TURBO EQUALIZATION WITH JOINTLY GAUSSIAN EQUALIZER

A Jointly Gaussian (JG) equalizer is derived for turbo equalization based on an augmented real matrix representation of channel model and a Gaussian approximation of the received symbol sequence. Using matrix inversion lemma and Cholesky decomposition, a lowcomplexity implementation of JG equalizer is also presented. The simulation results and complexity comparison confirm that turbo equalization with JG equalizer has a better performance and a lower complexity than the existing turbo equalization with linear minimum mean squared error equalizer.     

DFT-S-OFDM系统发射端IQ失衡的广义迭代均衡器

该文研究了离散傅里叶变换扩展正交频分复用 (DFT-S-OFDM) 系统的零中频(ZIF)射频(RF)前端非理想特性导致同相与正交分路失衡(IQI)干扰时,改进的频域迭代均衡技术。利用广义正交原理和迭代均衡原理,本文推导了频域广义线性最小均方误差(WLMMSE)迭代均衡器,并通过矩阵变换降低其复杂度。仿真结果表明,在DFT-S-OFDM系统发射端IQ失衡的情况下,所提出的迭代均衡算法性能显著优于常规迭代均衡算法,而复杂度只有少量提高。     

Reduced complexity in-phase/quadrature-phase M-QAM turbo equalization using iterative channel estimation

A reduced complexity trellis-based turbo equalizer known as the in-phase (I)/quadrature-phase (Q) turbo equalizer (TEQ-IQ) invoking iterative channel impulse response (CIR) estimation is proposed. The underlying principle of TEQ-IQ is based on equalizing the I and Q component of the transmitted signal independently. This requires the equalization of a reduced set of separate I and Q signal components in comparison to all of the possible I/Q phasor combinations considered by the conventional trellis-based equalizer. It was observed that the TEQ-IQ operating in conjunction with iterative CIR estimation was capable of achieving the same performance as the full-complexity conventional turbo equalizer (TEQ-CT) benefiting from perfect CIR information for both 4- and 16-quadrature amplitude modulation (QAM) transmissions, while attaining a complexity reduction factor of 1.1 and 12.2, respectively. For 64-QAM, the TEQ-CT receiver was too complex to be investigated by simulation. However, by assuming that only two turbo equalization iterations were required, which is the lowest possible number of iterations, the complexity of the TEQ-IQ was estimated to be a factor of 51.5 lower than that of the TEQ-CT. Furthermore, at BER = 10/sup -3/ the performance of the TEQ-IQ 64-QAM receiver using iterative CIR estimation was only 1.5 dB away from the associated decoding performance curve of the nondispersive Gaussian channel.     

Turbo equalization via constrained-delay APP estimation with decision feedback

We consider turbo equalization for intersymbol interference (ISI) channels, wherein soft symbol decisions generated by the channel detector are iteratively exchanged with the outer error-correction decoder based on the turbo principle. Our work is based on low-complexity suboptimal soft-output channel detection using a constrained-delay (CD) a posteriori probability (APP) algorithm. Central to the proposed idea is the incorporation of effective decision-feedback schemes, which significantly reduce complexity while providing immunity against error propagation that typically plagues decision-feedback schemes. We observe that the effect of decision feedback is quite different on turbo equalization versus traditional, hard-decision-generating and noniterative equalization. In particular, we demonstrate that when the feedback scheme applied is inadequate for the given equalizer parameters and ISI condition, the extrinsic information generated by the equalizer becomes distinctly non-Gaussian, and the quality of soft information, as monitored by the trajectory of mutual information, fails to improve in the iterative process. We identify parameters of feedback-based CD-APP schemes that offer favorable complexity/performance tradeoffs, compared with existing turbo-equalization techniques.     

