Abstract Efficient quantizer design is vital in high‐speed optical receivers. In this paper, the authors propose a three‐level (1.5‐bit) reliability‐based quantizer for low‐complexity soft decoding of low‐density parity‐check (LDPC) codes, and show that it outperforms a conventional quantizer employing eight levels (3 bits). Different approaches for obtaining the quantization thresholds are discussed, and it is shown that the achievable channel capacity with the proposed quantizer is within 0.4 dB of the Shannon limit of the unquantized channel. Rate‐compatible LDPC codes are also designed tailored to the asymmetric optical channel terminated with the proposed reliability‐based quantizer, and it is shown that the resulting quantizer‐aware LDPC codes significantly outperform other existing codes of similar rates.

We present a diversity multiplexing tradeoff (DMT) optimal tree pruning sphere decoding algorithm which visits merely a single branch of the search tree of the sphere decoding (SD) algorithm, while maintaining the DMT optimality at high signal to noise ratio (SNR) regime. The search tree of the sphere decoding algorithm is pruned via intersecting one dimensional spheres with the hypersphere of the SD algorithm, and the radii are chosen to guarantee the DMT optimality. In contrast to the conventional DMT optimal SD algorithm, which is known to have a polynomial complexity at high SNR regime, we show that the proposed method achieves the DMT optimality by solely visiting a single branch of the search tree at high SNR regime. The simulation results are corroborated with the claimed characteristics of the algorithm in two different scenarios.

The cooperative maximum ratio combiner (C‐MRC) is able to collect the maximum available diversity in decode and forward (DF) relay networks, and is simple to be implemented relative to the maximum likelihood (ML) detector. In this study, the authors provide some approximations for the ML detector, and they prove that the well‐known C‐MRC detector which was considered to be an intuitive method is, indeed, a linear approximation for the ML detector in DF relay networks. They also study the performance of the approximated ML detector in the presence of channel estimation error. This study determines the sensitivity of the diversity gain achieved by the approximated ML detector to the channel estimation error. Simulation results are also presented to corroborate the derived analytical results.

Based on the V-BLAST zero-padded block transmission scheme in the frequency-selective multiple-input multiple-output channels, we propose a two-stage lattice-reduction (LR)-aided decoder and prove analytically that it can achieve the maximum diversity gain, which is equal to the product of the number of receive-antennas and the number of multipath channel taps. In the proposed decoding method, at first, we decouple the detection problem into several reduced-size detection problems and perform the lattice reduction algorithm for the decoupled blocks. Then, by choosing a proper threshold, a clustering algorithm divides the blocks into the maximum two clusters. We prove that the corresponding blocks of the first cluster achieve the full diversity through their linear equalization. For the remainder of the blocks, based on the entire observations of the second cluster, we propose an LR-aided detection method, which decodes the information symbols in this cluster with full diversity. Our proposed two-stage LR-aided algorithm performs better than the conventional LR-aided detection in terms of both the decoding computational complexity and the error probability. Additionally, we prove analytically that at high signal-to-noise ratio, the decoding complexity of the proposed decoder is equal to that of decoding the first cluster.

In an interweave cognitive radio system, the spectrum sensing performance affects the rate and reliability of data transmission. In wireless communications, the tradeoff between the reliability and data rate can be evaluated by diversity-multiplexing tradeoff (DMT) analysis. In this paper, through the analysis of the error probability at the secondary receiver, we derive the DMT for the multiple-access channel and user-selection schemes in an interweave multiuser cognitive radio system considering the spectrum sensing effect on the rate and reliability. We show that the DMT of the system can be improved by cooperative spectrum sensing. Simulations also approve our analytical results.

Automatic modulation classification (AMC) techniques enable the estimation of the bit allocation table in adaptive orthogonal frequency division multiplexing (OFDM) systems. In this study, the authors investigate the classification performance of a low‐complexity maximum‐a‐posteriori (MAP) algorithm for AMC. Also, they derive an approximation of the probability of classification error in a subcarrier for this classifier. Furthermore, based on these theoretical derivations, a novel modified rate adaptive (RA) bit loading algorithm with additional classification error constraint is proposed. Numerical results show that the authors’ proposed method outperforms the RA algorithm significantly in terms of classification performance, while providing reasonable data throughput specifically at higher signal‐to‐noise ratios.

Although zero-forcing (ZF) detection is well-known for its low computational complexity in multiple-input multiple-output (MIMO) communication systems, it suffers from significantly poor performance. The sphere decoder (SD) method, on the other hand, achieves the maximum likelihood (ML) performance yet imposes a high computational complexity. We propose a low-complexity detection scheme, concatenated with the SD method, which verifies the reliability of the ZF equalized observations via some predefined regions and thresholds obtained by the channel realization. We design the threshold analytically, such that the method achieves the ML performance. With the designed threshold, we prove that the method achieves the ML performance and the ZF computational complexity at the same time with probability one, at high signal-to-noise ratio (SNR). The theoretical analysis is corroborated with numerical simulations. The simulation results also show that the proposed method achieves the ML performance very rapidly as the SNR increases.

