IQ-Imbalance Compensation for OFDM in the Presence of IBI and Carrier-Frequency Offset

In this paper, we propose a frequency-domain equalization technique for orthogonal frequency division multiplexing (OFDM) transmission over frequency-selective channels. We consider the case where the receiver analog front-end suffers from IQ-imbalance and the local oscillator suffers from carrier-frequency offset (CFO). While the IQ-imbalance results in a mirroring effect, the CFO induces inter-carrier interference (ICI). In addition to ICI, we consider the channel delay spread is larger than the cyclic prefix (CP). This means that inter-block interference (IBI) is present. The frequency-domain equalizer is obtained by transferring a time-domain equalizer (TEQ) to the frequency-domain resulting in a per-tone equalizer (PTEQ). Due to the presence of IQ-imbalance the conventional TEQ (where only one TEQ is applied to the received sequence) is not sufficient to cope with the mirroring effect. A sufficient TEQ consists of two time-domain filters; one applied to the received sequence and another applied to a conjugated version of the received sequence. For the case of IQ-imbalance and CFO, the TEQs are designed according the basis expansion model (BEM) which showed to be able to cope with the ICI problem. Finally, in addition to the frequency-domain PTEQ design procedure, a training-based RLS type initialization scheme for direct per-tone equalization is also proposed     

Time-Domain Block and Per-Tone Equalization for MIMO–OFDM in Shallow Underwater Acoustic Communication

Shallow underwater acoustic (UWA) channel exhibits rapid temporal variations, extensive multipath spreads, and severe frequency-dependent attenuations. So, high data rate communication with high spectral efficiency in this challenging medium requires efficient system design. Multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO–OFDM) is a promising solution for reliable transmission over highly dispersive channels. In this paper, we study the equalization of shallow UWA channels when a MIMO–OFDM transmission scheme is used. We address simultaneously the long multipath spread and rapid temporal variations of the channel. These features lead to interblock interference (IBI) along with intercarrier interference (ICI), thereby degrading the system performance. We describe the underwater channel using a general basis expansion model (BEM), and propose time-domain block equalization techniques to jointly eliminate the IBI and ICI. The block equalizers are derived based on minimum mean-square error and zero-forcing criteria. We also develop a novel approach to design two time-domain per-tone equalizers, which minimize bit error rate or mean-square error in each subcarrier. We simulate a typical shallow UWA channel to demonstrate the desirable performance of the proposed equalization techniques in Rayleigh and Rician fading channels.     

一种快变信道中的正交频分复用系统均衡算法

当信道参数随时间的快速变化时,正交频分复用通信系统(OFDM)子载波间的正交性遭到破坏,出现了载波间的相互干扰(ICI),传统的单抽头频域均衡不再适用。虽然可采用最小均方误差(MMSE)均衡来补偿信道失真,但其计算量太大。为此,常用的方法是:先对接收信号进行ICI消除,恢复载波间的正交性,然后再进行单抽头频域或均衡。现有文献对ICI的分析均在频域进行,在此基础上提出的ICI消除与均衡算法存在计算量大或频谱利用率低的缺点。本文对ICI的产生机理和性质进行了时域和频域两方面的分析,利用现有OFDM标准中的空闲子载波信息,提出了一种ICI消除与均衡算法。理论分析和计算机仿真结果表明:该算法具有ICI消除效果好、计算量小和频谱利用率高等优点。     

MIMO OFDM系统中的Turbo子载波均衡

在MIMO OFDM系统中,为了对抗同天线干扰及由于保护间隔不足而引起的码间干扰和载波间干扰,该文给出了一种基于MMSE的Turbo子载波均衡器。在该算法中,软输入软输出(SISO)的子载波均衡器与软输入软输出(SISO)解码器通过迭代进行软信息交换。仿真结果表明,与非迭代的子载波均衡器相比,该文给出的Turbo子载波均衡器能够有效利用时间和空间分集,使系统性能得到了改善。     

