systems

The application of trellis shaping was proposed to reduce the peak-to-average power ratio (PAR) of orthogonal frequency division multiplexing (OFDM) signals. In this letter, we review the trellis-shaping schemes presented in the literature, and we introduce modifications such as a new decoding metric and the use of sequential decoding. We conduct comprehensive complexity and performance comparisons for the different schemes, and one interesting result of this work is that, in terms of PAR-reduction capability, trellis shaping with time-domain metrics is generally superior to trellis shaping with frequency-domain metrics. Furthermore, the proposed modifications enable trellis shaping for PAR reduction with a flexible performance-complexity tradeoff.

Space–Time Trellis Code Design Based on QAM-MTCM With Trellis Shaping

In this letter, super-orthogonal space-time trellis codes (SOSTTCs) are extended for quadrature amplitude modulation (QAM) constellations. A systematic set-partitioning method for QAM constellations is given. Furthermore, trellis shaping based on set partitioning is incorporated in SOSTTCs with QAM symbols to achieve extra shaping gain. Peak constraints can be used to limit the constellation expansion ratio and peak-to-average power ratio

Space-Time Coded OFDM with Low PAPR

Recently the use of multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems has been proposed for signaling over frequency-selective fading channels. Although various aspects of these systems have been considered in the literature, the problem of the inherent high peak-to-average power ratio (PAPR) is not examined. In this paper, we consider PAPR reduction for MIMO-OFDM systems and propose alternate low-complexity algorithms that can be used in conjunction with the trellis shaping method. We show that a PAPR reduction in the order of 4- can be achieved at the cost of a slight reduction in the spectral efficiency. Furthermore, we compare the trellis shaping technique with other PAPR reduction techniques such as tone reservation and partial transmit sequences.