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.     

用滤波器组构成的传送多路复用器结构实现MMSE盲信道均衡

冗余滤波器组构成的传送多路复用器可以用来对FIR信道进行估计和均衡.本文提出一种在FIR滤波器组框架结构下,首先利用信号的相关矩阵对信道进行估计,然后在此基础上用MMSE准则下设计的FIR均衡器对数据进行均衡的盲算法.该均衡算法的性能要明显好于基于ZF准则的方法,并且在消除ISI的同时可以抑制噪声的影响,从而使系统的输出信噪比达到最优,而增加的复杂度很有限.文中最后在两种典型信道下对所提出的盲信道均衡算法进行了仿真,结果验证了上述性能.     

Blind channel identification and equalization using periodicmodulation precoders: performance analysis

The paper deals with blind identification and equalization of communication channels within the so-called modulation induced cyclostationarity (MIC) framework, where the input symbol stream is modulated by a P periodic precoder with the purpose of inducing cyclostationarity in the transmit sequence. By exploiting the cyclostationarity induced by the periodic precoder, a subspace-based channel identification algorithm that is resilient to the location of channel zeros, channel order overestimation errors, and color of additive stationary noise, is developed. The asymptotic performance of the subspace-based identification approach is analyzed and compared with the asymptotic lower bound provided by the nonlinear cyclic correlation matching approach. Criteria for optimally designing the periodic precoder are also presented. The performance of MMSE-FIR and MMSE-DFE equalizers is quantified for the proposed cyclostationarity-induced framework in terms of the MMSE. Although cyclostationarity-inducing transmitters present several advantages relative to their stationary counterparts from a channel estimation viewpoint, it is shown that from an equalization viewpoint, MIC-based systems exhibit a slightly increased MMSE/BER when compared with the stationary case     

Channel equalization for block transmission systems

In a block transmission system the information symbols are arranged in the form of blocks separated by known symbols. Such a system is suitable for communication over time-dispersive channels subject to fast time-variations, e,g., the HF channel. The known reliable receiver for this system is the nonlinear data-directed estimator (NDDE). This paper presents appropriate equalization methods for this system. A nonstationary innovations representation based on Cholesky factorization is used in order to define a noise whitener and a maximum-likelihood block detector. Also block linear equalizers and block decision-feedback equalizers are derived. For each type we give the zero-forcing and the minimum-mean-squared-error versions. Performance evaluations and comparisons are given. We show that they perform better than conventional equalizers. As compared to the NDDE, the derived block decision-feedback equalizers perform better and are much less complex. Whereas the NDDE uses the Levinson algorithm to solve M/2 Toeplitz systems of decreasing order (where M is the number of symbols per block), the derived equalizers need to process only one Toeplitz system. Moreover, the Schur algorithm, proposed for Cholesky factorization allows us to further reduce the complexity     

Minimum BER power loading for OFDM in fading channel

A novel approach to power loading for orthogonal frequency-division multiplexing (OFDM) systems is proposed. The corresponding algorithm minimizes the aggregate bit-error rate, but appears to be rather complicated. Consequently, a much simpler, quasi-optimal loading algorithm is developed. The performance of various power loading strategies known in the literature are compared with the proposed quasi-optimal algorithm in the Rayleigh frequency-selective fading channel.     

Deterministic linear prediction methods for blind channel estimation based on dual concept of zero-forcing equalization

This paper investigates a class of second-order blind channel estimation algorithms based on deterministic linear prediction, which includes double-sided as well as forward and backward single-sided, for single input multiple output (SIMO) finite impulse response (FIR) channels. By introducing the dual problem of well-known zero-forcing equalization concept, we first derive a double-sided deterministic linear prediction (D-DLP) algorithm that has, good channel estimation performance with the knowledge of exact channel order. By further exploiting the interference subspace cancellation technique and the triangular block-Toeplitz structure of a portion of the channel filtering matrix (upper-left or lower-right part), we obtain the forward and backward single-sided deterministic linear prediction (FS-DLP and BS-DLP) algorithms that can work in the absence of knowledge of channel order with a cost of relatively poor channel estimate. Moreover, a channel order estimation method is also studied based on results from both FS-DLP and BS-DLP. Simulation examples are finally presented to demonstrate the potential of the proposed methods.     

