Linear Frequency Domain Equalization Research Articles

Low-Complexity Adaptive Frequency-Domain Nonlinear Equalization for Analog RoF Mobile Fronthaul Using FFT/IFFT-Assisted Channel Aggregation

Addressing the nonlinearity induced signal degradation is of critical importance for harvesting the transparent benefits of an analog radio over fiber (A-RoF) architecture, to support mobile fronthaul (MFH) with high spectral efficiency and reduced latency. Here, for linearizing the low-latency A-RoF MFH using digital-domain fast Fourier transform /inverse fast Fourier transform (FFT/IFFT) assisted channel aggregation/de-aggregation (CA/DA), we propose and experimentally demonstrate a compatible adaptive frequency-domain (FD) nonlinear equalization scheme. This scheme is characterized by a much lower computational complexity compared with the popular time-domain Volterra nonlinear equalizer while delivering a comparable performance. The proposed equalization scheme is implemented using the FD two-box cascaded Hammerstein structure. It enables simplified coefficients estimation, computationally efficient equalization, FFT/IFFT calculation reusing in channel DA, and shared legacy one-tap FD linear equalization in the OFDM system. Experimental validations of the proposed nonlinear equalization approach are carried out via typical electroabsorption modulator (EAM) and Mach-Zehnder modulator (MZM) based intensity modulation and direct detection (IMDD) A-RoF links. Cost-effective fiber-optic (with EAM) and optical up-conversion enabled V-band millimeter-wave (mm-wave) fiber-wireless (with MZM) transmissions are demonstrated. Experimental results show that the proposed scheme can effectively improve the performances of both EAM and MZM based 10-km fiber-optic A-RoF MFH links, in terms of the (>8 dB) reduction of adjacent channel leakage ratio, (>10 dB) improvement of error-vector magnitude (EVM) and (>5 dB) enhancement of input intermediate-frequency (IF) power range, which retains an acceptable (below 8 %) EVM performance for the 64-QAM modulation. The input IF signal aggregates 8 125-MHz 64-QAM OFDM channels. Furthermore, the proposed scheme enables the transmission of a 5-Gbit/s aggregated IF 64-QAM signal over a 10-km fiber link and 1.2-m 60-GHz wireless channel, wherein a >12 dB improved input power margin is observed.

Nonlinear frequency domain PMD modeling and equalization for nonlinear frequency division multiplexing transmission.

Polarization mode dispersion (PMD) is one of the fundamental properties of a standard single-mode fiber. It affects the propagating signals and degrades the performance of high-speed optical fiber communication systems. PMD also gives an effect on the nonlinear spectra or scattering data in nonlinear frequency division multiplexing (NFDM) systems. However, PMD is usually described in the linear frequency domain, and there are few investigations about the influence of PMD in the nonlinear frequency domain (NFD). An NFD-PMD model is needed to understand the impact of PMD in the NFD. In this work, using a linear approximation method, we first propose an NFD-PMD model and verify its effectiveness. With the guide of the NFD-PMD model, a blind NFD-PMD equalization scheme is designed. The simulation results indicate that the proposed NFD-PMD equalization scheme has better performance than the training sequence method based on linear frequency domain equalization.

Broadband Analog Network Coding With Robust Processing for Two-Way Relay Networks

In this letter, we study the robust processing for a single carrier two-way relay network with broadband analog network coding and imperfect channel state information. Based on a statistical model for channel estimation error, we derive the optimal coefficients of self interference cancellation and linear frequency domain equalization in the sense of minimizing the conditional mean square error given a channel estimate. Simulation results show that the proposed robust design can achieve better bit error rate performance than the conventional non-robust scheme.