Linear and decision-feedback per tone equalization for DMT-based transmission over IIR channels

The per-tone equalizer (PTEQ) has been presented as an attractive alternative for the classical time-domain equalizer (TEQ) in discrete multitone (DMT) based systems, such as ADSL systems. The PTEQ is based on a linear minimum mean-square-error (L-MMSE) equalizer design for each separate tone. In this paper, we reconsider DMT modulation and equalization in the ADSL context under the realistic assumption of an infinite impulse response (IIR) model for the wireline channel. First, optimum linear zero-forcing (L-ZF) block equalizers for arbitrary IIR model orders and cyclic prefix (CP) lengths are developed. It is shown that these L-ZF block equalizers can be decoupled per tone, hence they lead to an L-ZF PTEQ. Then, based on the L-ZF PTEQ, low-complexity L-MMSE PTEQ extensions are developed: the linear PTEQ extension exploits frequency-domain transmit redundancy from pilot and unused tones; alternatively, a closely related decision-feedback PTEQ extension can be applied. The PTEQ extensions then add flexibility to a DMT-based system design: the CP overhead can be reduced by exploiting frequency-domain transmit redundancy instead, so that a similar bitrate as with the original PTEQ is achieved at a lower memory and computational cost or, alternatively, a higher bitrate is achieved without a considerable cost increase. Both PTEQ extensions are also shown to improve the receiver's robustness to narrow-band interference.     

Novel semi-blind ICI equalization algorithm for wireless OFDM systems

Intercarrier interference is deemed as one of the crucial problems in the wireless orthogonal frequency division multiplexing (OFDM) systems. The conventional ICI mitigation schemes involve the frequency-domain channel estimation or the additional coding, both of which require the spectral overhead and hence lead to the significant throughput reduction. Besides, the OFDM receivers using the ICI estimation rely on a large-dimensional matrix inverter with high computational complexity especially for many subcarriers such as digital video broadcasting (DVB) systems and wireless metropolitan-area networks (WMAN). To the best of our knowledge, no semi-blind ICI equalization has been addressed in the existing literature. Thus, in this paper, we propose a novel semi-blind ICI equalization scheme using the joint multiple matrix diagonalization (JMMD) algorithm to greatly reduce the intercarrier interference in OFDM. However, the well-known phase and permutation indeterminacies emerge in all blind equalization schemes. Hence we also design a few OFDM pilot blocks and propose an iterative identification method to determine the corresponding phase and permutation variants in our semi-blind scheme. Our semi-blind ICI equalization algorithm integrating the JMMD with the additional pilot-based iterative identification is very promising for the future high-throughput OFDM systems. Through Monte Carlo simulations, the QPSK-OFDM system with our proposed semi-blind ICI equalizer can achieve significantly better performance with symbol error rate reduction in several orders-of-magnitude. For the 16QAM-OFDM system, our scheme can also improve the performance over the plain OFDM system to some extent.     

一种针对双衰落信道OFDM的新均衡算法

在OFDM系统中，子载波间的正交性是保证OFDM性能的重要保障。针对双选择性衰落信道下的OFDM系统，该文在分析载波间干扰（ICI）的基础上，提出了一种采用频域迭代消除ICI的均衡算法。分析和仿真结果表明此方法能有效地保证载波间的正交性和改善了OFDM系统的误码率（BER）性能。     

高速移动下OFDM均衡器的FPGA实现

在高速移动下,OFDM系统载波间正交性被破坏,出现载波间干扰（ICI）,严重影响系统性能,必须采用适当的均衡技术以补偿ICI。为了保证通信的有效性和实时性要求,使用FPGA实现了一种低复杂度的最小均方误差（MMSE）OFDM均衡器算法。在ISE软件平台上使用Verilog语言编写程序,并在Xilinx公司Virtex-2实验板（XC2V930芯片）上对设计进行了验证。     