Due to the computational complexity of maximum-likelihood signal decoding, the equalizers with less complexity are considered in the literature. Employing the zero forcing (ZF) equalizer, zero-padded orthogonal frequency-division multiplexing (ZP-OFDM) is capable of benefiting the maximum available multipath diversity with the computational complexity of inverting a matrix of the size of data block length, which incurs an extra implementation cost relative to the fast Fourier transform-based OFDM decoder. In this paper, based on the ZP-OFDM encoding scheme, we propose a two-stage decoder that attains the maximum multipath diversity with lower computational complexity, as compared with the ZF ZP-OFDM and prove analytically that our proposed decoder is diversity-multiplexing tradeoff optimal. It has also been shown that by setting the decoder parameters, it can attain any arbitrary diversity gain smaller than the maximum multipath diversity. Moreover, the more the diversity gain is decreased the more the computational complexity is reduced.

Cooperation among distributed multiple-input-multiple-output (MIMO) nodes allows a relay network to improve the performance, enhance the coverage, and increase the capacity by exploiting the available space diversity. In this paper, considering the practical relay detect-and-forward strategy, we propose a lattice-reduction aided linear equalizer at the destination of the MIMO relay network to collect diversity when the cooperating relay adopts a zero forcing equalizer with a well-known adaptive power scaling strategy. We analytically prove that this link adaptive system design is capable of collecting the maximum available receive diversity. The theoretical analysis is corroborated with numerical simulations.

In cognitive radio (CR) networks, the channel sensing performance has significant impact on the throughput of the system. In this study, the authors formulate the spectrum sensing to maximise the total throughput of the system under some constraints on the interference to the primary users (Pus). The total throughput defined in this study accounts not only for the throughput achieved by the CR user but also by the PU over each subband. In the numerical results, the authors compare their proposed idea with the previous work which finds the threshold of the detector to maximise CR throughput.

In this paper, we present an Orthogonal Frequency Division Multiplexing (OFDM) based system, which is designed and implemented to transmit voice signal, over UnderWater Acoustic (UWA) channels. The system is software-based and using two Laptops, it would be possible to transmit and receive digital voice between two Underwater Vehicles (UV). System parameters are tuned for underwater acoustic channel observed in the Persian Gulf. The system may be used for speeds, up to 30 nautical miles per hour. Eventually some experimental results are presented that show the power of the system to achieve the desired performance.

The authors assume a linear equidistance antenna array as the receiver for a fixed frame-length multiple-access system, which employs variable-gain receiver power and repetition encoding. They propose a robust maximum a posteriori probability (MAP) blind bit-rate detector (BBRD). This detector considers the rate detection (RD) as a multi-hypothesis test and maximises the likelihood functions (LFs) to find the true bit-rate, whereas the complex amplitude of the received signal, the noise variance and the direction of arrival are unknown parameters. First, assuming that the location parameter is known and the information sequence are independent and uniformly distributed random variables, the authors propose a hybrid likelihood ratio test (HLRT). The proposed HLRT requires to solve a set of non-linear equations that have no closed-form solution. Thus, an iterative numerical algorithm is proposed. In addition, a quasi-HLR detector which has a significantly lower computational complexity is also proposed. In the case of unknown location parameter, the authors develop two quasi-HLR methods. They use fast Fourier transform and search to estimate the unknown location. In Q-HLRT-Method-I, the non-linear equation similar to the one in known location parameter is iteratively solved. In Q-HLRT-Method-II, a low complexity solution is proposed. Simulation examples evaluate and compare the performances of the proposed BBRDs.

Spectrum sensing is an essential capability that allows the cognitive radios (CRs) to detect spectral holes and opportunistically use underutilised frequency bands without causing deleterious interference to primary users. In this study the authors address two cooperative wideband spectrum sensing techniques for the frequency-selective and frequency-non-selective fading channels in which the primary user signals are detected over multiple frequency bands. The primary user signals, indices and the number of occupied subbands, the channels characteristics and the noise variance of the secondary receivers (SRs) are considered to be unknown. Thus, the problem of spectrum sensing in the fusion centre is modelled by a composite testing hypothesis in time domain and using generalised likelihood ratio (GLR) test the spectral holes are detected. In the frequency-selective case the authors have decreased the computational complexity using some approximations. Simulation results show that the proposed spectrum sensing schemes achieve satisfactory performance and also are robust against the SRs arrangement in the CR network.

