Minimum Mean Square Error Channel Estimation Research Articles

Optimal Training Design for Channel Estimation in Decode-and-Forward Relay Networks With Individual and Total Power Constraints

In this paper, we study the channel estimation and the optimal training design for relay networks that operate under the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">decode-and-forward</i> (DF) strategy with the knowledge of the interference covariance. In addition to the total power constraint on all the relays, we introduce individual power constraint for each relay, which reflects the practical scenario where all relays are separated from one another. Considering the individual power constraint for the relay networks is the major difference from that in the traditional point-to-point communication systems where only a total power constraint exists for all colocated antennas. Two types of channel estimation are involved: maximum likelihood (ML) and minimum mean square error (MMSE). For ML channel estimation, the channels are assumed as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deterministic</i> and the optimal training results from an efficient multilevel waterfilling type solution that is derived from the majorization theory. For MMSE channel estimation, however, the second-order statistics of the channels are assumed known and the general optimization problem turns out to be nonconvex. We instead consider three special yet reasonable scenarios. The problem in the first scenario is convex and could be efficiently solved by state-of-the-art optimization tools. Closed-form waterfilling type solutions are found in the remaining two scenarios, of which the first one has an interesting physical interpretation as pouring water into caves.

A Design of Segmented Data Rates for Recurrent Channel Estimation

In a conventional pilot-symbol assisted modulation design, the signals of a short period are composed of the pilot tones and an information symbol block. For improving the accuracy of the channel estimate, some recurrent methods use the detected information symbols as the additional pilots. Working on an orthogonal frequency division multiplexing system, we divide the information symbol block into several sub-blocks and assign them with different data rates. Then the recurrent channel estimations can exploit the potential strength of the new approach, and the averaged data rate can be increased with the minimum mean-square error channel estimator. The simulation results confirm the merit of the proposed approach.

Optimal diversity combining based on linear estimation of rician fading channels

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. The new receiver structure includes the conventional maximal ratio combining receiver as a special case. Exact analytical expressions for the symbol error rates (SERs) of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that, if an optimal detector is used, an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counterexample to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.

An OFDM Symbol Design for Reduced Complexity MMSE Channel Estimation

In this paper we revisit the minimum mean square error (MMSE) pilot-aided channel estimation for broadband orthogonal frequency division multiplexing (OFDM) systems. The careful design of OFDM symbol leads to the proposal of a simplified time-domain (TD) MMSE estimator. By exploring the Fourier properties of the symbol, the investigated method eliminates the need to use direct or inverse discrete Fourier transforms (DFT/IDFT) before the channel estimation, by using the TD received symbol samples as the input to the MMSE filter. Moreover, performing the estimation in TD (where the channel impulse response (CIR) energy is mainly limit to a small set of samples), makes way to a simple, nonetheless efficient estimation of the filter parameters. The performance of the channel estimation scheme, using the estimated parameters, presents a tolerable degradation when compared with the ideal situation (a-priori knowledge of the channel correlation and noise variance), while exhibiting a reduced computational load. The feasibility of the investigated method is substantiated by system simulation using indoor and outdoor wireless channel models.

A new MMSE channel estimation algorithm for OFDM systems

In this report, we propose a new MMSE channel estimation algorithm for OFDM systems. It is well-known that time domain maximum likelihood estimators (MSEs) show highly accurate impulse response estimation by using the time domain long preamble of the OFDM frame. On the other hand, the impulse response estimation based on the minimum mean square error (MMSE) criterion achieves superior channel estimation in low SNR conditions; however, it requires prior statistical information such as delay profiles of channels. In addition, the computational complexity becomes large because of the inverse matrix calculation. In order to overcome these issues, we propose to estimate the power delay profile of the channel by using the MLE, and to suppress the increase of the computational complexity for the matrix inverse calculation by applying the conjugate gradient method without degradation of the PER performance.

