Implementation of Reduced-Complexity ML Detector for Spatial Modulation System

In full-duplex orthogonal frequency-division multiplexing systems with IQ imbalances, a frequency-domain least-squares (FD-LS) channel estimator is proposed to estimate both source-to-destination (intended) and destination-to-destination (self-interference) channels. Subsequently, an optimal closed-form pilot matrix is derived to minimize the sum of mean square errors (sum-MSE) of the proposed FD-LS channel estimator. Then, an improved FD-LS estimator is presented and proved to further improve the performance of the FD-LS by exploiting the time-domain property of the channel. In the presence of channel estimation error, an optimal low-complexity maximum likelihood (ML) detector is developed by using eigenvalue and singular value decompositions and whitening the residual self-interference plus noise. Simulation results show that given the proposed FD-LS estimator, the optimal pilot matrix performs much better than those nonsingular pilot matrices with larger conditional numbers (CN). To be specific, the former achieves about 10-dB signal-to-noise ratio (SNR) gain over the latter with CN = 10, the improved FD-LS channel estimator provides about 6-dB SNR gain over the FD-LS estimator at a fixed bit error rate (BER), and the proposed whitening-filter ML detector performs at least 0.6 dB better than the conventional ML detector at a given BER of $10^{-3}$ in the medium-and high-SNR regions.

A low complexity maximum likelihood (ML) detection method is proposed for the square quadrature amplitude modulation (QAM) constellation. In order to reduce the implementation complexity of ML detection, set-partition, subset-selection, and subset-shift are recursively applied to the square QAM constellation. The estimated square QAM symbol is finally given in a closed form as a function of the received signal and the estimated channel. Complexity analysis and numerical simulation confirm that the proposed detection method reduces the implementation complexity substantially and achieves exactly the same performance as the conventional ML detection irrespective of the channel estimation error.

Spatial modulation (SM) is a transmission scheme that uses multiple transmit antennas but only one transmit RF chain. At each time instant, only one among the transmit antennas will be active and the others remain silent. The index of the active transmit antenna will also convey information bits in addition to the information bits conveyed through modulation symbols. Pseudo-random phase precoding (PRPP) is a technique that can achieve high diversity orders even in single antenna systems without the need for channel state information at the transmitter and transmit power control. In this paper, we exploit the advantages of both SM and PRPP simultaneously. We propose a pseudo-random phase precoded SM (PRPP-SM) scheme, where both the modulation bits and the antenna index bits are precoded by pseudo-random phases. The proposed PRPP-SM system gives significant performance gains over SM system without PRPP and PRPP system without SM. Since maximum likelihood (ML) detection becomes exponentially complex in large dimensions, we propose a low complexity local search based detection (LSD) algorithm suited for PRPP-SM systems with large precoder sizes. Our simulation results show that with 4 transmit antennas, 1 receive antenna, 5 × 20 pseudo-random phase precoder matrix and BPSK modulation, the performance of PRPP-SM using ML detection is better than SM without PRPP with ML detection by about 9 dB at 102 BER. This performance advantage gets even better for large precoding sizes. We also propose a precoder index modulation (PIM) scheme, which conveys additional information bits through the choice of a precoding matrix among a set of pre-determined PRPP matrices. Finally, combining the PIM and PRPP-SM schemes, we propose a PIM-SM scheme which conveys bits through both antenna index as well as precoder index.

Recently, a maximum likelihood (ML) detection rule for differential unitary space time modulation (DUSTM) under the existence of unknown carrier frequency offset (CFO) has been derived. However, the ML detection is based on the exhaustive search over all the unitary group codes. In this paper, we design an efficient detection algorithm for newly derived ML rule, by modifying the bound intersection detector (BID). Our proposed algorithm is seen as a generalization of the existing BID that is known to be an optimal detector for the conventional DUSTM. The simulation results show that the proposed algorithm can save a large portion of the computational complexity compared to the naive searching method.

As an alternative to classical multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM), MIMO-OFDM with index modulation (MIMO-OFDM-IM), which provides a flexible trade-off between spectral efficiency and error performance, has attracted considerable interest recently. However, in order to detect the active subcarrier indices and modulated symbols precisely, the receiver suffers from high complexity. In this paper, we propose two low-complexity K-best detectors for MIMO-OFDM-IM system. The first detector regards each OFDM with index modulation (OFDM-IM) subblock as a super symbol and retains K best nodes at each layer of the search tree. The second detector searches the K best nodes at the subcarrier level by reducing the size of the subblock to further reduce the complexity. Simulation results show that the proposed detectors offer comparable performance to the optimal maximum likelihood (ML) detector but with significantly reduced complexity.