Per-tone equalization for MIMO OFDM systems

This paper focuses on multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with channel order larger than the cyclic prefix (CP) length. Writing the demodulating fast Fourier transform (FFT) as a sliding FFT followed by a downsampling operation, we show in this paper that by swapping the filtering operations of the MIMO channel and the sliding FFT, the data model for the temporally smoothened received signal of each individual tone of the MIMO OFDM system is very similar to the data model for the temporally smoothened received signal of a MIMO single-carrier (SC) system. As a result, to recover the data symbol vectors, the conventional equalization approach for MIMO SC systems can be applied to each individual tone of the MIMO OFDM system. This so-called per-tone equalization (PTEQ) approach for MIMO OFDM systems is an attractive alternative to the recently developed time-domain equalization (TEQ) approach for MIMO OFDM systems. In the second part of this paper, we focus on direct per-tone equalizer design and adapt an existing semi-blind equalizer design method for space-time block coding (STBC) SC systems to the corresponding semi-blind per-tone equalizer design method for STBC OFDM systems.     

Bitrate-maximizing time-domain equalizer design for DMT-based systems

A time-domain equalizer (TEQ) is inserted in discrete multitone (DMT) receivers to impose channel shortening. Many algorithms have been developed to initialize this TEQ, but none of them really optimizes the bitrate. We present a truly bitrate-maximizing TEQ (BM-TEQ) cost function that is based on an exact formulation of the subchannel signal-to-noise ratio as a function of the TEQ taps. The performance of this BM-TEQ comes close to the performance of the per-tone equalizer.     

ICI cancellation for OFDM communication systems in time-varying multipath fading channels

In orthogonal frequency division multiplexing (OFDM) systems, time-varying multipath fading leads to the loss of subcarrier orthogonality and the occurrence of intercarrier interference (ICI). In this study, an efficient ICI suppression with less noise enhancement for multicarrier equalization is presented by using a parallel canceling scheme via frequency-domain equalization techniques, with the assumption that the channel impulse response (CIR) varies linearly during a block period. In order to avoid performance deterioration due to unreliable initial estimations in the parallel cancellation scheme, a cost function with proper weighting factor is introduced to improve the performance of the proposed equalizer. The proposed equalizer consists of a set of prefilters and a set of ICI cancellation filters, with two stages to perform different functions to achieve minimum mean square error (MMSE) equalization. The prefilters compensate for the multiplicative distortion at the first stage, and the ICI cancellation filters remove the effects of ICI by a parallel cancellation scheme at the second stage. Finally, the performance of the proposed equalizer is analyzed and compared with that of other equalizers, indicating significant performance improvement.     

Iterative MAP Equalization and Decoding in Wireless Mobile Coded OFDM

Orthogonal frequency division multiplexing (OFDM) system suffers extra performance degradation in fast fading channels due to intercarrier interference (ICI). Combining frequency domain equalization and bit-interleaved coded modulation (BICM), the iterative receiver is able to harvest both temporal and frequency diversity. Realizing that ICI channels are intrinsically ISI channels, this paper proposes a soft-in soft-out (SISO) maximum a posteriori (MAP) equalizer by extending Ungerboeck's maximum likelihood sequence estimator (MLSE) formulation to ICI channels. The SISO MAP equalizer employs BCJR algorithm and computes the bit log-likelihood ratios (LLR) for the entire received sequence by efficiently constructing a trellis that takes into account of the ICI channel structure. A reduced state (RS) formulation of the SISO MAP equalizer which provides good performance/complexity tradeoff is also described. Utilizing the fact that ICI energy is clustered in adjacent subcarriers, frequency domain equalization is made localized. This paper further proposes two computational efficient linear minimum mean square error (LMMSE) based equalization methods: recursive q-tap SIC-LMMSE equalizer and recursive Sliding-Window (SW) SIC-LMMSE equalizer respectively. Simulations results demonstrate that the iterative SISO RS-MAP equalizer achieves the performance of no ICI with normalized Doppler frequency f_dT_s up to 20.46% in realistic mobile WiMAX environment.     

