4-ary Pulse Amplitude Modulation Research Articles

Probabilistic Shaping-Based Spatial Modulation for Spectral-Efficient VLC

Visible light communication (VLC) is a promising technology for 6th-generation (6G) networks because of its attractive feature such as a wide unlicensed spectrum. In this paper, a novel adaptive coded spatial modulation scheme with probabilistic shaping (PS) is proposed to approach the capacity of the spatial modulation (SM) in visible light communication (VLC) channels with intensity modulation and direct detection (IM/DD). In the proposed scheme, spatial and constellation symbols are probabilistically shaped depending on the user’s location inside the room and the optical signal-to-noise ratio (OSNR). Moreover, we optimize the channel coding rate to maximize further the achievable rate of the proposed scheme for a given OSNR. Finally, we propose an algorithm to compute the capacity-achieving distribution of the proposed scheme with unipolar <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary pulse amplitude modulation (PAM) signaling. The proposed scheme outperforms uniform and an orthogonal frequency-division multiplexing (OFDM) based scheme in terms of spectral efficiency (SE) and/or frame error rate (FER). For example, for 8-PAM signaling with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N=8$ </tex-math></inline-formula> transmit antennas, the proposed scheme operates within 0.2 dB from the unipolar <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -PAM SM VLC channel signaling capacity and outperforms the uniform and OFDM based schemes in terms of FER by at least 1.1 dB and 1.3 dB at a normalized data rate of 1.33 bits per channel use per sub-carrier (b/cu/sc), respectively.

Space-Time Block Coded Spatial Modulation for Indoor Visible Light Communications

Visible light communication (VLC) has been recognized as a promising technology for handling the continuously increasing quality of service and connectivity requirements in modern wireless communications, particularly in indoor scenarios. In this context, the present work considers the integration of two distinct modulation schemes, namely spatial modulation (SM) with space time block codes (STBCs), aiming at improving the overall VLC system reliability. Based on this and in order to further enhance the achievable transmission data rate, we integrate quasi-orthogonal STBC (QOSTBC) with SM, since relaxing the orthogonality condition of OSTBC ultimately provides a higher coding rate. Then, we generalize the developed results to any number of active light-emitting diodes (LEDs) and any <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -ary pulse amplitude modulation size. Furthermore, we derive a tight and tractable upper bound for the corresponding bit error rate (BER) by considering a simple two-step decoding procedure to detect the indices of the transmitting LEDs and then decode the signal domain symbols. Notably, the obtained results demonstrate that QOSTBC with SM enhances the achievable BER compared to SM with repetition coding (RC-SM). Finally, we compare STBC-SM with both multiple active SM (MASM) and RC-SM in terms of the achievable BER and overall data rate, which further justifies the usefulness of the proposed scheme.

On Minimizing Symbol Error Rate Over Fading Channels With Low-Resolution Quantization

We analyze the symbol error probability (SEP) of $M$-ary pulse amplitude modulation ($M$-PAM) receivers equipped with optimal low-resolution quantizers. We first show that the optimum detector can be reduced to a simple decision rule. Using this simplification, an exact SEP expression for quantized $M$-PAM receivers is obtained when Nakagami-$m$ fading channel is considered. The derived expression enables the optimization of the quantizer and/or constellation under the minimum SEP criterion. Our analysis of optimal quantization for equidistant $M$-PAM receiver reveals the existence of error floor which decays at a double exponential rate with increasing quantization bits, $b$. Moreover, by also allowing the transmitter to optimize the constellation based on the statistics of the fading channel, we prove that the error floor can be eliminated but at a lower decay exponent than the unquantized case. Characterization of this decay exponent is provided in this paper. We also expose the outage performance limitations of SEP-optimal uniform quantizers. To be more precise, its decay exponent does not improve with $b$. Lastly, we demonstrate that the decay exponent of a quantized receiver can be complemented by receive antenna diversity techniques.