Robust and Efficient Intercarrier Interference Mitigation for OFDM Systems in Time-Varying Fading Channels

Due to its spectral efficiency and robustness over multipath channels, orthogonal frequency-division multiplexing (OFDM) has served as one of the major modulation schemes for high-speed communication systems. In the future, wireless OFDM systems are expected to operate at high carrier frequencies, high speed, and high throughput for mobile reception, where fast time-varying fading channels are encountered. Channel variation destroys the orthogonality among the subcarriers and leads to intercarrier interference (ICI). ICI poses a significant limitation on wireless OFDM systems. The aim of this paper is to find an efficient method of providing reliable communications using OFDM in fast time-varying fading channels. It is observed that ICI power arises from a few adjacent subcarriers. This observation motivates us to design low-complexity -tap ICI equalizers. To employ these equalizers, channel state information is also required. In this paper, we also design a pilot-aided minimum mean square error (MMSE) channel estimation scheme for a time-varying wide-sense stationary uncorrelated scatters channel model. The MMSE channel estimator utilizes the statistical channel properties to achieve computational efficiency. Simulation results show that our proposed low-complexity ICI suppression scheme, which incorporates the -tap equalizer with the MMSE channel estimator, can significantly improve the performance of OFDM systems in fast time-varying fading channels.

Frequency-Domain MMSE Channel Estimation for Frequency-Domain Equalization of DS-CDMA Signals

Frequency-domain equalization (FDE) based on minimum mean square error (MMSE) criterion can replace the conventional rake combining to significantly improve the bit error rate (BER) performance in a frequency-selective fading channel. MMSE-FDE requires an accurate estimate of the channel transfer function and the signal-to-noise power ratio (SNR). Direct application of pilot-assisted channel estimation (CE) degrades the BER performance, since the frequency spectrum of the pilot chip sequence is not constant over the spreading bandwidth. In this paper, we propose a pilot-assisted decision feedback frequency-domain MMSE-CE. The BER performance with the proposed pilot-assisted MMSE-CE in a frequency-selective Rayleigh fading channel is evaluated by computer simulation. It is shown that MMSE-CE always gives a good BER performance irrespective of the choice of the pilot chip sequence and shows a high tracking ability against fading. For a spreading factor SF of 16, the E b /N 0 degradation for BER=10 -4 with MMSE-CE from the ideal CE case is as small as 0.9 dB (including an E b /N 0 loss of 0.28 dB due to the pilot insertion).

Performance Analysis of Optimum and Suboptimum Selection Diversity Schemes on Rayleigh Fading Channels With Imperfect Channel Estimates

In this paper, we present a comparative analysis on the effects of channel estimation errors on the performance of optimum and suboptimum selection diversity (SD) receivers on Rayleigh-fading channels. By modeling the estimation errors as independent complex Gaussian random variables, we derive simple closed-form expressions for the average probability of error for both optimum and suboptimum SD schemes with noisy channel estimates. With dual diversity and imperfect estimates, we establish a connection between optimum SD and maximal-ratio combining (MRC), and between suboptimum SD and equal-gain combining diversity schemes. Interestingly, we show that the optimum SD receiver structure and the resulting performance for differential binary coherent phase-shift keying (DBPSK) signaling can be obtained, in a straightforward way, as a special case of the performance of the optimum SD scheme with binary PSK signaling and channel estimation errors. For a fixed average power and bit duration, in conjunction with pilot-assisted minimum mean-square error channel estimation, we show that the optimum coherent SD scheme coincides with that of the optimum noncoherent SD scheme with binary frequency-shift keying (BFSK) signaling, whereas the coherent MRC scheme coincides with the optimum noncoherent receiver (i.e., the square-law combiner) for BFSK. The optimum number of diversity channels, under an energy-sharing mode of operation, is also studied. Finally, we formulate the problem of optimal pilot placement, consider channel estimation with a practical pilot-symbol-assisted modulation technique, and present some numerical results illustrating the comparative performances of various SD receivers

A Low-Complexity Time-Domain MMSE Channel Estimator for Space-Time/Frequency Block-Coded OFDM Systems

