Training sequence versus cyclic prefix-a new look on single carriercommunication

Orthogonal frequency-division multiplexing (OFDM), with the help of a cyclic prefix, enables low complexity frequency domain equalization, but suffers from a high crest factor. Single carrier with cyclic prefix (SC-CP) has the same advantage with similar performance, but with a lower crest factor and enhanced robustness to phase noise. The cyclic prefix is overhead, so we put more information in it by implementing this cyclic prefix as a training sequence (TS). This new training aided frequency domain equalized single carrier (TASC) scheme offers us additional known symbols and enables better synchronization and (potentially) channel estimation, with the same performance as SC-CP     

SC-CP的迫零均衡和最小均方误差均衡性能比较

简要介绍了基于循环前缀的单载波调制,通过仿真比较了在基于循环前缀的单载波调制下迫零均衡和最小均方误差均衡的性能。结果表明在非理想信道及存在噪声的情况下,最小均方误差均衡的性能优于迫零均衡的性能。     

Multicarrier modulation with blind detection capability using cosine modulated filter banks

The cosine modulated filter bank (CMFB) is introduced as a multicarrier modulation (MCM) technique for wideband data transmission over wireless channels. Under the name discrete wavelet multitone modulation, CMFB has been considered for data transmission over digital subscriber lines. We propose a new receiver structure that is different from those proposed previously. The new structure simplifies the task of channel equalization, by reducing the number of equalizer parameters significantly. We also propose a novel blind equalization algorithm that fits very nicely in the proposed structure. Moreover, we discuss the bandwidth efficiency of the proposed CMFB-MCM system and show that it is superior to the conventional (single carrier) quadrature amplitude modulation (QAM) and orthogonal frequency-division multiplexing (OFDM). The CMFB is found to be a signal processing block that stacks a number of vestigial sideband modulated signals in a number of overlapping subchannels in the most efficient way. The proposed CMFB-MCM is also compared to OFDM with respect to bit-error rate performance. Under the conditions that the channel impulse response duration remains less than the length of cyclic prefix, OFDM is found marginally superior to CMFB-MCM. However, OFDM degrades very fast when the channel impulse response duration exceeds the length of the cyclic prefix. CMFB-MCM, on the other hand, is found less sensitive to variations in channel impulse response duration.     

On the comparison between OFDM and single carrier modulation with aDFE using a frequency-domain feedforward filter

Most comparisons between single carrier and multicarrier modulations assume frequency-domain linear equalization of the channel. We propose a new frequency-domain decision feedback equalizer (FD-DFE) for single carrier modulation, which makes use of a data block transmission format similar to that of the orthogonal frequency-division multiplexing with cyclic prefix (OFDM). The scheme is a nonadaptive DFE where the feedforward part is implemented in the frequency domain, while feedback signal is generated by time-domain filtering. Through simulations in a HIPERLAN-2 scenario, we show that FD-DFE yields a capacity very close to that of OFDM. This result is also confirmed by analytical derivations for a particular case. Furthermore, when no channel loading is considered, FD-DFE performs closely to OFDM for the same averaged frame error rate in a coded transmission. Design methods of the FD-DFE are investigated and a reduced complexity technique is developed, with the result that FD-DFE and OFDM have a similar computational complexity in signal processing     

Shifted Known Symbol Padding for Efficient Data Communication in a WLAN Context

To allow for a computationally efficient equalization scheme for the frequency-selective transmission channels encountered in wireless local area network (WLAN) applications, cyclic prefix (CP) block transmission schemes have been proposed, such as single-carrier CP (SC-CP) and multi-carrier CP (MC-CP) transmission, also known as orthogonal frequency division multiplexing (OFDM). In this letter, however, we focus on the known symbol padding (KSP) transmission scheme. In this scheme known padded sequences can be exploited for synchronization as well as for channel estimation. However, to simultaneously allow for low-complexity frequency-domain equalization and accurate channel estimation within the KSP context, a modified KSP scheme is proposed, namely shifted KSP (S-KSP). Comparing different block transmission schemes in the WLAN context, the S-KSP scheme is shown to offer a very good performance.     

无保护间隔的OFDM信道自适应均衡的一种新算法

近年来作为一种特殊的多载波调制方式——正交频分复用(OFDM)已得到越来越多的人的关注.对于传统的OFDM系统来说,如果循环前缀的长度大于信道的时延扩散值,则可以通过简单的频域均衡来解调OFDM信号.可是循环前缀的使用却降低了系统的传输效率,如果能压缩甚至去掉循环前缀,而保持系统性能不变,则是很有意义的,为此本文给出了一种新的均衡结构,利用循环迭代手段以减少甚至去掉循环前缀,最后通过计算机模拟,证实了这种结构的有效性.     