Energy-Efficient Index Modulation With In-Phase/Quadrature Format in the Generalized Fading Channel

Dual-mode (DM) or multi-mode (MM) index modulation (IM) techniques with the in-phase/quadrature (IQ) format have been investigated for improving the performance of the orthogonal frequency division multiplexing with IM (OFDM-IM) system in the frequency-selective Rayleigh fading channel. However, all subcarriers in these schemes must be activated so that the energy efficiency (EE) of the system inevitably decreases. In this paper, we propose a novel modulation scheme named quadrature tri-mode index modulation (QTM-IM) technique to achieve a trade-off between the spectral efficiency (SE) and EE. The proposed QTM-IM can also be flexibly extended into multi-mode form called MM with enhanced IQ (MM-EIQ). The multi-mode $M$ -ary pulse amplitude modulation (PAM) constellations containing the origin point are designed to map the information bits into the active subcarriers. On the other hand, the theoretical analysis of IM-based schemes over the Rician fading channel has been conducted since most previous papers only considered the Rayleigh fading channel. At the receiver, three kinds of detectors with different algorithm complexities are employed for signal demodulation. Finally, the computer simulation results demonstrate the enhancement of the proposed schemes. More specially, (i) QTM-IM achieves 4dB signal-to-noise ratio (SNR) gain at the BER level of 10−5 compared with quadrature DM (QDM) scheme with the same SE in the Rician fading channel and (ii) MM-EIQ harvests 0.89 bits/s/Hz SE gain and almost doubles the EE compared with MM-IQ scheme without any SNR loss over the Rayleigh fading channel.

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.

Generalized Spatial Modulation With Multi-Index Modulation

In this letter, we propose a novel scheme extending index dimension with two distinct signal constellations, named as generalized spatial modulation with multi-index modulation (GSM-MIM). Through this scheme, which exploits the spatial domain and index domain, more extra information bits are transmitted by the spatial indexes as compared with the traditional GSM system. More specifically, with the aid of a vector index bit, a transmitted spatial vector (TSV) is derived by combining two spatial vectors, one of which is obtained by mapping $M$ -ary pulse amplitude modulation ( $M$ -PAM) symbol on an antenna index (AI) vector with the aid of both a key index bit and a group of AI bits, and the other one of which is obtained by mapping $L$ -quadrature amplitude modulation ( $L$ -QAM) symbol on another AI vector with another group of AI bits. Furthermore, the modified $M$ -PAM ( $M$ -MoPAM) is designed for increasing the squared minimum Euclidean distance (SMED) between the TSVs, the average bit error probability (ABEP) and the SMED are provided and analyzed. Finally, simulation results using Monte Carlo demonstrate that the GSM-MIM scheme has a significantly lower bit error ratio (BER) than other MIMO schemes.

Polarity-Header Optical OFDM for Visible Light Communication Systems

Orthogonal frequency division multiplexing (OFDM) is a candidate modulation technique to achieve high-speed data transmission in visible light communication systems that provide both illumination and downlink data transmission. This paper proposes a method called polarity-header optical OFDM (PHO-OFDM) specially designed to account for the nonlinear response of the LED transmitters. To make the transmitted signal positive, as required for intensity modulation and direct detection systems, a signal header containing the sign information of the bipolar OFDM signal is transmitted followed by the amplitude of the signal. The binary sign information can be encoded and transmitted via a few samples using $M$ -ary pulse-amplitude modulation. The amplitude of the OFDM signal that is larger than the maximum LED power is sent in a subsequent frame to reduce the nonlinear distortion due to peak-power clipping. Furthermore, illumination requirements are taken into account, and their effects on the system performance are discussed. This paper also considers the overhead cost of adding a cyclic prefix to minimize intersymbol interference in dispersive channels. Compared with state-of-the-art optical OFDM techniques, the proposed PHO-OFDM achieves a better BER performance and higher data throughput, and provides a larger illumination flexibility.

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.

M-PAM Joint Optimal Waveform Design for Multiuser VLC Systems Over ISI Channels

Visible light communication is a candidate technique to provide high-speed data transmissions. This paper proposes a joint optimal waveform design algorithm for visible light communication systems using $M$ -ary pulse amplitude modulation to support multiple users. Transmitted waveforms and minimum mean squared error filters are jointly optimized to minimize the intersymbol and multiple access interferences. Based on different channel conditions, the designed waveforms and modulation constellation sizes can be adaptively adjusted to guarantee the highest bit rates. Channel uncertainty is also considered in this paper. Compared with optical code division multiple access and time division multiple access, the algorithm proposed can provide higher bit rates. In addition, the proposed algorithm can flexibly adjust the illumination level by changing the optimization constraints. An offline waveform design algorithm is then proposed to diminish the optimization computation time. A waveform lookup table can be established offline in advance, and the proper waveforms can be selected from the table based on the actual channel gains in real time. The performance of the offline algorithm can be estimated by using the channel uncertainty model.