This paper investigates optical orthogonal frequency division multiplexing (O-OFDM) systems with index modulation (IM) based on discrete Hartley transform (DHT) for visible light communications (VLC). An interesting trade-off between spectral efficiency (SE), energy efficiency, peak-to-average power ratio (PAPR) and bit error rate (BER) performance can be made by using the IM technique. And the DHT-based O-OFDM-IM systems can achieve higher SE compared with the DFT (discrete Fourier transform)-based counterparts. Employing DHT instead of DFT enables the removal of the Hermitian symmetry requirement, which contributes to transmitting more index bits and results in SE improvement. To acquire the same SE, the proposed systems can significantly lower the constellation order leading to better BER performance by contrast with the DFT-based counterparts. We employ DC (direct current) biasing and AC (Asymmetrically clipped) techniques to investigate the O-OFDM-IM systems in this paper. Simulation results indicate that SNR gains can be obtained by the DHT-based DCO/ACO-IM in comparison to the DFT-based counterparts. We also propose a novel reduced-complexity ML (maximum likelihood) detector specifically applicable to VLC. The new detector exhibits the same BER performance as the ML detector and performs better than the LLR (log-likelihood ratio) detector with reduced computational complexity.

In this paper, a common framework for maximum likelihood (ML) detection of spatial multiplexed (SM) and space time coded multiple-input multiple-output (MIMO) signals is proposed. It facilitates a common field programmable gate array (FPGA) based hardware design for the detection of both SM and space time block coded (STBC) MIMO signals with reduced computational complexity. We reduce the number of multipliers required for the ML detection by utilizing a set of precomputed combinations of the constellation symbols from lookup tables (LUT) without any degradation in the packet error rate (PER) performance. The reduction in the computational complexity is achieved by using the additional memory that is available in the FPGA. To evaluate the performance of the proposed method, we perform simulations for the WLAN system based on IEEE 802.11 standard using SM-MIMO and STBC-MIMO.

In this paper, symbol-by-symbol maximum likelihood (ML) detection is proposed for a cooperative diffusion-based molecular communication (MC) system. In this system, a fusion center (FC) chooses the transmitter's symbol that is more likely, given the likelihood of the observations from multiple receivers (RXs). We propose three different ML detection variants according to different constraints on the information available to the FC, which enables us to demonstrate trade-offs in their performance versus the information available. The system error probability for one variant is derived in closed form. Numerical and simulation results show that the ML detection variants provide lower bounds on the error performance of the simpler cooperative variants and demonstrate that majority rule detection has performance comparable to ML detection when the reporting is noisy.

A novel adaptive beamforming (BF) receiver is proposed for a multiple-input–multiple-output communication system over multipath fading channels. By dividing a large number of receive antennas into many adaptive beamformers (ABFs), the proposed system reduces the array dimension in order to simplify the signal detection process and enjoys the benefit of BF techniques to improve the symbol-error-rate (SER) performance. The effectiveness of the proposed system depends on the number of ABFs and the number of antennas per ABF. The statistical properties of complex Wishart matrices are applied to analyse the SER performance of the proposed system with both maximum-likelihood (ML) detection and zero-forcing detection. Furthermore, the authors have derived an upper bound for SER of the ML detection based on the smallest eigenvalue distribution. Through the authors analysis, it has been shown that the proposed system using ML detection provides comparable SER performance, but with a lower complexity as compared with that of a conventional ML receiver because of reduced array dimensions.

Orthogonal space-time block codes (OSTBCs) have attracted much attention owing to their simple code construction, maximal diversity gain, and low maximum-likelihood (ML) detection complexity when channel state information (CSI) is available at the receiver. This paper addresses the problem of ML OSTBC detection with unknown CSI. Focusing on the binary and quaternary PSK constellations, we show that blind ML OSTBC detection can be simplified to a Boolean quadratic program (BQP). From an optimization viewpoint the BQP is still a computationally hard problem, and we propose two alternatives for dealing with this inherent complexity. First, we consider the semidefinite relaxation (SDR) approach, which leads to a suboptimal, but accurate, blind ML detection algorithm with an affordable worst-case computational cost. We also consider the sphere decoding approach, which leads to an exact blind ML detection algorithm that remains computationally expensive in the worst case, but generally incurs a reasonable average computational cost. For the two algorithms, we study implementation methods that can significantly reduce the computational complexity. Simulation results indicate that the two blind ML detection algorithms are competitive, in that the bit error performance of the two algorithms is almost the same and is noticeably better than that of some other existing blind detectors. Moreover, numerical studies show that the SDR algorithm provides better complexity performance than the sphere decoder in the worst-case sense, and vice versa in the average sense.

