M-ary Pulse Amplitude Modulation Research Articles

Burst errors suppression for MLSE in high-speed IM/DD transmission systems using PAM.

Maximum likelihood sequence estimation (MLSE) is the optimal signal sequence detection that can remove the inter-symbol interference (ISI). However, we find that the MLSE causes burst consecutive errors alternating between +2 and -2 in M-ary pulse amplitude modulation (PAM-M) IM/DD systems with large ISI. In this paper, we propose to use precoding to suppress the burst consecutive errors resulted from MLSE. A 2 M modulo operation is employed to guarantee that the probability distribution as well as the peak-to-average power ratio (PAPR) of encoded signal remain unchanged. After the receiver-side MLSE, the decoding process that involves adding the current MLSE output to the previous one and applying a 2 M modulo is implemented to break the burst consecutive errors. We conduct experiments to transmit 112/150-Gb/s PAM-4 or beyond 200-Gb/s PAM-8 signals at C-band to investigate the performance of the proposed MLSE integrated with precoding. The results show that the precoding can break burst errors effectively. For 201-Gb/s PAM-8 signal transmission, the precoding MLSE can achieve 1.4-dB receiver sensitivity gain and reduce the maximum length of burst consecutive errors from 16 to 3.

PRBS orders required to train ANN equalizer for PAM signal without overfitting.

Artificial neural network (ANN)-based nonlinear equalizers (NLEs) have been gaining popularity as powerful waveform equalizers for intensity-modulation (IM)/direct-detection (DD) systems. On the other hand, the M-ary pulse amplitude modulation (PAM-M) format is now widely used for high-speed IM/DD systems. For the training of ANN-NLE in PAM-M IM/DD systems, it is common to employ pseudorandom binary sequences (PRBSs) for the generation of PAM-M training sequences. However, when the PRBS orders used for training are not sufficiently high, the ANN-NLE might suffer from the overfitting problem, where the equalizer can estimate one or more of the constituent PRBSs from a part of PAM-M training sequence, and as a result, the trained ANN-NLE shows poor performance for new input sequences. In this paper, we provide a selection guideline of the PRBSs to train the ANN-NLE for PAM-M signals without experiencing the overfitting. For this purpose, we determine the minimum PRBS orders required to train the ANN-NLE for a given input size of the equalizer. Our theoretical analysis is confirmed through computer simulation. The selection guideline is applicable to training the ANN-NLE for the PAM-M signals, regardless of symbol coding.

A capacity-approaching coding scheme for M-PAM VLC systems with dimming control

A visible light communication (VLC) system with intensity modulation and direct detection is considered. A channel coding scheme based on a binary low-density parity-check (LDPC) code and M-ary pulse amplitude modulation (PAM) is designed. The LDPC encoder is followed by a many-to-one mapper. This mapper induces the input distribution for the non-equally spaced M-PAM alphabet under a desired dimming target. No auxiliary coding technique for DC-balance is needed. The coded scheme using non-equally probable M-PAM levels outperforms the use of equally probable levels showing capacity-approaching performance. Moreover, the scheme is flicker-free for typical information rates of a VLC system. The main advantage of the proposed scheme is that it does not incur any coding rate loss compared to other similar schemes in the literature.

Asymptotic Performance of Box-RLS Decoders Under Imperfect CSI With Optimized Resource Allocation

This paper considers the problem of symbol detection in massive multiple-input multiple-output (MIMO) wireless communication systems. We consider hard-thresholding preceded by two variants of the regularized least squares (RLS) decoder; namely the unconstrained RLS and the RLS with a box constraint, which is called Box-RLS. For all schemes, we focus on the evaluation of the mean squared error (MSE) and the symbol error probability (SEP) for M-ary pulse amplitude modulation (M-PAM) symbols transmitted over a massive MIMO system when the channel is estimated using linear minimum mean squared error (LMMSE) estimator. Under such circumstances, the channel estimation error is Gaussian which allows for the use of the convex Gaussian min-max theorem (CGMT) to derive asymptotic approximations for the MSE and SEP when the system dimensions and the coherence duration grow large with the same pace. The obtained expressions are then leveraged to derive the optimal power distribution between pilot and data under a total transmit energy constraint. In addition, we derive an asymptotic approximation of the goodput for all schemes which is then used to jointly optimize the number of training symbols and their associated power. Numerical results are presented to support the accuracy of the theoretical results.