Multiple-Mode Orthogonal Frequency Division Multiplexing With Index Modulation

Orthogonal frequency division multiplexing with index modulation (OFDM-IM) performs transmission by considering two modes over OFDM subcarriers, which are the null and the conventional $M$ -ary signal constellation. The spectral efficiency (SE) of the system, however, is limited, since the null mode itself does not carry any information and the number of subcarrier activation patterns increases combinatorially. In this paper, a novel IM scheme, called multiple-mode OFDM-IM (MM-OFDM-IM), is proposed for OFDM systems to improve the SE by conveying information through multiple distinguishable modes and their full permutations. A practical and efficient mode selection strategy, which is constrained on the phase shift keying/quadrature amplitude modulation constellations, is designed. Two efficient detectors that provide different tradeoffs between the error performance and detection complexity are also proposed. The principle of MM-OFDM-IM is further extended to the in-phase and quadrature components of OFDM signals, and the method of generating multiple modes from the $M$ -ary pulse amplitude modulation constellation for this modified scheme is also introduced. Bit error rate (BER) analyses are provided for the proposed schemes. Monte Carlo simulations on BER corroborate the analyses and show that the proposed schemes appear as promising multi-carrier transmission alternatives by outperforming the existing OFDM-IM counterparts.

Bandlimited Optical Intensity Modulation Under Average and Peak Power Constraints

Bandlimited optical intensity channels, arising in applications such as visible light communications, require that all signals satisfy a bandwidth constraint as well as average, peak, and non-negativity amplitude constraints. In this paper, a 2-D signal space for bandlimited optical intensity channels is presented. A novel feature of this model is that the non-negativity and peak constraints are relaxed, and the signal space parameterizes the probability of the negative or peak amplitude excursions in the output. Although the intensity channel only supports non-negative amplitudes, the impact of clipping on system performance is shown to be negligible if the likelihood of the negative excursion is small. A tractable approximation using finite series is used to accurately compute the probability of clipping under average and peak optical power constraints. The optical power and spectral efficiencies using hexagonal lattice constellations are computed. Schemes designed in this paper have higher average and peak optical power gains than $M$ -ary pulse amplitude modulation (PAM) using previously established techniques for spectral efficiencies greater than 2.5 and 3.5 bits/s/Hz, respectively. For high spectral efficiency, e.g., greater than 6 bits/s/Hz, the proposed scheme attains a more than 2-dB average and peak optical power gain over 16-PAM using the previous approaches.

On the Information Loss of the Max-Log Approximation in BICM Systems

We present a comprehensive study of the information rate loss of the max-log approximation for $M$-ary pulse-amplitude modulation (PAM) in a bit-interleaved coded modulation (BICM) system. It is widely assumed that the calculation of L-values using the max-log approximation leads to an information loss. We prove that this assumption is correct for all $M$-PAM constellations and labelings with the exception of a symmetric 4-PAM constellation labeled with a Gray code. We also show that for max-log L-values, the BICM generalized mutual information (GMI), which is an achievable rate for a standard BICM decoder, is too pessimistic. In particular, it is proved that the so-called "harmonized" GMI, which can be seen as the sum of bit-level GMIs, is achievable without any modifications to the decoder. We then study how bit-level channel symmetrization and mixing affect the mutual information (MI) and the GMI for max-log L-values. Our results show that these operations, which are often used when analyzing BICM systems, preserve the GMI. However, this is not necessarily the case when the MI is considered. Necessary and sufficient conditions under which these operations preserve the MI are provided.