Reduced-Complexity Turbo Equalization for Turbo Coded MIMO/OFDM Systems

1IntroductionTowards wireless systems Beyondthe3G(B3G),it isa great challenge for the physical layer to support high-speed transmissioninthe mobile environment to providecomfortable Internet access.Multiple Input MultipleOutput(MI MO)technique is effectiv…     

The soft-feedback equalizer for turbo equalization of highly dispersive channels

The complexity of a turbo equalizer based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is manageable only for mildly dispersive channels having a small amount of memory. To enable turbo equalization of highly dispersive channels, we propose the soft-feedback equalizer(SFE). The SFE combines linear equalization and soft intersymbol-interference cancellation. Its coefficients are chosen to minimize the mean-squared error(MSE) between the equalizer output and the transmitted sequence, under a Gaussian approximation to the a priori information and the SFE output. The resulting complexity grows only linearly with the number of coefficients, as opposed to the quadratic complexity of previously reported minimum-MSE structures. We will see that an SFE-based turbo equalizer consistently outperforms another structure of similar complexity, and can outperform a BCJR-based scheme when complexity is taken into account.     

SC-FDE系统的一种新型判决反馈均衡器

针对单载波频域均衡系统MMSE均衡器存在残留码间干扰的缺点,提出MMSE-RISIC判决反馈均衡器消除残留码间干扰.MMSE-RISIC均衡器采用传统MMSE均衡后的判决数据,对残留码间干扰进行估计并消除.残留码间干扰的估计主要采用FFT和IFFT运算,与其他方法相比计算量较小.对该均衡器在不同信道下进行了计算机仿真,结果表明,在频率选择性衰落信道条件下,系统性能有了较为明显的提高.     

Low-Complexity Block Turbo Equalization for OFDM Systems in Time-Varying Channels

We propose low-complexity block turbo equalizers for orthogonal frequency-division multiplexing (OFDM) systems in time-varying channels. The presented work is based on a soft minimum mean-squared error (MMSE) block linear equalizer (BLE) that exploits the banded structure of the frequency-domain channel matrix, as well as a receiver window that enforces this banded structure. This equalization approach allows us to implement the proposed designs with a complexity that is only linear in the number of subcarriers. Three block turbo equalizers are discussed: two are based on a biased MMSE criterion, while the third is based on the unbiased MMSE criterion. Simulation results show that the proposed iterative MMSE BLE achieves a better bit error rate (BER) performance than a previously proposed iterative MMSE serial linear equalizer (SLE). The proposed equalization algorithms are also tested in the presence of channel estimation errors.      

Turbo equalization: principles and new results

We study the turbo equalization approach to coded data transmission over channels with intersymbol interference. In the original system invented by Douillard et al. (1995), the data are protected by a convolutional code and the receiver consists of two trellis-based detectors, one for the channel (the equalizer) and one for the code (the decoder). It has been shown that iterating equalization and decoding tasks can yield tremendous improvements in bit error rate. We introduce new approaches to combining equalization based on linear filtering, with decoding.. Through simulation and analytical results, we show that the performance of the new approaches is similar to the trellis-based receiver, while providing large savings in computational complexity. Moreover, this paper provides an overview of the design alternatives for turbo equalization with given system parameters, such as the channel response or the signal-to-noise ratio     

A Novel Interpolation Equalization Technique for Multicarrier Modulation/Demodulation Systems

This paper presents a novel multitap interpolation equalization technique for filter bank-based multicarrier modulation/demodulation systems. The proposed technique is based on the equalization of the channel fractional delay in each subchannel in time synchronization with the constituent receiver side decimator. The proposed synchronization is achieved by combining a subset of the polyphase components of the analysis filter output signal after having passed through a bank of interpolation equalizers. The resulting multitap interpolation equalization permits a trade-off between various equalization parameters, such as the number of used polyphase components, the length of the equalizer, and the interchannel interference terms, making it possible to achieve a high signal-to-noise ratio (SNR) involving moderate equalization cost or a moderate SNR involving very low equalization cost. Simulation results for the standard carrier serving area loop show that the proposed equalization technique gives rise to 15 dB improvement in SNR compared to the output combiner equalization technique and can achieve an SNR close to the matched-filter bound for the channel by employing a reasonable equalizer length. Compared to the output combiner equalization technique, the proposed equalization technique involves around three times less the storage requirement at the same computational cost or around three times less the computational cost at the same storage requirement for equalizer training. Two suboptimal solutions are also proposed to simplify the equalizer training at only a minor loss in SNR.     