Theoretical studies and efficient algorithm of semi-blind ICI equalization for OFDM

The intercarrier interference (ICI) due to the Doppler frequency shift, sampling clock offset, time-varying multipath fading and local oscillator frequency offset becomes the major difficulty for the data transmission via the wireless orthogonal frequency division multiplexing (OFDM) systems. The existing ICI mitigation schemes involve the frequency-domain channel estimation/equalization or the additional coding and therefore require the pilot symbols which reduce the throughput. The frequency-domain channel estimation/equalization relies on the huge matrix inversion with high computational complexity especially for the OFDM technologies possessing many subcarriers such as digital video broadcasting (DVB) systems and wireless metropolitan-area networks (WMAN). In our previous work, we proposed a semi-blind ICI equalization scheme using the joint multiple matrix diagonalization (JMMD) algorithm and empirically showed that the proposed method significantly improved the symbol error rates for QPSK- and 16QAM-OFDM systems. In this paper, we discuss the sufficient condition for the theoretical ICI equalizability and also propose an alternative semi-blind ICI equalization method based on the joint approximate diagonalization of eigen-matrices (JADE) algorithm, which is much more computationally efficient than our previous method.     

Adaptive bit rate maximizing time-domain equalizer design for DMT-based systems

The classical discrete multitone receiver as used in, e.g., digital subscriber line (DSL) modems, combines a channel shortening time-domain equalizer (TEQ) with one-tap frequency-domain equalizers (FEQs). In a previous paper, the authors proposed a nonlinear bit rate maximizing (BM) TEQ design criterion and they have shown that the resulting BM-TEQ and the closely related BM per-group equalizers (PGEQs) approach the performance of the so-called per-tone equalizer (PTEQ). The PTEQ is an attractive alternative that provides a separate complex-valued equalizer for each active tone. In this paper, the authors show that the BM-TEQ and BM-PGEQ, despite their nonlinear cost criterion, can be designed adaptively, based on a recursive Levenberg-Marquardt algorithm. This adaptive BM-TEQ/BM-PGEQ makes use of the same second-order statistics as the earlier presented recursive least-squares (RLS)-based adaptive PTEQ. A complete range of adaptive BM equalizers then opens up: the RLS-based adaptive PTEQ design is computationally efficient but involves a large number of equalizer taps; the adaptive BM-TEQ has a minimal number of equalizer taps at the expense of a larger design complexity; the adaptive BM-PGEQ has a similar design complexity as the BM-TEQ and an intermediate number of equalizer taps between the BM-TEQ and the PTEQ. These adaptive equalizers allow us to track variations of transmission channel and noise, which are typical of a DSL environment.     

基于MMSE准则的改进型并行迭代ICI消除算法

无线信道的时变性破坏了OFDM系统各子载波间的正交性,造成子载波间功率泄漏,从而产生子载波间干扰(ICI).ICI的产生严重影响了OFDM系统的性能.本文首先从ICI的特性出发,对MMSE准则进行了修正,在此基础上,提出一种改进的并行迭代(PIC)均衡算法消除ICI的影响.Jakes谱瑞利衰落信道上的仿真结果表明,该方...     