时域均衡在OFDM水声通信系统中的应用

为了对抗水声信道时延扩展大于循环前缀长度时引起的码间串扰问题,在基本的OFDM水声通信系统接收端进行DFT变换前加入相对较短的时域均衡器来限制信道冲激响应的长度。分析了基于MMSE准则的时域均衡算法的实现过程以及算法的复杂程度,对该算法在水声环境下的性能进行了仿真分析,并比较了影响系统性能的因素。结果表明通过加入时域均衡器能够有效对抗信道严重的时间离散性,改善OFDM水声通信系统在循环前缀不足时的系统性能。     

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.     

Efficient ISI cancellation for STBC OFDM systems using successive interference cancellation

In this letter, we propose an efficient detection scheme for space-time block coded (STBC) orthogonal frequency-division multiplexing (OFDM) with insufficient cyclic prefix (CP). The proposed scheme employs successive interference cancellation (SIC) and cyclic prefix reconstruction (CPR) concepts. Simulation results present that the proposed scheme outperforms the conventional scheme for STBC OFDM systems.     

Semi-Blind Time-Domain Equalization for MIMO-OFDM Systems

In this paper, a semi-blind time-domain equalization technique is proposed for general multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. The received OFDM symbols are shifted by more than or equal to the cyclic prefix (CP) length, and a blind equalizer is designed to completely suppress both intercarrier interference (ICI) and intersymbol interference (ISI) using second-order statistics of the shifted received OFDM symbols. Only a one-tap equalizer is needed to detect the time-domain signals from the blind equalizer output, and one pilot OFDM symbol is utilized to estimate the required channel state information for the design of the one-tap equalizer. The technique is applicable irrespective of whether the CP length is longer than, equal to, or shorter than the channel length. Computer simulations show that the proposed technique outperforms the existing techniques, and it is robust against the number of shifts in excess of the CP length.     

BER minimized OFDM systems with channel independent precoders

We consider the minimization of uncoded bit error rate (BER) for the orthogonal frequency division multiplexing (OFDM) system with an orthogonal precoder. We analyze the BER performance of precoded OFDM systems with zero forcing and minimum mean squared error (MMSE) receivers. In the case of MMSE receivers, we show that for quadrature phase shift keying (QPSK), there exists a class of optimal precoders that are channel independent. Examples of this class include the discrete Fourier transform (DFT) matrix and the Hadamard matrix. When the precoder is the DFT matrix, the resulting optimal transceiver becomes the single carrier system with cyclic prefix (SC-CP) system. We also show that the worst solution corresponds to the conventional OFDM system; the conventional OFDM system has the largest BER. In the case of zero forcing receivers, the design of optimal transceiver depends on the signal-to-noise ratio (SNR). For higher SNR, solutions of optimal precoders are the same as those of MMSE receivers.     

Equalization methods in OFDM and FMT systems for broadband wireless communications

Multicarrier systems are adopted in several standards for their ability to achieve optimal performance in very dispersive channels. In particular, orthogonal-frequency division multiplexing (OFDM) and filtered multitone (FMT) systems are two examples where the modulation filter has an ideal rectangular amplitude characteristic in time and frequency domains, respectively. In this letter, we propose new equalization schemes for FMT and compare their performances with OFDM. In general, FMT has a greater spectral efficiency than OFDM, due to the absence of the cyclic prefix and a reduced number of virtual carriers. However, it exhibits a higher distortion per subchannel, due to the imperfect equalization of the transmit filters. As a performance comparison, we considered both the achievable bit rate (ABR) and the bit error rate (BER) in a multipath Rayleigh fading channel. We note that while ABR gives a theoretical bound on the system bit rate, assuming the knowledge of the channel at the transmit side, the BER refers to an uncoiled system with a fixed modulation. Although FMT requires a fixed structure with a higher computational complexity than OFDM, it turns out that FMT, even with the simplest one tap per subchannel adaptive equalizer, yields a better performance than OFDM, both in terms of ABR and BER. Hence, FMT can be a valid alternative to OFDM for broadband wireless applications, also.     