Soft input soft output Kalman equalizer for MIMO frequency selective fading channels

We consider the Kalman filter for equalization of a multiple-input multiple-output (MIMO), frequency selective, quasi-static fading channel. More specifically, we consider a coded system, where the incoming bit stream is convolutionally encoded, interleaved and then spatially multiplexed across the transmit antennas. Each substream is modulated into M-ary symbols before being transmitted over a frequency selective channel. At the receiver, we propose to use the Kalman filter as a low complexity MIMO equalizer, as opposed to the trellis based maximum a-posteriori (MAP) equalizer whose computational complexity grows exponentially with the channel memory, the number of transmit antennas and the spectral efficiency (bits/s/Hz) of the system. We modify the structure of the Kalman filter and enable it to process the a-priori (soft) information provided by the channel decoder, thereby allowing us to perform iterative (turbo) equalization on the received sequence. The iterative equalizer structure is designed for general M-ary constellations. We also propose a low complexity version of the above algorithm whose performance is comparable to its full complexity counterpart, but which achieves a significant complexity reduction. We demonstrate via simulations that for higher order constellations, when sufficient number of receive antennas are available (e.g. for a 2 transmitter, 3 receiver system, QPSK), the performance of the proposed algorithms after 4 iterations is within 1.5 dB of the non-iterative MAP algorithm with close to an order of magnitude complexity reduction. By objectively quantifying the complexity of all the considered algorithms we show that the complexity reduction for the proposed schemes becomes increasingly significant for practical systems with moderate to large constellation sizes and a large number of transmit antennas     

Turbo equalization with sequential sequence estimation overmultipath fading channels

We investigate the performance of a turbo equalization scheme over frequency-selective fading channels, where a soft-output sequential algorithm is employed as the estimation algorithm. The advantage of this scheme comes from the low computational complexity of the sequential algorithm, which is only linearly dependent on the channel memory length. Simulation results of an 8-PSK trellis-coded modulation (TCM) system show that the performance of this scheme suffers approximately 2-dB loss compared with that of the turbo max-log maximum a posteriori (MAP) probability equalizer after 5 iterations     

Minimum mean squared error equalization using a priori information

A number of important advances have been made in the area of joint equalization and decoding of data transmitted over intersymbol interference (ISI) channels. Turbo equalization is an iterative approach to this problem, in which a maximum a posteriori probability (MAP) equalizer and a MAP decoder exchange soft information in the form of prior probabilities over the transmitted symbols. A number of reduced-complexity methods for turbo equalization have been introduced in which MAP equalization is replaced with suboptimal, low-complexity approaches. We explore a number of low-complexity soft-input/soft-output (SISO) equalization algorithms based on the minimum mean square error (MMSE) criterion. This includes the extension of existing approaches to general signal constellations and the derivation of a novel approach requiring less complexity than the MMSE-optimal solution. All approaches are qualitatively analyzed by observing the mean-square error averaged over a sequence of equalized data. We show that for the turbo equalization application, the MMSE-based SISO equalizers perform well compared with a MAP equalizer while providing a tremendous complexity reduction     

Mitigating multiple access interference and intersymbol interference in uncoded CDMA systems with chip-level interleaving

The presence of intersymbol interference (ISI), in addition to multiple access interference, severely hampers the performance of a code-division multiple-access (CDMA) communication system. In such a situation, channel coding can be used to obtain better performance, but at the cost of a reduction in rate of flow of information. In this paper, it is shown with the help of simulation results that the chip-interleaved CDMA system effectively combats ISI without requiring additional channel coding. The system differs from the conventional CDMA system in the sense that, the chip sequence resulting from the pseudo noise (PN) sequence modulation is interleaved before transmission. Two receivers are proposed, one based on the turbo equalization method which employs a maximum a posteriori equalizer of exponential complexity and the other based on minimum-mean square error-optimized iterative interference cancellation principles which is of linear complexity. Simulation results are provided which show that error rates close to the no-ISI single-user case can be obtained. The shortcomings of the coded CDMA with turbo detection system in the presence of ISI are also discussed.     