Reduced-state MLSE for an IM/DD system using PAM modulation.

The performance of a high-speed intensity-modulation (IM)/direct-detection (DD) transmission system could be limited by the bandwidth of optical transceivers. One popular way to cope with this performance limitation is to utilize the maximum likelihood sequence estimation (MLSE) at the receiver. However, a practical problem of MLSE is its high implementation complexity. Even though the channel impulse response can be truncated by using a two-tap filter before applying the MLSE, it still faces an implementation problem when used for multi-level modulation formats. In this paper, we propose and demonstrate a reduced-state MLSE for band-limited IM/DD transmission systems using M-ary pulse amplitude modulation (PAM-M) formats. We use a conventional Viterbi algorithm to search a reduced-state trellis, which is constructed by using the coarse pre-decision of the signal equalized by a feed-forward equalizer. Thus, the proposed MLSE reduces the implementation complexity significantly. We evaluate the performance of the proposed reduced-state MLSE over 100∼140-Gb/s PAM-4/6/8 transmission systems implemented by using a 1.3-µm directly modulated laser. The results show that the proposed MLSE achieves almost the same performance as the conventional MLSE but reduces the implementation complexity by a factor of 4∼10 when the complexity is assessed by the number of multiplications and additions.

Adaptive Coded Modulation for IM/DD Free-Space Optical Backhauling: A Probabilistic Shaping Approach

In this paper, we propose a practical adaptive coding modulation scheme to approach the capacity of free-space optical (FSO) channels with intensity modulation/direct detection based on probabilistic shaping. The encoder efficiently adapts the transmission rate to the signal-to-noise ratio, accounting for the fading induced by the atmospheric turbulence. The transponder can support an arbitrarily large number of transmission modes using a low complexity channel encoder with a small set of supported rates. Hence, it can provide a solution for FSO backhauling in terrestrial and satellite communication systems to achieve higher spectral efficiency. We propose two algorithms to determine the capacity and capacity-achieving distribution of the scheme with unipolar M-ary pulse amplitude modulation (M-PAM) signaling. Then, the signal constellation is probabilistically shaped according to the optimal distribution, and the shaped signal is channel encoded by an efficient binary forward error correction scheme. Extensive numerical results and simulations are provided to evaluate the performance. The proposed scheme yields a rate close to the tightest lower bound on the capacity of FSO channels. For instance, the coded modulator operates within 0.2 dB from the M-PAM capacity, and it outperforms uniform signaling with more than 1.7 dB, at a transmission rate of 3 bits per channel use.

Calculation and error bound of Min‐approximated bitwise log‐likelihood ratios of generalised M ‐ary PAM

In modern digital communication systems, a high-order modulation and advanced channel coding are often jointly used to increase the spectral efficiency and coding gain. In this work, the authors investigate a computationally efficient method for evaluating the bitwise log-likelihood ratios of generalised M-ary pulse amplitude modulation (PAM) signals with the Min approximation. The proposed scheme is simple and can be applied to demodulate the M-ary PAM having an arbitrary symbol spacing and a bit stream mapping. The computational complexity and upper bounds of the approximation error are also provided for a better understanding of the proposed scheme.

A Tunable Energy Signal for Intensity Modulation and Direct Detection Systems: Theory, Simulations, and Experiments

In this paper, we propose a novel method to generate real signal for Visible Light Communication (VLC) systems without using traditional hermitian symmetry on the data symbols obtained using M-ary Pulse Amplitude Modulation (PAM) which is named as Auxiliary PAM (Ax-PAM). We mathematically analyse this method to generate a real signal with tunable energy using auxiliary symbols at the transmitter and the corresponding receiver. Simulation results for Bit Error Rate (BER) show better performance over conventional PAM Discrete Multi-Tone (PAM-DMT) and Asymmetrically Clipped Optical Orthogonal Frequency Division Multiplexing (ACO-OFDM) even under clipping distortion and also demonstrate the tunable energy for the proposed scheme. Furthermore, the proposed scheme is implemented on a VLC test bed designed using Universal Software defined Radio Peripheral (USRP). The experimental results for estimated Signal to Noise Ratio (SNR) and achieved BER for Ax-PAM outperforms PAM-DMT and ACO-OFDM.