发射分集OFDM系统中子载波频域均衡接收机设计

针对发射分集下的OFDM系统,提出了一种子载波频域均衡接收机设计方法。在保持子载波数恒定的条件下减少循环前缀的长度,并推导出最优分集合并系数。仿真结果表明,在发射分集条件下,本文提出的子载波频域均衡器有效地抑制了OFDM系统中由于循环前缀小于信道最大时延扩展所造成干扰和各个信道信号之间的互干扰,获得了较好的系统性能。     

Turbo均衡在Non-CP SC-FDE系统中的应用

针对无循环前缀的单载波频域均衡(Non-CP SC-FDE)系统中的符号间干扰(ISI),提出了一种Turbo均衡与循环重构联合迭代算法。通过循环重构技术消除ISI,并采用频域均衡频域判决反馈(FDE-FDDF)方式,将Turbo均衡算法与循环重构算法结合在一起进行迭代。仿真结果表明,Non-CP SC-FDE系统使用该算法能实现与传统有CP系统近似的误码性能,在大幅提高传输效率的同时能够有效消除多径干扰。     

一种新的OFDM系统载波频率偏移估计和跟踪方案

针对载波偏移使OFDM系统出现严重的子载波干扰和性能的下降,该文提出一种OFDM频偏估计和跟踪方案,载频捕获阶段频偏估计采用时域内插入等值导频的方法,载频跟踪阶段不需要导频,而是利用循环前缀来估计频率偏移并进行校正。仿真结果证实,该方案中导频辅助的频率偏移估计和载频跟踪不仅估计范围大,而且估计值准确,频偏校正后系统的性能能达到信道理想估计条件下的误比特率。     

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。     

Receiver Design for Single-Carrier Block Transmission Over Doubly Selective Channels

Single-carrier block transmission is an alternative scheme to orthogonal frequency-division multiplexing (OFDM) for wireless broadband communications. In this paper, a receiver is designed for single-carrier block transmission with cyclic prefix for mobile broadband communications. As the wireless transmission is over doubly selective channels, a basis expansion model is used to capture both the time- and frequency-selectivity of the channel and is parameterized for the receiver design. The receiver estimates the channel model coefficients in the time domain and uses these coefficients for equalization in the frequency domain. The channel estimation is assisted by time-domain pilot insertion. The structure of the frequency-domain channel matrix is exploited and a linear minimum mean-square error equalizer is used for the equalization. When the basis expansion model well matches the physical channel, simulation results show superior receiving performance of the proposed system compared with the OFDM system with a similar complexity.     

Performance analysis of WPM‐based transmission with equalization‐aware bit loading

Wavelet packet modulation (WPM) is a multicarrier modulation (MCM) technique that has emerged as a potential alternative to the widely used orthogonal frequency‐division multiplexing (OFDM) method. Because WPM has overlapped symbols, equalization cannot rely on the use of the cyclic prefix (CP), which is used in OFDM. This study applies linear minimum mean‐square error (MMSE) equalization in the time domain instead of in the frequency domain to achieve low computational complexity. With a modest equalizer filter length, the imperfection of MMSE equalization results in subcarrier attenuation and noise amplification, which are considered in the development of a bit‐loading algorithm. Analytical expressions for the bit error rate (BER) performance are derived and validated using simulation results. A performance evaluation is carried out in different test scenarios as per Recommendation ITU‐R M.1225. Numerical results show that WPM with equalization‐aware bit loading outperforms OFDM with bit loading. Because previous comparisons between WPM and OFDM did not include bit loading, the results obtained provide additional evidence of the benefits of WPM over OFDM.     

Iterative Estimation and Equalization for SCCP Over Doubly Selective Channels

In time varying channels, symbol recovery for single carrier cyclic prefix (SCCP) systems becomes complicated, because the orthogonality of channel frequency response (CFR) matrix is destroyed. In response, we propose a block turbo equalization algorithm in the time domain for SCCP to cope with channel time variations. In particular, the band structure of the channel time response (CTR) matrix is exploited to reduce the computational complexity of matrix inversion. In order to use this equalization scheme, accurate channel state information (CSI) must be available. Accordingly, we present a doubly selective channel estimation method for SCCP block transmissions with the aid of a Karhunen-Loeve basis expansion model (KL-BEM). In this method, the channel estimates are firstly obtained by using the cyclic prefix (CP) of each block, and then further refined by employing an expectation maximization (EM) based iterative algorithm. Combining the iterative estimator with the proposed equalizer naturally results in a doubly iterative receiver, the performance of which is shown to come close to the performance with perfect CSI.     

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.