Low complexity LMMSE turbo equalization for combined error control coded and linearly precoded OFDM

The turbo equalization approach is studied for Orthogonal Frequency Division Multiplexing （OFDM） system with combined error control coding and linear precoding. While previous literatures employed linear precodcr of small size for complexity reasons, this paper proposes to use a linear precoder of size larger than or equal to the maximum length of the equivalent discrete-time channel in order to achieve full frequency diversity and reduce complexities of the error control coder/decoder. Also a low complexity Linear Minimum Mean Square Error （LMMSE） turbo equalizer is derived for the receiver. Through simulation and performance analysis, it is shown that the performance of the proposed scheme over frequency selective fading channel reaches the matched filter bound; compared with the same coded OFDM without linear precoding, the proposed scheme shows an Signal-to-Noise Ratio （SNR） improvement of at least 6dB at a bit error rate of 10 6 over a multipath channel with exponential power delay profile. Convergence behavior of the proposed scheme with turbo equalization using various type of linear precoder/transformer, various interleaver size and error control coder of various constraint length is also investigated.     

无人机数据链信道线性Turbo均衡研究

Turbo均衡是一种基于Turbo迭代解码原理的均衡技术,利用的是均衡器与解码器之间信息的迭代使用来达到消除码间干扰的目的。Turbo均衡技术中通常采用基于最大后验概率的最大后验概率(MAP)均衡器,虽然性能较好,但计算量较大,系统延时较长。为降低延时,保证均衡性能,针对无人机遥控遥测数据链信道,设计了一种相对于MAP均衡器计算量较少的线性最小均方误差(MMSE)均衡器,通过仿真验证了这种线性Turbo均衡的性能,分析了其应用的可行性。     

A new class of iterative equalizers for space-time BICM over MIMO block fading multipath AWGN channel

This paper addresses the issue of advanced equalization methods for space-time communications over multiple-input multiple-output block fading channel with intersymbol interference. Instead of resorting to conventional multiuser detection techniques (based on the straightforward analogy between antennas and users), we adopt a different point of view, and separate time equalization from space equalization, thus introducing a higher degree of freedom in the overall space-time equalizer design. Time-domain equalization relies on minimum mean-square error criterion and operates on multidimensional modulation symbols, whose individual components can be detected in accordance with another criterion. In particular, when the optimum maximum a posteriori criterion is chosen, substantial performance gains over conventional space-time turbo equalization have been observed for different transmission scenarios, at the price of an increased, albeit manageable, computational complexity.     

Low-complexity MMSE turbo equalization: a possible solution for EDGE

This paper deals with a low complexity receiver scheme where equalization and channel decoding are jointly optimized in an iterative process. We derive the theoretical transfer function of the infinite length linear minimum mean square error (MMSE) equalizer with a priori information. A practical implementation is exposed which employs the fast Fourier transform (FFT) to compute the equalizer coefficients, resulting in a low-complexity receiver structure. The performance of the proposed scheme is investigated for the enhanced general packet radio service (EGPRS) radio link. Simulation results show that significant power gains may be achieved with only a few (3-4) iterations. These results demonstrate that MMSE turbo equalization is an attractive candidate for single-carrier broadband wireless transmissions in long delay-spread environments.     

Doubly Iterative Equalization of Continuous-Phase Modulation

In this paper, a doubly iterative receiver is proposed for joint turbo equalization, demodulation, and decoding of coded binary continuous-phase modulation (CPM) in multipath fading channels. The proposed receiver consists of three soft-input soft-output (SISO) blocks: a front-end soft-information-aided minimum mean square error (MMSE) equalizer followed by a CPM demodulator and a back-end channel decoder. The MMSE equalizer, combined with an a priori soft-interference canceler (SIC) and an a posteriori probability mapper, forms a SISO processor suitable for iterative processing that considers discrete-time CPM symbols which belong to a finite alphabet. The SISO CPM demodulator and the SISO channel decoder are both implemented by the a posteriori probability algorithm. The proposed doubly iterative receiver has a central demodulator coupled with both the front-end equalizer and the back-end channel decoder. A few back-end demodulation/decoding iterations are performed for each equalization iteration so as to improve the a priori information for the equalizer. As presented in the extrinsic information transfer (EXIT) chart analysis and simulation results for different multipath fading channels, this provides not only faster convergence to low bit error rates, but also lower computational complexity.