OFDM系统在循环前缀不足时的两种高效迭代均衡方法

本文提出两种新的用于循环前缀(CP)不足时正交频分复用(OFDM)系统的迭代均衡方法。首先,我们提出并行迭代均衡(PIE)方法,该方法分别使用时域判决反馈方法和频域并行迭代方法来消除符号间干扰(ISI)和子载频间干扰(ICI)。为了改进PIE的性能,提出基于高斯-塞德尔迭代的串行迭代均衡(SIE)方法。在不增加计算复杂度的情况下,SIE具有比PIE更快的收敛速度。仿真结果表明,新方法可以在几次迭代后得到接近CP足够情况下的系统性能,PIE的性能与传统的迭代干扰消除方法相同,而SIE则提供好得多的收敛性能。     

An equalization technique for orthogonal frequency-divisionmultiplexing systems in time-variant multipath channels

A loss of subchannel orthogonality due to time-variant multipath channels in orthogonal frequency division multiplexing (OFDM) systems leads to interchannel interference (ICI) which increases the error floor in proportion to the Doppler frequency. A simple frequency-domain equalization technique which can compensate for the effect of ICI in a multipath fading channel is proposed. In this technique, the equalization of the received OFDM signal is achieved by using the assumption that the channel impulse response (CIR) varies in a linear fashion during a block period and by compensating for the ICI terms that significantly affect the bit-error rate (BER) performance     

Simple equalization of time-varying channels for OFDM

We present a block minimum mean-squared error (MMSE) equalizer for orthogonal frequency-division multiplexing (OFDM) systems over time-varying multipath channels. The equalization algorithm exploits the band structure of the frequency-domain channel matrix by means of a band LDL/sup H/ factorization. The complexity of the proposed algorithm is linear in the number of subcarriers and turns out to be smaller with respect to a serial MMSE equalizer characterized by a similar performance.     

Channel estimation for MC-CDMA uplink transmissions with combined equalization

Combined equalization has recently been proposed to enhance the error rate performance of conventional multicarrier code-division multiple-access (MC-CDMA) systems. This technique applies pre-equalization at the transmitter in conjunction with post-equalization at the receiver, thereby splitting the overall equalization process into two separate parts. In this way, efficient power allocation over the available subcarriers is possible at the transmitter, while leaving the interference cancellation task at the receiver. In this paper, we consider the uplink of an MC-CDMA system employing combined equalization. As the users transmit from different locations, the uplink signals arrive at the base station after passing through different multipath channels and the goal is to estimate the pre-equalized channel frequency response of each user. This is pursued following two different approaches. The first operates in the frequency-domain and treats the channel gains over adjacent subcarriers as independent unknown parameters. The second operates in the time-domain and achieves better performance by reducing the number of unknown parameters. Both schemes are based on maximum-likelihood reasoning and require knowledge of the transmitted symbols. Numerical examples are given to highlight the effectiveness of the proposed methods.     

Modified Frequency-Domain Equalization for Channel Shortening in Reduced-CP OFDMA Systems

In orthogonal frequency-division multiple access (OFDMA) systems, the cyclic prefix (CP) length needs to be no less than the longest delay spread of the channels of many users, reducing bandwidth efficiency more significantly than in single-user orthogonal frequency division multiplexing systems. In this paper, we address OFDMA downlink data transmission when a short CP is used to mitigate the inefficient bandwidth usage. Previous time-domain equalizers (TEQs) can be used to shorten the channel; however, they tend to increase noise by introducing spectral nulls. A previous work on per-tone equalization (PTEQ) structure involves a multitap frequency-domain equalizer (FEQ) for each tone, and shows better performance than TEQ-based receiver structure. We propose a novel receiver structure with only one-tap FEQ for OFDMA systems with a reduced CP, exploiting the unused subchannels for a user. We formulate an optimization problem to set the FEQ coefficients at the unused subchannels such that the channel is shortened (approximation is involved) and noise is not enhanced at the used subchannels. With the aid of computer simulations, it is demonstrated that the proposed equalization method is superior to the conventional TEQ-based receivers, and is comparable to the previous PTEQ-based receiver in terms of the achievable SNR, error performance, and bandwidth efficiency. Although the throughput curve versus synchronization delay of the PTEQ is smoother than that of the proposed receiver, the proposed method shows proper throughput over a wider range of the delay values than PTEQ receiver when the system parameters are set so that the complexities are comparable.