Suboptimal Receiver Research Articles

Channel Norm-Based Energy Detection With Diversity Reception for Amplitude-Shift Keying in Rayleigh Fading

Optimum and suboptimum energy detection receivers with diversity reception in Rayleigh fading, that only require limited channel state information based on the channel norm, are introduced. The importance of these channel norm based energy detection (CNBED) receivers is that they achieve the same diversity order as that of a coherent receiver. Furthermore, their performance degradation when compared to a coherent receiver can be made sufficiently low by appropriate choice of parameters. Due to their performance and the low complexity of energy detection, the CNBED techniques have potential applications to internet of things. Analysis of the CNBED receivers is performed for multi-level amplitude-shift keying (ASK). For the optimum receiver, an analytical approximation of the symbol error probability (SEP) as a sum of univariate integrals involving averaging of Gaussian Q-functions is derived. For the suboptimum receiver, closed form expressions for the exact SEP and for the approximate SEP under the condition of high signal-to-noise ratio (SNR) are obtained; in addition, using asymptotic approximations, expressions for the optimal ASK transmit levels with high SNR and large number of receive diversity branches, that minimize the SEP subject to an energy constraint, are found. Numerical results are provided to demonstrate the performance of the receivers.

Channel Estimation and Multipath Diversity Reception for RIS-Empowered Broadband Wireless Systems Based on Cyclic-Prefixed Single-Carrier Transmission

In this paper, a cyclic-prefixed single-carrier (CPSC) transmission scheme with phase shift keying (PSK) signaling is presented for broadband wireless communications systems empowered by a reconfigurable intelligent surface (RIS). In the proposed CPSC-RIS, the RIS is configured according to the transmitted PSK symbols such that different cyclically delayed versions of the incident signal are created by the RIS to achieve multipath diversity. A practical and efficient channel estimator is developed for CPSC-RIS and the mean square error of the channel estimation is expressed in closed-form. We analyze the bit error rate (BER) performance of CPSC-RIS over frequency-selective Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channels. An upper bound on the BER is derived by assuming maximum-likelihood detection. Furthermore, by applying the concept of index modulation (IM), we propose an extension of CPSC-RIS, termed CPSC-RIS-IM, which enhances the spectral efficiency. In addition to conventional constellation information of PSK symbols, CPSC-RIS-IM uses the full permutations of cyclic delays caused by the RIS to carry information. A sub-optimal receiver is designed for CPSC-RIS-IM to aim at low computational complexity. Our simulation results in terms of BER corroborate the performance analysis and the superiority of CPSC-RIS(-IM) over the conventional CPSC without an RIS and orthogonal frequency division multiplexing with an RIS.

Optimal Fractional Pilot Duration for a Correlated Receive Diversity Reliable PLC System With Imperfect CSI in Nakagami-m Noise Environment

The paper presents a single-input-multiple-output-based power line communication (PLC) system employing <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 phase-shift keying signaling for data transmission, with the channels subjected to correlated Rayleigh multipath channels and corrupted by Nakagami- <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> noise environment. The channel state information for the PLC system is obtained prior to data transmission using the minimum mean square error estimation technique, utilizing which a maximum likelihood-based sub-optimal receiver is proposed. The closed-form expression for the symbol error probability (SEP) is derived, for the cases of the channels following exponential and uniform correlations, using a characteristic function approach. Furthermore, the optimal pilot symbol duration is obtained to maximize the normalized error-free data rate of the system, which simultaneously saves on the energy of the pilot symbols and reduces the SEP of the data symbols. The numerical results demonstrate the effect of variation of different system parameters such as signal-to-noise ratio, channel diversity, pilot symbol quality, correlation factor, and the noise shape parameter <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> of the background noise on the maximum normalized error-free data rate and thereby providing various insights into the system design for a reliable and energy-efficient PLC system with imperfect knowledge of the channels at the receiver.