Joint Probabilistic-Nyquist Pulse Shaping for an LDPC-Coded 8-PAM Signal in DWDM Data Center Communications

M-ary pulse-amplitude modulation (PAM) meets the requirements of data center communication because of its simplicity, but coarse entropy granularity cannot meet the dynamic bandwidth demands, and there is a large capacity gap between uniform formats and the Shannon limit. The dense wavelength division multiplexing (DWDM) system is widely used to increase the channel capacity, but low spectral efficiency of the intensity modulation/direct detection (IM/DD) solution restricts the throughput of the modern DWDM data center networks. Probabilistic shaping distribution is a good candidate to offer us a fine entropy granularity and efficiently reduce the gap to the Shannon limit, and Nyquist pulse shaping is widely used to increase the spectral efficiency. We aim toward the joint usage of probabilistic shaping and Nyquist pulse shaping with low-density parity-check (LDPC) coding to improve the bit error rate (BER) performance of 8-PAM signal transmission. We optimized the code rate of the LDPC code and compared different Nyquist pulse shaping parameters using simulations and experiments. We achieved a 0.43 dB gain using Nyquist pulse shaping, and a 1.1 dB gain using probabilistic shaping, while the joint use of probabilistic shaping and Nyquist pulse shaping achieved a 1.27 dB gain, which offers an excellent improvement without upgrading the transceivers.

Energy Efficient ${M}$ -ary Frequency-Shift Keying-Based Modulation Techniques for Visible Light Communication

In this article, we introduce two variants of energy efficient M-ary frequency-shift keying (FSK) for low data rate/low power Internet-of-Things (IoT) applications. Both variants, i.e., M-ary direct current (DC)-FSK and M-ary unipolar (U)-FSK are compatible with intensity-modulation and direct detection (IM-DD) implementation of visible light communication (VLC). The two techniques intrinsically differ in the manner of attaining a non-negative signal for intensity-modulation. M-ary DC-FSK uses a DC-offset, while, M-ary U-FSK sequentially transmits the positive and the sign flipped negative halves of the bipolar M-ary FSK symbols. The spectral efficiencies of M-ary DC-FSK and M-ary U-FSK are augmented by biorthogonal extension of frequency waveforms resulting in 2M-ary biDC-FSK and 2M-ary biU-FSK, respectively. Two optimal maximum likelihood (ML) receiver configurations with different complexities are introduced for M-ary DC-FSK/2M-ary biDC-FSK. Whereas, for M-ary U-FSK/2M-ary biU-FSK, an optimal ML and a suboptimal receiver are proposed. We appraise the performance of these methods in terms of Euclidean distance, bit error rate (BER) in additive white Gaussain noise and time dispersive channels, energy efficiency with respect to spectral efficiency and computational complexity. Simulations confirm that the proposed techniques are more energy efficient than classical M-ary pulse-amplitude modulation (PAM) in an absolute sense.

Differential pulse‐amplitude modulation signalling for free‐space optical communications

To improve the bandwidth efficiency of free-space optical systems and at the same time to reduce the impact of the background noise, a differential M -ary pulse-amplitude modulation ( M -PAM) signalling scheme that uses two laser transmitters is proposed. The authors first consider the condition that the receiver perfectly knows the instantaneous channel coefficient and compare the performance of the proposed differential PAM with the conventional PAM signalling and show the improved performance when the background noise level is relatively high. Second , the practical situation where the receiver has to estimate the channel for signal detection is considered. The authors propose an estimation scheme based on the characteristics of the differential PAM signalling while requiring no pilot symbol transmission. The proposed data-aided channel estimation is performed on a sequence of received PAM symbols. The authors also show that for a sufficiently large observation window, the proposed estimation method allows achieving a performance close to the perfect channel knowledge.