Approximate Minimum BER Power Allocation for MIMO Spatial Multiplexing Systems

Precoding for multiple-input multiple-output (MIMO) spatial multiplexing generally requires high feedback overhead and/or high-complexity processing. Simultaneous reduction in transmitter complexity and feedback overhead is proposed by imposing a diagonal structural constraint to precoding, i.e., power allocation. Minimum bit-error rate (MBER) is employed as the optimization criterion, and an approximate MBER (AMBER) power-allocation algorithm is proposed for a variety of receivers, including zero-forcing (ZF), successive interference cancellation (SIC), and ordered SIC (OSIC). While previously proposed precoding schemes either require ZF equalization for MBER, or use a minimum mean-squared error (MMSE) criterion, we provide a unified MBER solution to power allocation for ZF, SIC, and OSIC receiver structures. Improved error-rate performance is shown both analytically and by simulation. Simulation results also indicate that SIC and OSIC with AMBER power allocation offer superior performance over previously proposed MBER precoding with ZF equalization, as well as over MMSE precoding/decoding. Performance under noisy channels and power feedback is analyzed. A modified AMBER algorithm that mitigates error propagation in interference cancellation is developed. Compared with existing precoding methods, the proposed schemes significantly reduce both transmit processing complexity and feedback overhead, and improve error-rate performance     

Joint equalization and decoding for QAM block transmissions

A method of joint equalization and decoding for block transmission with coding across blocks is presented. It is well suited for bandwidth efficient QAM transmission using large transmit symbol alphabets, whereby the blocking structure can be arbitrary in principle. The method consists in multiple iterations of equalization and decoding, whereby information is exchanged back and forth between the decoder and the equalizer. The equalizer is based on Cholesky factorization of the equivalent discrete-time channel matrix (Eur. Trans. Telecommun 10 (1999) 351; Grundlagen der Kommunikationstechnik, Springer, Berlin, 2004). The convergence behavior of the iterative equalization and decoding method is analyzed by means of an upper bound on the extrinsic information transfer. It is shown that the method has improved bit error performance versus separate equalization and decoding without decoder feedback and, thus, yields superior power efficiency.     

Redundant filterbank precoders and equalizers. II. Blind channelestimation, synchronization, and direct equalization

For pt.I see ibid., vol.47, no.7, p.1988-2006 (1999). Transmitter redundancy introduced using finite impulse response (FIR) filterbank precoders offers a unifying framework for single- and multiuser transmissions. With minimal rate reduction, FIR filterbank transmitters with trailing zeros allow for perfect (in the absence of noise) equalization of FIR channels with FIR zero-forcing equalizer filterbanks, irrespective of the input color and the channel zero locations. Exploiting this simple form of redundancy, blind channel estimators, block synchronizers, and direct self-recovering equalizing filterbanks are derived in this paper. The resulting algorithms are computationally simple, require small data sizes, can be implemented online, and remain consistent (after appropriate modifications), even at low SNR colored noise. Simulations illustrate applications to blind equalization of downlink CDMA transmissions, multicarrier modulations through channels with deep fades, and superior performance relative to CMA and existing output diversity techniques relying on multiple antennas and fractional sampling     

Blind and semi-blind equalization for generalized space-time block codes

This paper presents a general framework for space-time codes (STCs) that encompasses a number of previously proposed STC schemes as special cases. The STCs considered are block codes that employ arbitrary redundant linear precoding of a given data sequence together with embedded training symbols, if any. The redundancy introduced by the linear precoding imposes structure on the received data that under certain conditions can be exploited for blind or semi-blind estimation of the transmitted sequence, a linear receiver that recovers the sequence, or both simultaneously. Algorithms based on this observation are developed for the single-user flat-fading case and then extended to handle multiple users, frequency-selective fading, as well as situations where the channel is rank deficient, or there are fewer receive than transmit antennas.     

