Frequency-domain Equalization Technique Research Articles

Robust equalization for single-carrier underwater acoustic communication in sparse impulsive interference environment

Impulse noise significantly distorts the background noise within communication systems, causing a notable departure from the Gaussian distribution. This distortion, in turn, exerts a detrimental influence on the performance of conventional single-carrier frequency domain equalization techniques. In this paper, we introduce a novel algorithm for joint channel, interference, and symbol estimation within single-carrier systems. This algorithm is grounded in the framework of variational Bayesian inference and possesses the unique capability of simultaneously accounting for the sparsity inherent in the channel and impulse interference. In the course of processing, it leverages multi-parameter probability distributions to effectively model the intricate posteriori probabilities associated with impulse interference vectors and channel vectors. This, in turn, facilitates the computation of maximum a posteriori estimates and subsequently enables the estimation and elimination of interference. We validate the efficacy of our proposed method through both numerical simulations and the processing of experimental data. Our results unequivocally demonstrate the robustness and manageable computational complexity of our approach within the context of impulse interference-prone environments.

Continuous phase modulation with chaotic interleaving for visible light communication systems based on orthogonal frequency division multiplexing

AbstractVisible light communication (VLC) is one of the most promising technologies which offers high data rates and flexible cost‐effective networking solutions for indoor applications. In VLC systems, the optical orthogonal frequency division multiplexing (OFDM) is considered as an efficient technique to avoid VLC channel selectivity. However, OFDM suffers from the high peak‐to‐average‐power‐ratio (PAPR) problem, which degrades the VLC system performance. In this article, we consider the use of a chaotic‐interleaver‐based continuous‐phase‐modulation (CI‐CPM) scheme together with frequency domain equalization (FDE) at the receiver end of the VLC system. A direct current bias is added to the signal to provide real‐valued non‐negative signals for intensity modulation. The proposed scheme outperforms the conventional ones in terms of PAPR. Additionally, it takes the advantages of CPM power efficiency and frequency diversity. Furthermore, three types of FDE techniques are considered and compared including the zero‐forcing (ZF) equalizer, the minimum mean square error equalizer and the regularized ZF equalizer.

On the Physical Layer Security Characteristics for MIMO-SVD Techniques for SC-FDE Schemes.

Multi-Input, Multi-Output (MIMO) techniques are seeing widespread usage in wireless communication systems due to their large capacity gains. On the other hand, security is a concern of any wireless system, which can make schemes that implement physical layer security key in assuring secure communications. In this paper, we study the physical layer security issues of MIMO with Singular Value Decomposition (SVD) schemes, employed along with Single-Carrier with Frequency-Domain Equalization (SC-FDE) techniques. More concretely. the security potential against an unintended eavesdropper is analysed, and it is shown that the higher the distance between the eavesdropper and the transmitter or receiver, the higher the secrecy rate. In addition, in a scenario where there is Line of Sight (LOS) between all users, it is shown that the secrecy rate can be even higher than in the previous scenario. Therefore, MIMO-SVD schemes combined with SC-FDE can be an efficient option for highly secure MIMO communications.

Soft-Output Detection Methods for Sparse Millimeter-Wave MIMO Systems With Low-Precision ADCs

The use of low-precision analog-to-digital converters (ADCs) is a low-cost and power-efficient solution for a millimeter wave (mmWave) multiple-input multiple-output (MIMO) system operating at sampling rates higher than a few Gsample/sec. This solution, however, can make significant frame-error-rates (FERs) degradation due to inter-subcarrier interference when applying conventional frequency-domain equalization techniques. In this paper, we propose computationally-efficient yet near-optimal soft-output detection methods for the coded mmWave MIMO systems with low-precision ADCs. The underlying idea of the proposed methods is to construct an extremely sparse inter-symbol-interference (ISI) channel model by jointly exploiting the delay-domain sparsity in mmWave channels and a high quantization noise caused by low-precision ADCs. Then we harness this sparse channel model to create a trellis diagram with a reduced number of states or a factor graph with very sparse edge connections. Using the reduced trellis diagram, we present a soft-output detection method that computes the log-likelihood ratios (LLRs) of coded bits by optimally combining the quantized received signals obtained from multiple receive antennas using a forward-and-backward algorithm. To reduce the computational complexity further, we also present a low-complexity detection method using the sparse factor graph to compute the LLRs in an iterative fashion based on a belief propagation algorithm. Simulations results demonstrate that the proposed soft-output detection methods provide significant FER gains compared to the existing frequency-domain equalization techniques in a coded mmWave MIMO system using one- or two-bit ADCs.