The authors propose a computationally efficient spectrum sensing solution for an orthogonal frequency division multiplexing (OFDM) signal in a frequency-selective fading channel with additive white Gaussian noise (AWGN). The authors’ assumption is that the data symbols, channel coefficients and the noise variance are all unknown. The nature of the problem leads them to find an invariant detector. The optimum one is uniformly most powerful invariant (UMPI); their effort shows that this test does not exist, as the final decision statistic depends on some unknown parameters; although, they derive the most powerful invariant (MPI) detector, implanting these parameters, to provide an upper bound for invariant detectors. Instead, the authors develop the generalised likelihood ratio test (GLRT), substituting the unknown parameters by their maximum likelihood (ML) estimates in the Neyman–Pearson likelihood ratio. Furthermore, they propose a computationally efficient implementation of the resulting detector. Simulation results show a slight decrease in efficiency against gaining so much computational complexity (CC) improvement. For more comparisons they also derive the conventional energy detector, namely, generalised energy detector (GED) for a binary phase shift keying (BPSK) signal, to show the adequacy of the GLR detector performance which would be demonstrated by simulation results.

A generalised modified multimodulus cost function for blind equalisation in digital communication systems is introduced. This generalisation is achieved by dividing the complex plane of modulated signals into several disjoint regions where the regions have different constant modulus. Then an adaptive learning algorithm that employs the pseudo Newton method is presented and based on the predefined generalised cost function its corresponding steady-state mean square error (MSE) is derived. Also, the number of disjoint regions is evaluated so that the minimum of the steady-state MSE is achieved. Here it is proved that the cost function with a single region in the complex plane achieves the minimum MSE. Then the resulting steady-state MSE of pseudo Newton method is compared with the one obtained from stochastic gradient algorithm (SGA). It is concluded that the pseudo Newton method converges to the desired steady-state MSE with a step size larger than the one used in SGA. Additionally, based on the pseudo Newton method and the SGA, a new method is developed that has better convergence speed compared to the other two methods. Finally, various simulation results are presented to verify the previous stated results.

In this letter, we develop a computationally efficient algorithm for the Maximum Likelihood (ML) sequences estimation (MLSE) of an M-ary Phase Shift keying (M-PSK) signal transmitted over a frequency non-selective slow fading channel with an unknown complex amplitude and an unknown variance additive white Gaussian noise. The proposed algorithm also provides the ML estimates of the complex amplitude and the noise variance that are critical in signal activity detection and demodulation in the modern cognitive communication receivers. We prove the optimality of the proposed algorithm and compare its performance via simulation with a recent suboptimal algorithm.

The authors propose invariant tests for the detection of a complex signal with unknown constant amplitude and unknown phase variation in additive white Gaussian noise (AWGN). The authors show that in this problem, the uniformly most powerful invariant (UMPI) detector does exist only if the number of samples N is two. For more than two samples N≥3, the authors derive the most powerful invariant (MPI) detector in known signal-to-noise ratio (SNR) and use its performance as the upper bound benchmark for any invariant test. In addition, the authors derive the generalised likelihood ratio (GLR) detector and evaluate its performance against the MPI performance bound. This detector is very simple and represents the ratio of the L1-norm to the L2-norm of the data. Simulation results illustrate the close performances of the two detectors even at low SNRs, whereas in contrast to the MPI test the SNR is not required in the proposed GLR test. In order to understand why the knowledge of SNR is not so important in this detection problem, the authors also derive the GLR test for the case of known SNR. Interestingly, the resulting GLR detector (derived for the case of known SNR) turns out to be equivalent to the one derived for unknown SNR, i.e. a knowledge of the SNR is not used in any of the GLR tests. This reveals why the knowledge of the SNR is not so useful in this detection problem.

We propose computationally inexpensive and efficient solutions for signal activity detection of phase-shift keying (PSK) signals in additive white Gaussian noise. We consider the complex amplitude of the signal as well as the information sequence as the unknown parameters. In addition, the noise variance is assumed unknown. We derive the generalized likelihood ratio test (GLRT) and suggest a computationally efficient implementation thereof. Furthermore, we develop a new inexpensive detector for binary PSK signals, which we will refer to as the generalized energy detector. To evaluate the performance of these detectors, we attempt to derive a uniformly most powerful invariant test (UMPI) as an optimal detector. It turns out that the UMPI test exists only if the signal-to-noise ratio is known. We use this UMPI test in order to obtain an upper-bound performance for the evaluation of invariant detectors, such as the above-mentioned GLRT. Simulation results illustrate and compare the performance and the efficiency of the proposed signal activity detectors.

We propose computationally inexpensive and efficient solutions for signal activity detection of phase-shift keying (PSK) signals in additive white Gaussian noise. We consider the complex amplitude of the signal, as well as the information sequence, as the unknown parameters. In addition, the noise variance is assumed unknown. We derive the generalized likelihood ratio test (GLRT) and suggest a computationally efficient implementation thereof. Furthermore, we develop a new inexpensive detector for binary PSK signals, which we will refer to as the generalized energy detector. To evaluate the performance of these detectors, we attempt to derive a uniformly most powerful invariant (UMPI) test as an optimal detector. It turns out that the UMPI test exists only if the signal-to-noise ratio is known. We use this UMPI test in order to obtain an upper-bound performance for the evaluation of invariant detectors, such as the GLRT. Simulation results illustrate and compare the performance and the efficiency of the proposed signal activity detectors