Minimum BER Block-Based Precoder Design for Zero-Forcing Equalization: An Oblique Projection Framework

This work devises a minimum bit error rate (BER) block-based precoder used in block transmission systems with the proposed cascaded zero-forcing (ZF) equalizer. The study framework is developed as follows. For a block-based precoder, a received signal model is formulated for the two redundancy schemes, viz., trailing-zeros (TZ) and cyclic-prefix (CP). By exploiting the property of oblique projection, a cascaded equalizer for block transmission systems is proposed and implemented with a scheme, in which the inter-block interference (IBI) is completely eliminated by the oblique projection and followed by a matrix degree-of-freedom for inter-symbol interference (ISI) equalization. With the available channel state information at the transmitter side, the matrix for ISI equalization of the cascaded equalizer is utilized to design an optimum block-based precoder, such that the BER is minimized, subject to the ISI-free and the transmission power constraints. Accordingly, the cascaded equalizer with the ISI-free constraint yields a cascaded ZF equalizer. Theoretical derivations and simulation results confirm that the proposed framework not only retains identical BER performance to previous works for cases with sufficient redundancy, but also allows their results to be extended to the cases of insufficient redundancy.     

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     

Low complexity soft-input soft-output block decision feedback equalization

A low complexity soft-input soft-output (SISO) block decision feedback equalizer (BDFE) is presented for turbo equalization. The proposed method employs a sub-optimum sequence-based detection, where the soft-output of the equalizer is calculated by evaluating an approximation of the sequence-based a posteriori probability (APP) of the data symbol. The sequence-based APP approximation is enabled by the adoption of both soft a priori information and soft decision feedback, and it leads to better performance and faster convergence compared to symbol-based detection methods as used by most other low complexity equalizers. The performance and convergence property of the proposed algorithm is analyzed by using extrinsic information transfer (EXIT) chart. Both analytical and simulation results show that the new equalizer can achieve a performance similar to that of trellis-based equalization algorithms, with a complexity similar to linear SISO minimum mean square error equalizers.     

BER improvement of PRCPM in mobile radio channels withdiscriminator detection using decision feedback equalization

The authors investigate the bit error rate (BER) improvement of partial-response continuous-phase modulation (PRCPM) signals in mobile radio channels, when decision feedback equalization (DFE) to cancel the effect of intersymbol interference (ISI) of one adjacent bit is added to the limiter discriminator. A closed-form expression for the average probability of error as a function of the Doppler shift is derived for discriminator detection with decision feedback. Numerical results are presented to compare the BER performance of discriminator detection with and without feedback equalization     

BER analysis of MPSK space-time block codes with differential detection

Closed-form expressions of the bit error rate (BER) are derived for space-time block codes based on Alamouti's (1998) scheme and utilizing M-ary phase shift keying modulation with noncoherent differential encoding/decoding. The analysis is carried out for the flat block-fading Rayleigh channel, and the BER expression is an approximation for high signal to noise ratio. Theoretical results are validated by simulations for BPSK and QPSK modulations.     

Improved space-time processing for X channel using precoders

The article investigates how to send perfect space-time codes with low feedback amount and symbol-by-symbol decoding for X channel using precoders. It is assumed that two users are introduced with two antennas and two receivers. Each user employs a rate-2 space-time block code and follows certain rule when sending codewords. The multi-user interference is eliminated by pre-coding at the transmitter and linear processing at the receiver. Compared with the existing scheme for the same scene, the proposed scheme greatly reduces feedback amount and improves the transmission efficiency, while keeping the same decoding complexity. Simulations demonstrate the validity of the proposed scheme.