Multiuser Detection for Time-Frequency-Packed Systems

We consider time-frequency-packed systems in an additive white Gaussian noise scenario. With respect to systems employing time packing, thus introducing intentional intersymbol interference only, a further improvement of the spectral efficiency is obtained by packing the adjacent carriers closer in frequency. The adoption of a multiuser detector can allow coping with the resulting intentional intercarrier interference. The optimal detector for time-frequency-packed systems has a complexity that increases exponentially with the number of interferers in both time and frequency dimensions and thus becomes unmanageable. We propose a suboptimal receiver, which is derived by using the framework based on factor graphs and the sum-product algorithm, with a complexity that is linear in the number of adjacent carriers and takes also advantage of a multi-user channel shortener to further reduce the complexity. We assess the performance by means of computer simulations and show that, when compared with other suboptimal receivers available in the literature and with the optimal detector, the proposed receiver results very promising in terms of trade-off between performance and computational complexity.

Near-Optimal Low-Complexity Harmonic Receiver for Unipolar-FSK

In this letter, we propose a near-optimal low-complexity frequency-domain (FD) harmonic receiver for visible light communication based unipolar frequency-shift keying (U-FSK). The time-domain (TD) maximum-likelihood (ML) receiver for U-FSK is computationally complex, while the sub-optimal receiver increases the noise variance. The proposed harmonic receiver determines the transmitted frequency from the cross-correlations between the FD received waveform and the FD dictionary waveforms reduced to their strongest harmonics. The results shall demonstrate that besides affording a linerarithmic complexity, the performance of the harmonic receiver closely approaches that of TD ML receiver which exhibits quadratic complexity.

BER Performance Analysis of Non-Coherent Q-Ary Pulse Position Modulation Receivers on AWGN Channel.

This paper introduces the structure of a Q-ary pulse position modulation (PPM) signal and presents a noncoherent suboptimal receiver and a noncoherent optimal receiver. Aiming at addressing the lack of an accurate theoretical formula of the bit error rate (BER) of a Q-ary PPM receiver in the additive white Gaussian noise (AWGN) channel in the existing literature, the theoretical formulas of the BER of a noncoherent suboptimal receiver and noncoherent optimal receiver are derived, respectively. The simulation results verify the correctness of the theoretical formulas. The theoretical formulas can be applied to a Q-ary PPM system including binary PPM. In addition, the analysis shows that the larger the Q, the better the error performance of the receiver and that the error performance of the optimal receiver is about 2 dB better than that of the suboptimal receiver. The relationship between the threshold coefficient of the suboptimal receiver and the error performance is also given.

Cyclic Delay Diversity With Index Modulation for Green Internet of Things

Cyclic delay diversity (CDD) is a simple and yet effective transmit diversity technique. Thanks to its strong power saving capability, CDD is very promising for green Internet of Things (IoT) networks. However, the reduced degrees of freedom in data transmission and the overhead of cyclic prefix lead to unsatisfactory spectral efficiency (SE), hindering the direct application of CDD to IoT networks where short-packet communication prevails. To tackle this problem, in this article, we propose to convey additional information via the varying cyclic delays for improving the SE of the CDD system based on the concept of index modulation (IM), which applies to both OFDM and cyclic-prefixed single-carrier (CPSC) signals. The methods to generate all possible cyclic delays and the optimal receivers are designed for both proposed systems. To aim at low computational complexity, we further propose a suboptimal receiver for the CDD-CPSC-IM system. Moreover, a closed-form upper bound on the bit error rate (BER) of the CDD-OFDM-IM system is derived, from which the coding gain is characterized. Simulation results in terms of BER corroborate the analysis and the superiority of the proposed systems over the pure CDD-OFDM and CDD-CPSC systems, uncovering the potential of CDD in the application to green IoT networks.