Error performance of digital modulations over Fisher-Snedecor F fading channels

In this paper, symbol error probability (SEP) and the average symbol error rate (ASER) of digital modulation schemes are derived in the presence of Fisher-Snedecor F fading. First, an analytical SEP expression is proposed based on complementary cumulative distribution function (CDF) for M-ary phase shift keying (M-PSK) and M-ary pulse amplitude modulation (M-PAM). Then, an asymptotic solution is also presented for the SEP of M-PSK and M-PAM modulations in order to get more insights on the performance at high signal-to-noise ratio (SNR) regime. Finally, an exact ASER expression for rectangular quadrature amplitude modulation (RQAM) is derived and then, the ASER performance is analyzed based on two different upper bound approximations of Gaussian Q-function in Fisher-Snedecor F fading channels. The proposed expressions are not only valid for integer values of fading and shadowing parameters but also valid for non-integer values. The performance results which are in good agreement with the exact simulations are illustrated for different modulation schemes and various configurations of fading and shadowing parameters.

Comparison of Optical OFDM and M-PAM for LED-Based Communication Systems

Light-emitting diode (LED)-based communications, such as visible light communications and infrared communications, are candidate techniques to provide short-range and high-speed data transmission. In this letter, $M$ -ary pulse amplitude modulation (M-PAM), used as a high bandwidth efficiency scheme, is compared with three well-known optical orthogonal frequency-division multiplexing (OFDM) schemes. Considering the bandwidth limit and constrained peak transmitted power characteristics of LEDs, a bit loading algorithm and a single-tap equalizer with an optimized modulation index are used for the optical OFDM schemes tested. To reduce the inter-symbol interference caused by the bandlimited channel, an optimized pulse shape and a minimum mean squared error equalizer are applied to the M-PAM system. From numerical results, M-PAM can provide a substantially higher data rate than OFDM for bandlimited channels. When the channel bandwidth is ample compared with the symbol rate, optical OFDM outperforms M-PAM.

Modelling and performance evaluation over Nakagami-m/log-normal fading environments

In this paper, we present the closed-form expressions of composite Nakagami-m/log-normal (NL) fading channel by Holtzman approximation. The obtained expressions are used to derive the important performance parameters of wireless communications systems. These performance matrices are amount of fading (AF), outage probability (PO), average channel capacity (CC) and average symbol error probability (ASEP) of coherent modulation comprising binary orthogonal, antipodal, M-ary phase shift keying (M-PSK) and M-ary pulse amplitude modulation (M-PAM). Furthermore, energy detection (ED) is one of the ways to determine whether the signal is present or not. The performance of ED is studied in terms of complementary receiver operating characteristics (CROC) curve. To verify the correctness of our analysis, the derived closed-form expressions are corroborated via exact result and Monte Carlo simulations.

Resource Allocation in HS-OFDM-based PLC Systems: A Tutorial

This work organizes and discusses important information on resource allocation in power line communication (PLC) systems based on the Hermitian symmetric orthogonal frequency-division multiplexing scheme. In the context of this work, the term resource refers to bits and transmission power, which can be optimally or sub-optimally allocated to subcarriers on the basis of the knowledge of the normalized signal-to-noise ratio (nSNR) of power line subchannels. In this sense, we thoroughly discuss the formulation of the resource allocation for PLC systems and accordingly derive expressions for the nSNR as well as bit and transmission power allocation in all subchannels. Additionally, we precisely detail greedy algorithms to assist practitioners and researchers in the implementation of the resource allocation procedure. Considering a frequency-selective PLC channel corrupted by additive colored Gaussian noise as well as M-ary pulse amplitude modulation and quadrature amplitude modulation as modulation schemes, the influence of the gap from the Shannon capacity curve on symbol error rate probability is discussed. On top of the carried out discussion, numerical results are presented in order to emphasize the usefulness of a proper comprehension of this subject.

On Optimal Non-Equally Spaced M-PAM in Dimmable Visible Light Communication

In this letter, channel capacity of dimmable visible light communication systems with M-ary pulse amplitude modulation (M-PAM) channel input alphabets is investigated. Mutual information is maximized considering both the probability input distribution and the M-PAM levels simultaneously. Schemes with non-equally spaced M-PAM levels are obtained as a result of this maximization process and they lead to gains in capacity when compared with previous schemes proposed in the literature.

Performance Characterization of a Hybrid Satellite-Terrestrial System with Co-Channel Interference over Generalized Fading Channels.