Recent Advances in DSP Techniques for Mode Division Multiplexing Optical Networks with MIMO Equalization: A Review

This paper provides a technical review regarding the latest progress on multi-input multi-output (MIMO) digital signal processing (DSP) equalization techniques for high-capacity fiber-optic communication networks. Space division multiplexing (SDM) technology was initially developed to improve the demanding capacity of optic-interconnect links through mode-division multiplexing (MDM) using few-mode fibers (FMF), or core-multiplexing exploiting multicore fibers (MCF). Primarily, adaptive MIMO filtering techniques were proposed to de-multiplex the signals upon different modes or cores, and to dynamically compensate for the differential mode group delays (DMGD) plus mode-dependent loss (MDL) via DSP. Particularly, the frequency-domain equalization (FDE) techniques suggestively lessen the algorithmic complexity, compared with time-domain equalization (TDE), while holding comparable performance, amongst which the least mean squares (LMS) and recursive least squares (RLS) algorithms are most ubiquitous and, hence, extensively premeditated. In this paper, we not only enclose the state of the art of MIMO equalizers, predominantly focusing on the advantage of implementing the space–time block-coding (STBC)-assisted MIMO technique, but we also cover the performance evaluation for different MIMO-FDE schemes of DMGD and MDL for adaptive coherent receivers. Moreover, the hardware complexity optimization for MIMO-DSP is discussed, and a joint-compensation scheme is deliberated for chromatic dispersion (CD) and DMGD, along with a number of recent experimental demonstrations using MIMO-DSP.

Performance Enhancement of Faster-Than-Nyquist Signaling Based Single-Carrier Frequency-Domain Equalization Systems

This paper provides a method that appends and removes efficiently the cyclic prefix and the cyclic suffix by means of an inter-block interference elimination for a frequency domain equalization (FDE) in faster-than-Nyquist (FTN) signaling schemes. Furthermore, we propose various transmission schemes to integrate such an FTN signaling in the single-carrier FDE system. We propose FTN transmission schemes combined with various FDE techniques such as a post-equalization, a pre-equalization, and a balanced equalization in the FTN-SC-FDE system. We prove that the proposed transmission schemes yield improved performances by deriving the instantaneous bit error rate and error probability. Finally, we evaluate the analytical results and the simulation results of the performance of various FTN-SC-FDE schemes. Our proposed schemes can be applied to enhance the spectral efficiency of the satellite broadcasting systems like DVB-S2/S2X as well as the return channels of interactive broadcasting systems.

Uplink Achievable Rate and Power Allocation in Cooperative LTE-Advanced Networks

This paper studies the achievable rate and power allocation to improve the uplink (UL) spectrum efficiency in a Long-Term Evolution Advanced (LTE-A) cooperative cellular network with the deployment of Type-II in-band decode-and-forward (DF) relay stations (RSs). The physical-layer UL transmission technology is based on single-carrier frequency-division multiple access (SC-FDMA) with frequency-domain equalization (FDE). Different from the downlink (DL) orthogonal FDMA system, signals on all subcarriers in the SC-FDMA system are transmitted sequentially rather than in parallel; thus, the user's achievable rate is not simply the summation of the rates on all allocated subcarriers. Moreover, each user equipment (UE) device has its own transmission power constraint instead of a total power constraint at the base station in the DL case. Therefore, the UL resource allocation problem in the LTE-A system is more challenging. To this end, we first derive the achievable rates of the SC-FDMA system with two commonly used FDE techniques, namely, zero-forcing (ZF) equalization and minimum-mean-square-error (MMSE) equalization, based on the joint superposition coding for cooperative relaying. We then propose optimal power allocation schemes among subcarriers at both the UE and RS to maximize the overall throughput of the system. Both theoretical analysis and numerical results demonstrate that our proposed power allocation schemes can drastically improve system throughput.