Switched-Power Two-Layer Superposition Coding in Cooperative Decode-Forward Relay Systems

In this paper, we consider a decode-forward relay system with a source, a relay, and a destination, where two-layer superposition codes are used at the source and the relay. An equivalent squared minimum distance (ESMD) that determines the error performance is derived by using an upper bound on the pair-wise error probability. Without deriving error probabilities, the error performance level for each of superimposed symbols can be shown in a straightforward manner by the ESMD. An optimal superposition-coded relay scheme and a suboptimal switched-power superposition coding scheme are proposed by improving the ESMD. Closed-form power allocation that maximizes the ESMD for the switched scheme is derived for 2-ary pulse amplitude modulation (PAM). An $M$ -ary PAM generalization for the switched-power superposition-coded relay scheme is also presented. Simulation results show that significant signal-to-noise ratio gains are achieved in the optimal and switched-power superposition coding strategies for 2-ary and 4-ary PAM over the Rayleigh fading channel.

Novel Tight Closed-Form Bounds for the Symbol Error Rate of EGC and MRC Diversity Receivers Employing Linear Modulations Over $$\alpha -\mu $$ α - μ Fading

In this paper, we propose novel lower and upper bounds on the average symbol error rate (SER) of the dual-branch maximal-ratio combining and equal-gain combining diversity receivers assuming independent branches. $$M$$ M -ary pulse amplitude modulation and $$M$$ M -ary phase shift keying schemes are employed and operation over the $$\alpha -\mu $$ ? - μ fading channel is assumed. The proposed bounds are given in closed form and are very simple to calculate as they are composed of a double finite summation of basic functions that are readily available in the commercial software packages. Furthermore, the proposed bounds are valid for any combination of the parameters $$\alpha $$ ? and $$\mu $$ μ as well as $$M$$ M . Numerical results presented show that the proposed bounds are very tight when compared to the exact SER obtained via performing the exact integrations numerically making them an attractive much simpler alternative for SER evaluation studies.

Capacity Analysis of M-PAM Inverse Source Coding in Visible Light Communications

We previously proposed inverse source coding (ISC) to maximize the transmission rate in visible light communications with dimming capability using ON-OFF keying. First, this paper extends the proposed ISC approach to -ary pulse amplitude modulation and obtains the optimal probability distributions. Then, dimming capacity is used to compare the existing analog dimming approach, the extended ISC approach, and the hybrid of these approaches. We conclude that ISC is the best approach, and threshold values for adaptive modulation are derived depending on signal quality and dimming target.

Comparison of Orthogonal Frequency-Division Multiplexing and ON–OFF Keying in Direct-Detection Multimode Fiber Links

We compare the performance of several direct-detection orthogonal frequency-division multiplexing (OFDM) schemes to that of ON-OFF keying (OOK) in combating modal dispersion in multimode fiber links. We review known OFDM techniques, including dc-clipped OFDM (DC-OFDM), asymmetrically clipped optical OFDM (ACO-OFDM) and pulse-amplitude modulated discrete multitone (PAM-DMT). We describe an iterative procedure to achieve optimal power allocation for DC-OFDM and compare analytically the performance of ACO-OFDM and PAM-DMT. We also consider unipolar <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary pulse-amplitude modulation ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -PAM) with minimum mean-square error decision-feedback equalization (MMSE-DFE). For each technique, we quantify the optical power required to transmit at a given bit rate in a variety of multimode fibers. For a given symbol rate, we find that unipolar <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -PAM with MMSE-DFE has a better power performance than all OFDM formats. Furthermore, we observe that the difference in performance between <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -PAM and OFDM increases as the spectral efficiency increases. We also find that at a spectral efficiency of 1 bit/s/Hz, OOK performs better than ACO-OFDM using a symbol rate twice that of OOK. At higher spectral efficiencies, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -PAM performs only slightly better than ACO-OFDM using twice the symbol rate, but requires less electrical bandwidth and can employ analog-to-digital converters at a speed only 81% of that required for ACO-OFDM.