Mixed-ADC Massive MIMO Uplink in Frequency-Selective Channels

The aim of this paper is to investigate the recently developed mixed-ADC architecture for frequency-selective channels. Multi-carrier techniques such as orthogonal frequency division multiplexing (OFDM) are employed to handle inter-symbol interference (ISI). A frequency-domain equalizer is designed for mitigating the inter-carrier interference (ICI) introduced by the nonlinearity of one-bit quantization. For static single-input-multiple-output (SIMO) channels, a closed-form expression of the generalized mutual information (GMI) is derived, and based on which the linear frequency-domain equalizer is optimized. The analysis is then extended to ergodic time-varying SIMO channels with estimated channel state information (CSI), where numerically tight lower and upper bounds of the GMI are derived. The analytical framework is naturally applicable to the multi-user scenario, for both static and time-varying channels. Extensive numerical studies reveal that the mixed-ADC architecture with a small proportion of high-resolution ADCs does achieve a dominant portion of the achievable rate of ideal conventional architecture, and that it remarkably improves the performance as compared with one-bit massive MIMO.

Multi-channel iterative FDE for single carrier block transmission over underwater acoustic channels

Recently, single carrier block transmission (SCBT) has received much attention in high-rate phase-coherent underwater acoustic communication. However, minimum-mean-square-error (MMSE) linear FDE may suffer performance loss in the severely time dispersive underwater acoustic channel. To combat the channel distortion, a novel multi-channel receiver with maximum ratio combining and a low complex T/4 fractional iterative frequency domain equalization (FDE) is investigated to improve diversity gain and the bit error rate (BER) performance. The proposed method has been verified by the real data from a lake underwater acoustic communication test in November 2011. At 1.8 km, the useful data rates are around 1500 and 3000 bits/ s for BPSK and QPSK respectively. The results show the improvements of system performance. Compared with MMSE FDE system, the output SNR improvement is 6.9 dB, and the BER is from 10-3 to no error bits for BPSK. The output SNR improvement is 5.3 dB, and the BER is from 1.91×10-2 to 2.2×10-4 for QPSK.

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.

Impact of Channel Estimation Errors on SC-FDE Systems

Single carrier transmissions with frequency domain equalization (SC-FDE) have gained widespread use in emergent broadband wireless systems becoming an attractive alternative to popular Orthogonal Frequency Division Multiplexing (OFDM) schemes, particularly at the uplink. Since coherent receivers are usually employed with SC-FDE, accurate channel estimates are required so as to avoid substantial performance degradation. Several channel estimation strategies have been proposed for SC-FDE, but a thoroughly evaluation of the degradation caused by channel estimation errors and a comparison against OFDM is still lacking. In this paper we study the impact of imperfect channel knowledge on SC transmission with focus on the linear frequency domain equalizer (FDE) and on the Iterative Block Decision Feedback Equalizer (IB-DFE). We propose a modified IB-DFE which incorporates knowledge of the channel estimation error model and show that its performance becomes more robust against the presence of strong error components in the channel estimates. We also evaluate, analytically and through simulations, the degradation caused by imperfect channel estimation in SC-FDE and compare it against OFDM schemes (Orthogonal Frequency Division Multiplexing). It is shown that the channel estimation requirements for SC-FDE are higher than for OFDM unless a channel estimation error aware receiver is employed.

Spectral Efficiency of Interleaved SC-FDMA With Adaptive Modulation and Coding Over Nakagami-<formula formulatype="inline"><tex Notation="TeX">$m$</tex></formula> Fading Channels

Because it achieves similar performance to that of orthogonal frequency-division multiple access (OFDMA) with much more favorable envelope characteristics and lower peak-to-average power ratio (PAPR), single-carrier frequency-division multiple access (SC-FDMA) was chosen as the uplink transmission technology for Long Term Evolution (LTE) and LTE-Advanced systems. This choice has provoked a growing interest in this transmission technology; therefore, there is extensive literature on its performance in terms of bit error rate (BER) and PAPR. However, research on its spectral efficiency has been scarce until now. This paper aims to help fill this gap with an analytical study of the spectral efficiency in SC-FDMA when adaptive modulation and coding (AMC) and linear frequency-domain equalization are applied. This paper therefore computes the spectral efficiency for zero-forcing (ZF) and minimum-mean-square-error frequency-domain equalization (MMSE-FDE) for different Nakagami-m fading channels.

Linear Frequency Domain Equalization of SOQPSK-TG for Wideband Aeronautical Telemetry Channels

This work explores multipath interference mitigation for a single transmit antenna, single receive antenna system with SOQPSK-TG using a linear single-carrier frequency domain equalization (SCFDE) technique. Linear SCFDE with maximum likelihood (ML) channel estimation is shown to greatly improve system Bit Error Rates (BER). Simulation results also demonstrate that three samples per bit at the receiver are adequate to achieve the best BER performance.