The transmission of signals in a hybrid satellite-terrestrial system (HSTS) in the presence of co-channel interference (CCI) is considered in this study. Specifically, we examine the problem of amplify-and-forward (AF)-based relaying in a hybrid satellite-terrestrial link, where the relay node is operating in the presence of a dominant co-channel interferer. It is assumed that direct connection between a source node (satellite) and a destination node (terrestrial receiver) is not available due to masking by obstacles in the surrounding. The destination node is only able to receive signals from the satellite with the help of a relay node located at the ground. In the proposed HSTS, the satellite-relay channel follows the shadowed Rice fading; and the channels of interferer-relay and relay-destination links experience generalized Nakagami-m fading. For the considered AF-based HSTS, we first develop the analytical expression for the moment generating function (MGF) of the overall output signal-to-interference-plus-noise ratio (SINR). Then, based on the derived exact MGF, we derive novel expressions for the average symbol error rate (SER) of the considered HSTS for the following digital modulation techniques: M-ary phase shift keying (M-PSK), M-ary quadrature amplitude modulation (M-QAM) and M-ary pulse amplitude modulation (M-PAM). To significantly reduce the computational complexity for utility in system-level simulations, simple analytical approximation for the exact SER in the high signal-to-noise ratio (SNR) regime is presented to provide key insights. Finally, numerical results and the corresponding analysis are presented to demonstrate the effectiveness of the developed performance evaluation framework and to view the impact of CCI on the considered HSTS under varying channel conditions and with different modulation schemes.

Universal soft demapper for M-ary PAM with reduced complexity

In this paper, we propose an efficient soft demapper for M-ary pulse amplitude modulation (PAM) schemes. The proposed demapper estimates soft decision bit information (SDBI) for any M-ary PAM symbols using a universal type of hardware structure. The proposed method performs as well as the Max-log method, without any exhaustive search process. Instead, it maps a detected PAM symbol to a specific region, with only one constellation symbol to estimate the distance. In this way, the proposed method requires approximately one distance estimation per bit. We first derive the equations to estimate SDBI for a few Gray-mapped M-ary PAM schemes, and subsequently present compact universal equations applicable to any M-ary PAM scheme. The simulation results confirm that the proposed method produces exactly the same performance as the Max-log method with greatly reduced computational complexity.

Integration of variable-rate OWC with OFDM-PON for hybrid optical access based on adaptive envelope modulation

In this paper, we investigate an integrated optical wireless communication (OWC) and orthogonal frequency division multiplexing based passive optical network (OFDM-PON) system for hybrid wired and wireless optical access, based on an adaptive envelope modulation technique. Both the outdoor and indoor wireless communications are considered in the integrated system. The data for wired access is carried by a conventional OFDM signal, while the data for wireless access is carried by an M-ary pulse amplitude modulation (M-PAM) signal which is modulated onto the envelope of a phase-modulated OFDM signal. By adaptively modulating the wireless M-PAM signal onto the envelope of the wired phase-modulated constant envelope OFDM (CE-OFDM) signal, hybrid wired and wireless optical access can be seamlessly integrated and variable-rate optical wireless transmission can also be achieved. Analytical bit-error-rate (BER) expressions are derived for both the CE-OFDM signal with M-PAM overlay and the overlaid unipolar M-PAM signal, which are verified by Monte Carlo simulations. The BER performances of wired access, indoor OWC wireless access and outdoor OWC wireless access are evaluated. Moreover, variable-rate indoor and outdoor optical wireless access based on the adaptive envelope modulation technique is also discussed.

Method for carrier frequency‐offset estimation of faster‐than‐Nyquist signalling

A new non-data aided frequency-offset estimation scheme for faster-than-Nyquist (FTN) signalling system is proposed. Considering the intentionally introduced intersymbol interference, the envelope of carrier signals is time varying, which makes it difficult to estimate the carrier frequency-offset at the receiver. In order to improve the estimation performance, a new estimation scheme is proposed which is based on Newton's method for minimising the non-linear least-squares error. Moreover, the proposed estimation scheme can be also applied into M-ary pulse-amplitude modulation. Further, the performance of proposed frequency-offset estimation scheme for FTN is verified and tested.