Focusing on transmit diversity orthogonal frequency-division multiplexing (OFDM) transmission through frequency-selective channels, this paper pursues a channel estimation approach in time domain for both space-frequency OFDM (SF-OFDM) and space-time OFDM (ST-OFDM) systems based on AR channel modelling. The paper proposes a computationally efficient, pilot-aided linear minimum mean-square-error (MMSE) time-domain channel estimation algorithm for OFDM systems with transmitter diversity in unknown wireless fading channels. The proposed approach employs a convenient representation of the channel impulse responses based on the Karhunen-Loeve (KL) orthogonal expansion and finds MMSE estimates of the uncorrelated KL series expansion coefficients. Based on such an expansion, no matrix inversion is required in the proposed MMSE estimator. Subsequently, optimal rank reduction is applied to obtain significant taps resulting in a smaller computational load on the proposed estimation algorithm. The performance of the proposed approach is studied through the analytical results and computer simulations. In order to explore the performance, the closed-form expression for the average symbol error rate (SER) probability is derived for the maximum ratio receive combiner (MRRC). We then consider the stochastic Cramer-Rao lower bound(CRLB) and derive the closed-form expression for the random KL coefficients, and consequently exploit the performance of the MMSE channel estimator based on the evaluation of minimum Bayesian MSE. We also analyze the effect of a modelling mismatch on the estimator performance. Simulation results confirm our theoretical analysis and illustrate that the proposed algorithms are capable of tracking fast fading and improving overall performance.

Training-based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals

In this paper, we study the performance of multiple-input multiple-output channel estimation methods using training sequences. We consider the popular linear least squares (LS) and minimum mean-square-error (MMSE) approaches and propose new scaled LS (SLS) and relaxed MMSE techniques which require less knowledge of the channel second-order statistics and/or have better performance than the conventional LS and MMSE channel estimators. The optimal choice of training signals is investigated for the aforementioned techniques. In the case of multiple LS channel estimates, the best linear unbiased estimation (BLUE) scheme for their linear combining is developed and studied.

Diversity Combining With Imperfect Channel Estimation

The optimal diversity-combining technique is investigated for a multipath Rayleigh fading channel with imperfect channel state information at the receiver. Applying minimum mean-square error channel estimation, the channel state can be decomposed into the channel estimator spanned by channel observation, and the estimation error orthogonal to channel observation. The optimal combining weight is obtained from the first principle of maximum a posteriori detection, taking into consideration the imperfect channel estimation. The bit-error performance using the optimal diversity combining is derived and compared with that of the suboptimal application of maximal ratio combining. Numerical results are presented for specific channel models and estimation methods to illustrate the combined effect of channel estimation and detection on bit-error rate performance.

A Low-Complexity KL Expansion-Based Channel Estimator for OFDM Systems

This paper first proposes a computationally efficient, pilot-aided linear minimum mean square error (MMSE) batch channel estimation algorithm for OFDM systems in unknown wireless fading channels. The proposed approach employs a convenient representation of the discrete multipath fading channel based on the Karhunen-Loeve (KL) orthogonal expansion and finds MMSE estimates of the uncorrelated KL series expansion coefficients. Based on such an expansion, no matrix inversion is required in the proposed MMSE estimator. Moreover, optimal rank reduction is achieved by exploiting the optimal truncation property of the KL expansion resulting in a smaller computational load on the estimation algorithm. The performance of the proposed approach is studied through analytical and experimental results. We then consider the stochastic Cramér-Rao bound and derive the closed-form expression for the random KL coefficients and consequently exploit the performance of the MMSE channel estimator based on the evaluation of minimum Bayesian MSE. We also analyze the effect of a modelling mismatch on the estimator performance. To further reduce the complexity, we extend the batch linear MMSE to the sequential linear MMSE estimator. With the fast convergence property and the simple structure, the sequential linear MMSE estimator provides an attractive alternative to the implementation of channel estimator.