Performance Analysis of a Receive Diversity PLC System With Imperfect CSI in Nakagami-m Noise Environment

The letter proposes a receive diversity PLC system subject to uncorrelated Rayleigh multipath channels and corrupted by Nakagami- m background noise employing M-ary phase-shift keying modulation for data transmission. The estimates of the channel gains are obtained prior to data transmission by the minimum mean square estimation technique utilizing pilot symbol transmission. A suboptimal receiver structure employing the maximum likelihood decision rule is proposed for the PLC system which is further used to obtain the closed form and the asymptotic expressions for the symbol error probability of the system via a characteristic function approach. The improvement of the system performance with the increase in the channel diversity, the effects of the pilot-to-signal strength ratio, and the noise shape parameter m of the background noise on the system performance are studied via numerical results providing various insights into the design of the PLC system with various system parameters.

Simplified Receivers for Generic Binary Single Side Band CPM Using PAM Decomposition

This paper investigated the pulse amplitude modulation (PAM) decomposition of a class of continuous phase modulation (CPM) signal, which has the property to be a single-side band. We used the PAM decomposition as a convenient solution to provide a large reduced complexity trellis detection to approach the theoretical optimal performance. Moreover, we developed an algorithm to obtain the necessary PAM pulses to approach the optimal performance bound using suboptimal receivers. The algorithm is generic; it can provide the results for any parameter combinations. The proposed demodulation system exhibits excellent performance with minimal complexity with respect to the maximum likelihood sequence detection (MLSD) optimal receiver.

Visible Light Communication with Input-Dependent Noise: Channel Estimation, Optimal Receiver Design and Performance Analysis

In this paper, single-input single-output (SISO) visible light communication (VLC) subject to signal-dependent shot noise (SDSN) is investigated. We discuss both channel estimation and data transmission. In the former, we introduce least square (LS) and maximum likelihood (ML) estimators. Moreover, we derive the Cram´er–Rao lower bound (CRLB) of the channel estimation error. With regard to data transmission, we present optimal and sub-optimal receiver designs and discuss their bit error rate (BER) performance. In particular, a closed-form expression of the BER is derived for a sub-optimal receiver using the on-off-keying (OOK) modulation technique. An approximated expression is then derived for the optimal receiver. Our analysis shows that the CRLB performance does not have a linear relation with the SDSN, thermal noise, or the fading channel. On the other hand, the SDSN has a dramatic effect on the channel estimation error bound, and it can degrade the BER performance. Increased performance degradation can also be noticed due to the joint effects of the channel estimation error and SDSN.

Optical Energy-Constrained Slot-Amplitude Modulation for Dimmable VLC: Suboptimal Detection and Performance Evaluation

Energy-constrained slot-amplitude modulation (ECSAM) enables light dimming, eliminates light flicker and constrains the peak optical power while providing robust communication links. However, the complexity of the maximum-likelihood (ML) based ECSAM receiver increases exponentially with required spectral efficiency. This paper provides a comprehensive performance evaluation of ECSAM for the indoor visible light communication (VLC) channel with multipath propagation under realistic illumination constraints and imperfect channel estimation. A sub-optimal receiver that employs a slot-by-slot detection algorithm followed by a slot-correction mechanism for reducing the receiver complexity is proposed. Additionally, the method for optimal selection of parameters when designing the signal waveform is presented. The analytical upper bound on the symbol error rate of ECSAM is derived using the union-bound technique. The results show that the error performance of the sub-optimal receiver are comparable to that of the optimal ML receiver. Compared with conventional power or bandwidth efficient VLC modulation techniques such as multiple pulse position modulation (MPPM) and pulse amplitude modulation (PAM), ECSAM provides complete flexibility in modifying the signal constellation for a desired dimming level to maximise the spectral efficiency and provide a robust bit error rate performance especially in the multipath propagation channel induced intersymbol interference.