Performance Analysis of Hybrid Carrier System with MMSE Equalization over Doubly-Dispersive Channels

A hybrid carrier (HC) system employing a frequency domain linear equalization based on minimum mean square error (MMSE) criterion is analyzed in this letter. The analytical studies prove that HC modulation scheme achieves a trade-off between circularly prefixed orthogonal frequency division multiplexing (OFDM) and single-carrier (SC) systems in terms of resisting doubly-selective fading. By dispersing the aggregated residual interference effectively, the HC system with particular modulation orders outperform OFDM and SC systems within a specific signal noise ratio (SNR) interval. Both analysis and simulation results over a typical double selective fading channel verify the superiority of HC modulation in suppressing residual interferences.

SC-FDE for Offset Modulations: An Efficient Transmission Technique for Broadband Wireless Systems

It is widely accepted that SC-FDE (Single-Carrier with Frequency-Domain Equalization) is an excellent candidate for broadband wireless systems, especially when an efficient power amplification is intended. If grossly nonlinear power amplifiers are employed, conventional QPSK (Quaternary Phase Shift Keying) or QAM (Quadrature Amplitude Modulation) modulations should be replaced by offset modulations such as OQPSK (Offset QPSK) and OQAM (Offset QAM). In fact, offset signals have much lower dynamic range than non-offset signals, with OQPSK signals being able to have an almost constant envelope. This paper considers frequency-domain receiver design for OQPSK and OQAM schemes. It is shown that FDE (Frequency Domain Equalization) designed for non-offset modulations are not suitable for offset modulations due to the residual IQI (In-phase/Quadrature Interference), i.e. the interference between in-phase (I) and quadrature (Q) components at the sampling instants. Therefore, we propose several FDE designs where there is no IQI in the sampling instants as well as iterative FDE receivers with IQI cancellation. Our receivers have excellent performance, with the linear designs significantly outperforming linear FDE for non-offset modulations and the iterative designs with performance close to the MFB (Matched Filter Bound).

SC-FDE for Offset Modulations: An Efficient Transmission Technique for Broadband Wireless Systems

It is widely accepted that SC-FDE (Single-Carrier with Frequency-Domain Equalization) is an excellent candidate for broadband wireless systems, especially when an efficient power amplification is intended. If grossly nonlinear power amplifiers are employed, conventional QPSK (Quaternary Phase Shift Keying) or QAM (Quadrature Amplitude Modulation) modulations should be replaced by offset modulations such as OQPSK (Offset QPSK) and OQAM (Offset QAM). In fact, offset signals have much lower dynamic range than non-offset signals, with OQPSK signals being able to have an almost constant envelope. This paper considers frequency-domain receiver design for OQPSK and OQAM schemes. It is shown that FDE (Frequency Domain Equalization) designed for non-offset modulations are not suitable for offset modulations due to the residual IQI (In-phase/Quadrature Interference), i.e. the interference between in-phase (I) and quadrature (Q) components at the sampling instants. Therefore, we propose several FDE designs where there is no IQI in the sampling instants as well as iterative FDE receivers with IQI cancellation. Our receivers have excellent performance, with the linear designs significantly outperforming linear FDE for non-offset modulations and the iterative designs with performance close to the MFB (Matched Filter Bound).

Cooperative Beamforming for Single-Carrier Frequency-Domain Equalization Systems with Multiple Relays

We consider cooperative beamforming (BF) for block-based single-carrier frequency-domain equalization (SC- FDE) in a wireless network consisting of one single-antenna source, one single-antenna destination, and multiple multi- antenna relays. Adopting the minimum mean squared error as optimality criterion, the optimal frequency-domain linear equalization (LE) and decision-feedback equalization (DFE) receivers are derived and corresponding objective functions for relay BF matrix optimization are specified. For a sum relay power constraint, we obtain the structure of the optimal relay BF matrices in closed form. While the structure of the optimal relay BF matrices is identical for LE and DFE as well as for an idealized matched filter receiver, the solution of the remaining power allocation problem depends on the adopted receiver. The power allocation problem is shown to be convex for all considered receivers and an efficient numerical algorithm for finding the optimal power allocation is provided. Furthermore, to reduce complexity, two suboptimal power allocation schemes assigning identical powers to all relays and/or frequencies are proposed and shown to lead to only a small loss in performance and a remarkable robustness against imperfect channel state information.