In this paper, we consider spatial modulation (SM) operating in a frequency-selective single-carrier (SC) communication scenario and propose zero-padding instead of the cyclic-prefix considered in the existing literature. We show that the zero-padded single-carrier (ZP-SC) SM system offers full multipath diversity under maximum-likelihood (ML) detection, unlike the cyclic-prefix based SM system. Furthermore, we show that the order of ML detection complexity in our proposed ZP-SC SM system is independent of the frame length and depends only on the number of multipath links between the transmitter and the receiver. Thus, we show that the zero-padding applied in the SC SM system has two advantages over the cyclic prefix: 1) achieves full multipath diversity, and 2) imposes a relatively low ML detection complexity. Furthermore, we extend the partial interference cancellation receiver (PIC-R) proposed by Guo and Xia for the detection of space-time block codes (STBCs) in order to convert the ZP-SC system into a set of narrowband subsystems experiencing flat-fading. We show that full rank STBC transmissions over these subsystems achieves full transmit, receive as well as multipath diversity for the PIC-R. Furthermore, we show that the ZP-SC SM system achieves receive and multipath diversity for the PIC-R at a detection complexity order which is the same as that of the SM system in flat-fading scenario. Our simulation results demonstrate that the symbol error ratio performance of the proposed linear receiver for the ZP-SC SM system is significantly better than that of the SM in cyclic prefix based orthogonal frequency division multiplexing as well as of the SM in the cyclic-prefixed and zero-padded single carrier systems relying on zero-forcing/minimum mean-squared error equalizer based receivers.

Generalized space shift keying (GSSK) proposed for large scale MIMO systems promises significant advantages in terms of hardware costs. However, the maximum likelihood (ML) detection for GSSK is computationally intractable. Detection schemes using compressive sensing (CS) offer a favorable performance-complexity tradeoff. In this letter, we propose a novel GSSK detection framework, where CS algorithms are used to reduce the complexity of ML detection. The proposed framework significantly reduces the performance gap between existing CS-based detection schemes and ML detection while retaining the complexity advantage of CS algorithms. Simulation results demonstrate the superiority of proposed scheme over popular CS-based detection schemes.

In order to establish the optimal receiver strategy, in terms of error rate for Single Input Multi Output (SIMO) wireless channels, the Maximum Likelihood (ML) detection should be performed following a multi-dimensional matched filter. However, the implementation of the matched filter and the ML detection both need the estimation of the channel impulse response in advance. In this work, we propose a novel method to establish the matched filters of the SIMO channel blindly alongside a three-step technique for the blind and adaptive ML detection of the symbol vector. With the use of the novel method, the system will benefit from the bandwidth efficiency point of view due to the use of blind schemes. The constant modulus algorithm is utilized to perform the blind matched filtering operation and later Least Mean Squared algorithm is introduced for further correction on the matched filter estimate. The blindly estimated matched filters are incorporated into the ML detector so that the transmitted symbols are found and therefore the channel is equalized. Simulations are provided to present the equalization performance and convergence speed of the novel technique.

Cooperative communication technique is an emerging trend in communication systems and offers benefits of multiple-input-multiple-output (MEMO) systems. Decode-and-forward (DF) method is one of most the known methods that is utilized in cooperative communication systems. Its lower complexity and higher practicality benefits make DF very useful. However, DF is affected negatively by erroneous transmission and performance could be limited. Several approaches are proposed for this drawback. An effective solution is a maximum likelihood (ML) detector that is based on maximization of probability density function in orthogonal transmissions. In this study, ML detector is utilized with orthogonal frequency division multiple access (OFDMA) technique and performance are measured by using software defined radio (SDR) nodes. In order to further improve that solution, a low complex suboptimal detector based on ML detector is proposed. The performance of the suboptimal detector is also quantified with SDR nodes.

In this paper, we present three new detection schemes for the nonorthogonal amplify and forward (NAF) protocol in a cooperative diversity system based on a multiuser detection approach, namely, a channel inversion type detector, a maximal-ratio combining (MRC) type detector, and a biased maximum likelihood (ML) detector. The decision variables in these schemes are linear functionals of the transmitted symbol vector and therefore they are termed as ldquolinearrdquo detectors. A cooperative relay network using the NAF protocol with N - 1 relays is considered where the source transmits symbols in N - 1 blocks of two time slots in a Rayleigh fading environment. For the case of a general linear space-time block coding scheme using K symbols, we present the performance of this protocol in terms of the code symbol error probability when the symbols come from an M-ary phase-shift keying constellation. The approach is further extended to the transmission in N - 1 blocks of L time slots. Numerical results show that the performance of the MRC type detector is superior to that of the channel inversion type detector, while the biased ML detector has the best performance. However, the MRC type detector has the lowest complexity while the biased ML detector the highest.