Dense SDM (12-Core x 3-Mode) Transmission Over 527 km With 33.2-ns Mode-Dispersion Employing Low-Complexity Parallel MIMO Frequency-Domain Equalization

We propose long-haul space-division-multiplexing (SDM) transmission systems employing parallel multiple-input multiple-output (MIMO) frequency-domain equalization (FDE) and transmission fiber with low differential mode delay (DMD). We first discuss the advantages of parallel MIMO FDE technique in long-haul SDM transmission systems in terms of the computational complexity, and then, compare the complexity required for parallel MIMO FDE as well as the conventional time-domain equalization techniques. Proposed parallel MIMO FDE that employs low baud rate multicarrier signal transmission with a receiver-side FDE enables us to compensate for 33.2-ns DMD with considerably low-computational complexity. Next, we describe in detail the newly developed fiber and devices we used in the conducted experiments. A graded-index (GI) multicore few-mode fiber (MC-FMF) suppressed the accumulation of DMD as well as intercore crosstalk. Mode dependent loss/gain effect was also mitigated by employing both a ring-core FM erbium-doped fiber amplifier and a free-space optics type gain equalizer. By combining these advanced techniques together, we finally demonstrate 12-core $\times$ 3-mode dense SDM transmission over 527-km GI MC-FMF without optical DMD management.

Frequency-domain Equalization Techniques for Multi-h Continuous Phase Modulation

Two receiver architectures are presented for equalization of multi-h continuous phase modulation (CPM). In the first approach, the receiver front end is a matched-filter bank, which is derived from Laurent decomposition of the signal. A circulant-matrix model derived for the samples of the matched filter is used to perform the equalization in frequency domain. The second technique employs a receiver with a simple front end consisting of a low-pass filter and a fractional sampler. We also develop a circulant matrix model for the latter approach, which relates the Laurent pseudo-symbols to each polyphase component at the output of the sampler. A linear frequency-domain equalizer (FDE) is also proposed using this model. In addition to providing the details of these approaches, the paper proposes several simplifications applicable to each of the two cases, and provides a detailed discussion on the performance/complexity trade-off. Bit-error rate (BER) results are presented for the IRIG-106 aeronautical telemetry dual-h CPM waveform.

Spectrally Efficient Frame-Format-Aided Turbo Equalization With Channel Estimation

Chained turbo equalization (CHATUE) has been recently recognized as a low-complexity frequency-domain turbo equalization technique that eliminates the necessity of transmitting the cyclic prefix (CP), and hence allows for spectrally efficient signaling in wireless communications. However, two issues arise from the original version of CHATUE (referred to as CHATUE1) as a consequence of eliminating the CP, which are the noise enhancement and the latency due to the time-concatenated structure. This paper proposes a new version of CHATUE (referred to as CHATUE2) to solve the noise enhancement problem. CHATUE2 retrieves the circulant structure of the channel matrix, originally inherent within the CP transmission, by utilizing composite replica signals that combine the received signals and the soft reference signals replicated from the log-likelihood ratio (LLR) fed back from the decoder. For this purpose, this paper determines the optimal combining ratio based on the minimum-mean-square-error (MMSE) criterion. CHATUE2 is hence able to achieve an improvement in bit-error-rate (BER) performance over CHATUE1. In addition, this paper provides a solution to solving the latency problem by making a practical assumption on the training sequence (TR) transmission, which is required to perform channel estimation generally, in practical systems. Furthermore, this paper proposes a new channel estimation technique, i.e., chained turbo estimation (CHATES), which improves the spectrum efficiency and asymptotically achieves the Cramer–Rao bound (CRB). CHATES assumes that the TR length is exactly equal to the channel impulse response (CIR) length, although the conventional technique requires twice as long or even longer TR lengths. Numerical results show that CHATUE2 with CHATES achieves a gain of 1 dB over conventional turbo equalization with a CP at a BER of $\hbox{10}^{-5}$ in realistic propagation scenarios represented by channel sounding measurement data and in model-based frequency-selective fading channels.