Hybrid Carrier CDMA Communication System Based on Weighted-Type Fractional Fourier Transform

Recently, an approach based on carrier scheme convergence was proposed based on the weighted-type fractional Fourier transform (WFRFT). Meanwhile, in the high-speed wireless communication systems, code division multiple access (CDMA) is an efficient technique for interference in the frequency-selective fading channels. In this letter, we combine the hybrid carrier (HC) scheme with CDMA and frequency domain linear equalization. The proposed system can not only provide the compatibility with single carrier (SC) CDMA and multi-carrier (MC) CDMA systems, but also achieve a smooth and seamless transition between the two. The proposed system can switch to single carrier or multi-carrier scheme under the specific conditions. Moreover, HC-CDMA outperforms SC-CDMA and MC-CDMA systems over the frequency-selective fading channel and single frequency jamming channel.

SC-FDMA 수신기를 위한 잡음 백색화 판정궤환 등화기

이 논문에서는 SC-FDMA 수신기를 위한 잡음 백색화 판정궤환 등화기를 제안하였다. SC-FDMA 방식은 다중경로의 영향을 제거할 수 있는 OFDMA 방식의 장점을 유지하면서 OFDMA의 단점인 높은 PAPR 문제를 해결할 수 있는 장점을 가지고 있다. 또 SCFDMA 방식은 기본적으로 단일 반송파 전송방식이지만, 주파수 영역에서 채널 등화기를 구현함으로써 OFDMA 수신기와 마찬가지로 등화기의 복잡도를 크게 감소시킬 수 있다. 뿐만 아니라 시간 영역 신호가 디지털 변조된 복소심볼이므로 시간 영역에서 추가적으로 비선형 등화인 판정궤환 등화를 함으로써 주파수 영역의 선형 등화에 의해 잔류해 있는 심볼간 간섭을 더 제거할 수 있다. 한편 지금까지 제시된 SC-FDMA용 판정궤환 등화기는 판정기에 입력되는 신호에 포함된 잡음이 백색화되어 있지 않기 때문에 최적판정을 수행하고 있지 않다. 이 논문에서는 이러한 문제를 해결하기 위해 선형 잡음 백색화 필터를 판정기 앞에 연결하여 판정궤환 등화기의 성능을 더 향상 시킬 수 있는 방법을 제시한다. 또 컴퓨터 모의실험을 통해 기존의 등화기와 제안된 등화기의 비트 오율 성능을 비교한다. In this paper, we propose a noise whitening decision feedback equalizer for single carrier frequency division multiple access (SC-FDMA) receivers. SC-FDMA has the same advantage as that of orthogonal frequency division multiple access (OFDMA) in which the multipath effect can be removed easily, and also solves the problem of high peak to average power ratio (PAPR) which is the main drawback of OFDMA. Although SC-FDMA is a single carrier transmission scheme, a simple frequency domain linear equalizer (FD-LE) can be implemented as in OFDMA, which can dramatically reduce the equalizer complexity. Moreover, some residual intersymbol interference in the output of the FD-LE can be further removed by an additional nonlinear decision feedback equalizer (DFE) in time domain, because the time domain signal is a digitally modulated symbol. In the conventional DFE, however, the noise is not white at the input of the decision device and correspondingly the decision is not optimum. In this paper, we propose an improved DFE scheme for SC-FDMA systems where a linear noise whitening filter is inserted before the decision device of the conventional DFE scheme. Through computer simulations, we compare the bit error rate performance of the proposed DFE scheme with the conventional equalizers.