Iterative-Detection-Aided Tomlinson-Harashima Precoding for Faster-Than-Nyquist Signaling

Faster-than-Nyquist(FTN) is a promising technique due to higher spectral efficiency, but at a cost of introducing the inter-symbol interference (ISI) which usually requires the computationally demanding detection algorithms. In order to reduce the detection complexity at the receiver, in this paper, a novel Tomlinson-Harashima precoding (THP) scheme is proposed for FTN system. In the conventional THP (CTHP) scheme, the ISI introduced by time-packing can only be diminished from several preceding information symbols, which results in large residual ISI and an unattractive bit-error-rate (BER) performance. Moreover, due to the suboptimal receiver - a simple modulo operation which ignores the correlation between received symbols, CTHP faces obvious capacity loss and is ineffective to execute interference cancellation for FTNS. In this paper, residual ISI of FTNS in CTHP is formulated in detail and modeled mathematically. Further more, an improved THP method with an optimized receiver based on the soft interference cancelation (SIC) algorithm and iterative turbo process is proposed to combat residual ISI for FTNS. Computational complexity analysis and numerical simulation results show that the proposed scheme not only has inexpensive computational cost but also greatly outperforms CTHP and other cited schemes. Moreover, for moderate time-packing, it can approach the ISI-free BER performance boundary and is also competitive to the MAP equalization technique.

Hybrid Frequency and Phase-Shift Keying Modulation for Energy Efficient Optical Wireless Systems

In this letter, we introduce direct-current (DC) offset hybrid frequency and phase-shift keying (DC-FPSK) modulation for Internet-of-Things based on optical wireless systems. For DC-FPSK, non-negative phase-modulated frequency waveforms are generated by combining frequency-shift keying (FSK), phase-shift keying (PSK) and a DC offset. We propose optimal maximum likelihood and sub-optimal receivers for DC-FPSK. The performance is appraised in terms of Euclidean distance, bit-error-rate (BER) performance and energy efficiency. We determine that combining 4-PSK with conventional DC-FSK is the optimal approach to enhance the energy and spectral efficiencies.

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.

Efficient error correcting scheme for chaos shift keying signals

An effective error-correction scheme based on normalized correlation for a non coherent chaos communication system with no redundancy bits is proposed in this paper. A modified logistic map is used in the proposed scheme for generating two sequences, one for every data bit value, in a manner that the initial value of the next chaotic sequence is set by the second value of the present chaotic sequence of the similar symbol. This arrangement, thus, has the creation of successive chaotic sequences with identical chaotic dynamics for error correction purpose. The detection symbol is performed prior to correction, on the basis of the suboptimal receiver which anchors on the computation of the shortest distance existing between the received sequence and the modified logistic map’s chaotic trajectory. The results of the simulation reveal noticeable Eb/No improvement by the proposed scheme over the prior to the error- correcting scheme with the improvement increasing whenever there is increase in the number of sequence N. Prior to the error-correcting scheme when N=8, a gain of 1.3 dB is accomplished in E&lt;sub&gt;b&lt;/sub&gt;/N&lt;sub&gt;o&lt;/sub&gt; at 10&lt;sup&gt;-3 &lt;/sup&gt;bit error probability. On the basis of normalized correlation, the most efficient point in our proposed error correction scheme is the absence of any redundant bits needed with minimum delay procedure, in contrast to earlier method that was based on suboptimal method detection and correction. Such performance would render the scheme good candidate for applications requiring high rates of data transmission.

Adaptive threshold device for detection of reflections based visible light communication

One of the major restriction of existing visible light communication (VLC) systems is the limitation of channel transmission bandwidth which can be used in such systems. In this paper, an optimal and a suboptimal receiver are proposed to increase the on-off keying (OOK) transmission rate and hence to increase bandwidth efficiency of VLC system when a multiple reflections channel model is used to characterize the impacts of reflections in VLC signal propagation. Optimal detector consists of a simple receiver with a memory to find the optimal threshold based on the previous detected data. The error probability of the proposed detector is derived in the closed form and compared with the simulation results. It is demonstrated that the proposed detectors can improve the transmitting bandwidth close to the 3-dB bandwidth of the LOS channel model (which is several hundred MHz), whereas bit-error-rate (BER) remains low, in particular where the optimal detection is utilized.