Iterative Frequency-Domain Packet Combining Techniques for UWB Systems with Strong Interference Levels

UWB (Ultra Wideband) systems tend to suffer strong interference from signals that occupy a significant part of the transmission band. This is an important constraint, especially when the channel remains fixed for a long period of time. In order to overcome this limitation, this paper considers UWB systems employing Single-Carrier with Frequency-Domain Equalization techniques. We propose the corresponding receiver, which also allows the soft packet combining associated to different Automatic Repeat ReQuest transmission attempts, as a measure to improve the performance through the exploitation of diversity. Our techniques are able to cope with strong interference levels as well as deep fading, even for fixed channels.

1024 QAM (60 Gbit/s) single-carrier coherent optical transmission over 150 km

We demonstrate a record QAM multiplicity of 1024 levels in a single-carrier coherent transmission. A frequency-domain equalization technique and a back-propagation method are adopted to compensate for distortions caused by hardware imperfections and fiber impairments, respectively. As a result, 60 Gbit/s polarization-multiplexed transmission over 150-km has been achieved at 3 Gsymbol/s within an optical bandwidth of only 4.05 GHz.

2 × 2 MIMO radio-over-fiber system at 60 GHz employing frequency domain equalization

This work experimentally demonstrates the efficacy of the 2 × 2 multiple-input multiple-output (MIMO) technique for capacity improvement of a 60-GHz radio-over-fiber (RoF) system employing single-carrier modulation format. We employ frequency domain equalization (FDE) to estimate the channel response, including frequency response of the 60 GHz RoF system and the MIMO wireless channel. Using FDE and MIMO techniques, we experimentally demonstrate the doubling the of wireless data capacity of a 60 GHz RoF system to 27.15 Gb/s using 16-QAM modulation format, with transmission over 25 km of standard single-mode fiber and 3 m wireless distance.

Power Allocation in MMSE Relaying over Frequency-Selective Rayleigh Fading Channels

This paper develops an amplify-and-forward relaying scheme for multiuser wireless cooperative networks under frequency-selective block-fading. Single-carrier frequency division multiple-access with frequency-domain equalization technique is employed at both the relay and destination to combat the inter-block and inter-symbol interference caused by multipath propagation. With the assumption that the full channel state information (CSI) is available at the destination, the relay only knows the uplink channels while no CSI is available at the sources, two power allocation schemes are developed for the relay: (i) to minimize the total transmit power at the relay while maintaining the signal-to-interference-plus-noise ratio (SINR) for each user at the destination above a certain level, and (ii) to maximize the worst SINR among all the users subject to a constraint on total relay power. In the first problem, it is shown that SINR adaptation is needed not only to guarantee a feasible solution but also to significantly reduce the transmit power at the relay for certain channel conditions. In the second problem, a flexible multi-level water-filling scheme is developed, which can be easily modified to adapt to the different channel conditions as well as different quality-of-service provision strategies.

Single Carrier Modulation With Nonlinear Frequency Domain Equalization: An Idea Whose Time Has Come—Again

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In recent years single carrier modulation (SCM) has again become an interesting and complementary alternative to multicarrier modulations such as orthogonal frequency division multiplexing (OFDM). This has been largely due to the use of nonlinear equalizer structures implemented in part in the frequency domain by means of fast Fourier transforms, bringing the complexity close to that of OFDM. Here a nonlinear equalizer is formed with a linear filter to remove part of intersymbol interference, followed by a canceler of remaining interference by using previous detected data. Moreover, the capacity of SCM is similar to that of OFDM in highly dispersive channels only if a nonlinear equalizer is adopted at the receiver. Indeed, the study of efficient nonlinear frequency domain equalization techniques has further pushed the adoption of SCM in various standards. This tutorial paper aims at providing an overview of nonlinear equalization methods as a key ingredient in receivers of SCM for wideband transmission. We review both hybrid (with filters implemented both in time and frequency domain) and all-frequency-domain iterative structures. Application of nonlinear frequency domain equalizers to a multiple input multiple output scenario is also investigated, with a comparison of two architectures for interference reduction. We also present methods for channel estimation and alternatives for pilot insertion. The impact on SCM transmission of impairments such as phase noise, frequency offset and saturation due to high power amplifiers is also assessed. The comparison among the considered frequency domain equalization techniques is based both on complexity and performance, in terms of bit error rate or throughput. </para>