A sub-block orthogonal single carrier frequency domain equalization system in fast Rayleigh fading channel

In this paper, we analyze the frequency domain linear equalization (FDLE) of single carrier block transmission (SCBT) systems under fast fading channel. First, we propose a new approximating model in which the channel is assumed to be static in sub-blocks vary each other. Based on this model, we derive a new 2-orthogonal-sub-blocked frequency domain equalization method. Then, we derive the conditions of the channel under which the equalization method can be applied to the 2-orthogonal-sub-blocked systems. Simulation demonstrates that the proposed method can improve the anti-Doppler ability of SC-FDLE and at the same time keep its high efficiency and low complexity.

On the Information Rate of Single-Carrier FDMA Using Linear Frequency Domain Equalization and Its Application for 3GPP-LTE Uplink

This paper compares the information rate achieved by SC-FDMA (single-carrier frequency-division multiple access) and OFDMA (orthogonal frequency-division multiple access), where a linear frequency-domain equalizer is assumed to combat frequency selective channels in both systems. Both the single user case and the multiple user case are considered. We prove analytically that there exists a rate loss in SC-FDMA compared to OFDMA if decoding is performed independently among the received data blocks for frequency selective channels. We also provide a geometrical interpretation of the achievable information rate in SC-FDMA systems and point out explicitly the relation to the well-known waterfilling procedure in OFDMA systems. The geometrical interpretation gives an insight into the cause of the rate loss and its impact on the achievable rate performance. Furthermore, motivated by this interpretation we point out and show that such a loss can be mitigated by exploiting multiuser diversity and spatial diversity in multi-user systems with multiple receive antennas. In particular, the performance is evaluated in 3GPP-LTE uplink scenarios.

Frequency-domain precoding for single carrier frequency-division multiple access

At present there is considerable interest in the use of single carrier frequency-division multiple access. This interest is justified by the inherent single carrier structure of the SC-FDMA scheme, which is more robust against phase noise and has a lower peak-to-average power ratio than orthogonal frequency-division multiple access. This consequently makes it more attractive for uplink transmission from low-cost devices with limited transmit power. SC-FDMA commonly makes use of frequency domain linear equalization in order to combat the frequency selectivity of the transmission channel. Frequency domain decision feedback equalization, composed of a frequency domain feed forward filter and a time domain feedback filter, outperforms LE due to its ability to cancel precursor echoes. Although these solutions suffer from error propagation, results show that DFE still offers a significant performance gain over conventional LE for uncoded SC-FDMA. In this article we show how precoding can be used on the uplink of the LTE standard to overcome the frequency selective nature of the radio channel. We propose a frequency domain implementation of Tomlinson- Harashima precoding and investigate the bit error rate and the PAPR performance for SCFDMA using ZF and MMSE THP.

Low-complexity linear frequency domain equalization for continuous phase modulation

In this paper, we develop a new low-complexity linear frequency domain equalization (FDE) approach for continuous phase modulated (CPM) signals. As a CPM signal is highly correlated, calculating a linear minimum mean square error (MMSE) channel equalizer requires the inversion of a nondiagonal matrix, even in the frequency domain. In order to regain the FDE advantage of reduced computational complexity, we show that this matrix can be approximated by a block-diagonal matrix without performance loss. Moreover, our MMSE equalizer can be simplified to a low-complexity zero-forcing equalizer. The proposed techniques can be applied to any CPM scheme. To support this theory we present a new polyphase matrix model, valid for any block-based CPM system. Simulation results in a 60 GHz environment show that our reduced-complexity MMSE equalizer significantly outperforms the state of the art linear MMSE receiver for large modulation indices, while it performs only slightly worse for small ones.

Frequency-Domain Equalization with Iterative Block Noise-Prediction for Single-Carrier Systems

In this letter, we propose a novel frequency-domain equalizer (FDE) for single-carrier systems characterized by severe inter-symbol interference (ISI) channels; it consists of a linear FDE and an iterative block noise-predictor (IBNP). Unlike the FDE with time-domain noise predictor (FDE-NP), the proposed scheme allows the feedback equalizer being an uncausal filter, and performs the noise prediction in an iterative manner. For this reason, FDE-IBNP can remove both precursor and postcursor ISI, and alleviate the impact of error-propagation. Besides, our scheme has lower computational complexity than the present iterative block equalizers.