Linear expansions for frequency selective channels in OFDM

Modeling the frequency selective fading channels as random processes, we employ a linear expansion based on the Karhunen–Loeve (KL) series representation involving a complete set of orthogonal deterministic vectors with a corresponding uncorrelated random coefficients. Focusing on OFDM transmissions through frequency selective fading, this paper pursues a computationally efficient, pilot-aided linear minimum mean square error (MMSE) uncorrelated KL series expansion coefficients estimation algorithm. Based on such an expansion, no matrix inversion is required in the proposed MMSE estimator. Moreover, truncation in the linear expansion of channel is achieved by exploiting the optimal truncation property of the KL expansion resulting in a smaller computational load on the estimation algorithm. The performance of the proposed approach is studied through analytical and experimental results. We first exploit the performance of the MMSE channel estimator based on the evaluation of minimum Bayesian MSE. We also provide performance analysis results studying the influence of the effect of SNR and correlation mismatch on the estimator performance. Simulation results confirm our theoretical results and illustrate that the proposed algorithm is capable of tracking fast fading and improving performance.

Space–Time Spreading and Block Coding for Correlated Fading Channels in the Presence of Interference

We consider point-to-point wireless links with multiple antennas in the presence of interference, and exploit channel's spatial correlation and the temporal covariance of the interference to design multiantenna transmitters. We develop a space-time spreading scheme that maximizes average signal-to-interference-and-noise ratio, and an optimally power-loaded space-time beamforming (STBF) scheme which improves error-probability performance. In order to increase transmission rates, we combine orthogonal space-time block coding with STBF, optimize power loading across beams, and develop low-complexity receivers. Optimal training for least-squares error channel estimation, and STBF for minimum mean-square error channel estimation, are also studied. Our analytical and simulated results corroborate that STBF with optimal power loading can considerably reduce error probability and channel-estimation errors.

Enhanced MMSE Channel Estimation Using Timing Error Statistics for Wireless OFDM Systems

Estimation and tracking of the frequency-selective time-varying channel response is a challenging task for wireless communication systems incorporating coherent OFDM. In pilot-symbol-assisted (PSA) OFDM systems, the minimum mean-square-error (MMSE) estimator provides the optimum performance based on the channel statistics (channel correlation function and SNR). In OFDM systems, FFT-block timing error introduces a linear phase rotation to data modulated on individual subcarriers. An MMSE channel estimator designed only using the wireless channel statistics performs only sub-optimally when subcarrier phase rotations due to block timing errors are present. In this paper, we show that by using the block timing error statistics of the OFDM time-synchronizer the performance of the MMSE channel estimation can be significantly improved. Numerical results show that the bit-error-probability (BEP) performance degradation due to timing errors can be almost completely recovered by the proposed technique.

Effects of frequency offset compensation error on channel estimation for OFDM system under mobile radio channels

In this paper, we analyze the effects of frequency offset compensation on the pilot-assisted channel estimation for the orthogonal frequency division multiplexing system under a time-variant multipath fading channel. The analysis focuses on the pilot arrangement of a pilot-assisted channel estimation scheme, in which the minimum mean-square error channel estimation is employed to exploit both time- and frequency-domain correlation characteristics of the frequency response of time-variant multipath fading channels. We also investigate the effect of the length of the training signal used for frequency offset estimation on the channel estimation and subsequently, on the bit error rate performance, subject to varying signal-to-noise power ratio under mobile radio channel. Numerical results show that the maximum allowable pilot carrier spacing in time-domain is critically affected by the frequency offset error. In addition, a proper length of the training signal must be configured to suppress the noise influence while reducing a systematic error due to the time-variant behavior of the channel.

Analysis of low-complexity windowed DFT-based MMSE channel estimator for OFDM systems

Low-complexity windowed discrete Fourier transform (DFT)-based minimum mean square error (MMSE) channel estimators are proposed and analyzed for both the interpolation and noninterpolation cases for orthogonal frequency-division multiplexing (OFDM) mobile communications systems. In the proposed method, the frequency domain data windowing is used to reduce the aliasing errors for the interpolation case and get better noise filtering performance for the noninterpolation case. The time domain MMSE weighting is also used to suppress the channel noise for both cases. Moreover, the optimal generalized Hanning window shape is searched to minimize the channel estimation mean square error (MSE). Analysis and simulation results show that the proposed method performance is close to the optimal MMSE estimator and is much better than the direct DFT-based estimator for both cases. Compared with the optimal MMSE estimator, however, the computation load of the proposed method can be significantly reduced because the IDFT/DFT transforms can be implemented with the fast algorithms IFFT/FFT.