PDF approximations to estimation and detection in time-correlated alpha-stable channels

This paper considers the estimation and detection problems for statistically dependent heavy-tailed signals with no closed-form probability density function (PDF). We propose two parametric PDF approximations for symmetric α-stable (SαS) distribution to be utilized in approaches based on the Maximum likelihood (ML) criterion. The nonlinear least square (LS) and curve fitting are used to compute parameters of the new formulations which are functions of the characteristic exponent. Moreover, we study binary signal detection in channels with time-dependent heavy-tailed noise modeled by SαS distribution and first order autoregressive (AR(1)) process. Using the novel PDF approximations in the ML estimator, an algorithm for model parameters estimation of the noise is initially developed. Then, new suboptimal receivers are designed through the use of the new PDF formulations and parameter estimates. Numerical results demonstrate the superiority of the proposed approximations over the existing formulations, and also good accuracy for the estimation algorithm. Additionally, it is shown that the proposed detectors operate near optimal receiver and also outperform the other suboptimal detectors, especially when α is small.

Low PAPR Spatial Modulation for SC-FDMA

Although spatial modulation (SM) presents an attractive multiple-input-multiple-output (MIMO) technique, it increases peak-to-average power ratio (PAPR) on all transmit antennas when applied directly to single-carrier frequency-division multiple access (SC-FDMA). Therefore, we propose an SM modification, which is called low-PAPR SM (LPSM), to preserve the low PAPR level of SC-FDMA and to achieve the benefits of SM. In addition, as the optimal maximum-likelihood detection (MLD) receiver has a very high computational complexity when applied to SC-FDMA system, we observed suboptimal receivers for SC-FDMA with LPSM. In addition to low-complexity linear receivers, we proposed and analyzed two receivers: near-MLD and improved minimum mean square error (iMMSE) receivers. The near-MLD receiver achieves performance very near to MLD with significantly lower complexity, whereas the iMMSE receiver presents a tradeoff between MLD and linear receivers in terms of performance and complexity.

Spectral Efficiency of Random Time-Hopping CDMA

Traditionally paired with impulsive communications, time-hopping code-division multiple access (TH-CDMA) is a multiple access technique that separates users in time by coding their transmissions into pulses occupying a subset of $N_ \mathsf {s}$ chips out of the total $N$ included in a symbol period, in contrast with the traditional direct-sequence CDMA (DS-CDMA), where $N_ \mathsf {s}=N$ . This paper analyzes the TH-CDMA with random spreading, by determining whether peculiar theoretical limits are identifiable, with both optimal and suboptimal receiver structures, in particular in the archetypal case of sparse spreading, that is, $N_ \mathsf {s}=1$ . Results indicate that the TH-CDMA has a fundamentally different behavior than DS-CDMA, where the crucial role played by energy concentration, typical of TH, directly relates with its intrinsic uneven use of degrees of freedom.

Energy and spectral efficient Doppler diversity transmissions in high-mobility systems with imperfect channel estimation

This paper studies energy and spectral efficient Doppler diversity transmissions in the presence of imperfect channel state information (CSI). Fast time-varying fading in high-mobility communication systems introduces Doppler diversity that can benefit system performance. On the other hand, it is more difficult to estimate and track fast time-varying channel; thus, channel estimation errors might seriously degrade system performance in high-mobility systems. The trade-offs between channel estimation errors and Doppler diversity are studied by using two precoding schemes, a simple repetition code, and a rate 1 Doppler domain multiplexing (DDM) scheme. The repetition code can achieve the maximum Doppler diversity at the cost of a lower spectral efficiency, and the DDM scheme can achieve the energy and spectral efficient Doppler diversity transmissions. Unlike many other Doppler diversity systems that assume perfect CSI, we explicitly consider the impacts of imperfect CSI on the design and performance of both precoding schemes. Optimum and suboptimum receivers for both schemes are developed by studying the statistical properties of channel estimation errors. The analytical error probabilities of the receivers are expressed as functions of a number of system parameters, such as the maximum Doppler spread, the percentage of pilot symbols for channel estimation, the energy allocation between the pilot and data symbols, etc. The analytical and simulation results indicate that both precoding schemes can achieve the maximum Doppler diversity order through the optimization of the various parameters, even in the presence of imperfect CSI.