Interference Suppression for Multiuser Downlink Transmission in Frequency-Selective Fading Channels

This paper presents an interference suppression scheme for multiuser downlink transmission in severe frequency-selective fading environments. Frequency-domain transmit beamforming and pre-equalization based on single-carrier frequency-domain equalization (SC-FDE) technique are employed to cancel co-channel interference (CCI) and to suppress intersymbol interference (ISI) with relatively low complexity. The proposed scheme effectively suppresses the ISI with a zero-forcing constraint on the CCI, and provides a viable solution to an otherwise analytically complex, if not unsolvable, problem. This paper also shows that, in frequency-selective fading channels, a multiuser system with K users and Mt base transceiver station antennas can offer lower bit error rate than a single-user system with Mt - K + 1 BTS antennas, if the proposed frequency-domain multiuser beamforming is employed.

Frequency-Domain Turbo Equalization and Multiuser Detection for DS-UWB Systems

One of the major challenges in direct sequence-ultra wideband (DS-UWB) receiver design is intersymbol interference (ISI). Several equalization schemes to eliminate ISI in DS-UWB systems have been proposed in the literature. It was shown that frequency-domain (FD) equalization techniques can offer better trade off between performance and complexity compared to time- domain equalization schemes for DS-UWB systems on highly dispersive channels. In this paper, we derive low-complexity FD minimum mean square error turbo equalization schemes for single-user binary phase shift keying (BPSK) and quaternary bi-orthogonal keying (4BOK) DS-UWB systems. For multiuser DS-UWB systems, we combine FD turbo equalization schemes with soft interference cancelation to obtain multiuser FD turbo detectors. The bit error rate performance gain due to turbo detection is shown to be significant, particularly for multiuser DS-UWB systems.

Iterative Overlap FDE for Multicode DS-CDMA

Recently, a new frequency-domain equalization (FDE) technique, called overlap FDE, that requires no GI insertion was proposed. However, the residual inter/intra-block interference (IBI) cannot completely be removed. In addition to this, for multicode direct sequence code division multiple access (DS-CDMA), the presence of residual interchip interference (ICI) after FDE distorts orthogonality among the spreading codes. In this paper, we propose an iterative overlap FDE for multicode DS-CDMA to suppress both the residual IBI and the residual ICI. In the iterative overlap FDE, joint minimum mean square error (MMSE)-FDE and ICI cancellation is repeated a sufficient number of times. The bit error rate (BER) performance with the iterative overlap FDE is evaluated by computer simulation.

BER Performance Analysis of MC-CDMA with Overlap-FDE

Recently, multi-carrier code division multiple access (MC-CDMA) has been attracting much attention as a broadband wireless access technique for the next generation mobile communication systems. Frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can take advantage of the channel frequency-selectivity and improve the average bit error rate (BER) performance due to frequency-diversity gain. The conventional FDE requires the insertion of the guard interval (GI) to avoid the inter-block interference (IBI), resulting in the transmission efficiency loss. In this paper, an overlap FDE technique, which requires no GI insertion, is presented for MC-CDMA transmission. An expression for the conditional BER is derived for the given set of channel gains. The average BER performance in a frequency-selective Rayleigh fading channel is evaluated by Monte-Carlo numerical computation method using the derived conditional BER and is confirmed by computer simulation of the signal transmission.

Coherent optical OFDM: has its time come? [Invited

There has been growing interest in coherent optical orthogonal frequency-division multiplexing (CO-OFDM). We aim to present the case that the time for CO-OFDM has come, in terms of the demand from today's ever-advancing optical networks and the availability of its underlying technologies. We first lay out the signal processing aspect for CO-OFDM and then show a 2×2 multiple-input-multiple-output (MIMO) OFDM representation for the single-mode fiber optical channel. Through numerical simulation and experimental demonstration, we further present and discuss various MIMO-OFDM systems focusing on their polarization-mode dispersion resilience. Among those systems, the 2×1 MIMO-OFDM configuration incorporating polarization-time coding shows promise for optical access networks and broadcast networks. Finally, another class of the frequency-domain equalization techniques, namely, incoherent or coherent optical single-carrier frequency-domain equalization (CO-SCFDE) is discussed and experimentally demonstrated.