Selection Relaying Schemes for Cooperative Wireless Networks With Adaptive Modulation

Due to the half-duplex transmission nature of cooperative protocols, almost all cooperative diversity systems suffer from low spectral efficiency. In general, adaptive modulation can offer a good tradeoff between spectral efficiency and bit-error-probability (BEP) performance of wireless communication systems. In this paper, we propose two adaptive modulation schemes for the cooperative system with detect-and-forward relaying that simultaneously exploit the cooperative diversity gain and improve the spectral efficiency of the system. In the first scheme, which is similar to conventional selection relaying, the relay decides independently whether to forward the source messages to the destination or not by comparing the instantaneous received signal-to-noise ratio (SNR) with a predetermined fixed threshold, which is independent of the instantaneous modulation scheme. In contrast, in the second scheme, the relay and the destination jointly decide whether the relay will participate in the second phase of the protocol or remain silent. This second scheme can be viewed as a combination of selection and incremental relaying and achieves higher spectral efficiency in comparison with its nonincremental counterparts. We evaluate the performance of the protocols in terms of the end-to-end BEP, the average spectral efficiency, and the outage probability for both identically and nonidentically distributed Rayleigh fading environments. In our analysis, we consider M-ary phase-shift keying ( M-PSK) modulation, M -ary pulse-amplitude modulation (M-PAM), and M-ary quadrature-amplitude modulation ( M-QAM) schemes and examine the impact of error propagation from the relay to the destination on the end-to-end performance of the system in detail. Moreover, we derive a closed-form expression for the optimal relaying threshold that effectively mitigates error propagation and minimizes the end-to-end BEP of the system. The high-SNR analysis demonstrates that both proposed schemes provide full diversity.

Signal Processing by Generalized Receiver in DS-CDMA Wireless Communication Systems with Optimal Combining and Partial Cancellation

Symbol error rate (SER) of quadrature subbranch hybrid selection/maximal-ratio combining (HS/MRC) scheme for 1-D modulations in Rayleigh fading under employment of the generalized receiver (GR), which is constructed based on the generalized approach to signal processing (GASP) in noise, is investigated. diversity input branches are split into in-phase and quadrature subbranches. -ary pulse amplitude modulation, including coherent binary phase-shift keying (BPSK), with quadrature subbranch HS/MRC is investigated. GR SER performance for quadrature HS/MRC and HS/MRC schemes is investigated and compared with the conventional HS/MRC receiver. Comparison shows that the GR with quadrature subbranch HS/MRC and HS/MRC schemes outperforms the traditional HS/MRC receiver. Procedure of partial cancellation factor (PCF) selection for the first stage of hard-decision partial parallel interference cancellation (PPIC) using GR employed by direct-sequence code-division multiple access (DS-CDMA) systems under multipath fading channel in the case of periodic code scenario is proposed. Optimal PCF range is derived based on Price's theorem. Simulation confirms that the bit error rate (BER) performance is very close to potentially achieved one and surpasses the BER performance of real PCF for DS-CDMA systems discussed in the literature.

Gallager's decoding algorithm Α over high order modulations

Gallager's decoding algorithm A (GDA) for low density parity check (LDPC) codes is of interest mainly due to its good performance with extremely low complexity. In this paper, we analyze GDA over 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> -ary pulse-amplitude modulation (2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> -PAM). Firstly, we represent its average error probability by means of a recursion formula. We then define its threshold for additive white Gaussian noise (AWGN) channels and derive its stability condition. The bit-to-symbol mapping strategies have a strong influence on the performance of LDPC-coded modulation systems. Finally, we show that the bit-reliability mapping strategy proposed by Li and Ryan maximizes the threshold of the LDPC coded modulation system with GDA over Gray-mapped 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> -PAM in the AWGN channel.

Error Performance of Selection Combining and Switched Combining Systems in Rayleigh Fading Channels With Imperfect Channel Estimation

In this paper, we present a general analysis of the performance of selection combining (SC), switch-and-stay combining (SSC), and switch-and-examine combining (SEC) systems in Rayleigh fading channels with imperfect channel estimation (ICE). The complex channel estimate and the actual fading are modeled as jointly Gaussian random variables. For SC systems with channel estimation error, closed-form expressions are obtained for the error rates of M/sub s/-ary pulse amplitude modulation (PAM) and rectangular-quadrature amplitude modulation (QAM), and simple single integral formulas with finite integration limits are derived for the symbol error probability of arbitrary two-dimensional (2-D) modulation formats. These error probability expressions are then applied to three types of channel estimation errors potentially encountered in practical systems to study their impact on the performance of selection diversity. Moreover, single integral formulas with finite integration limits are derived for the performance of SSC and SEC systems with minimum mean square error (MMSE) channel estimation. Optimum switching thresholds for 2-D modulation formats with MMSE based switched combining are acquired through numerical computation.