Fast Array Multichannel 2D-RLS Based OFDM Channel Estimator
01 Jun 2013-Circuits Systems and Signal Processing (SP Birkhäuser Verlag Boston)-Vol. 32, Iss: 3, pp 1419-1432
TL;DR: A Fast Array Multichannel Two-Dimensional Recursive Least Square (FAM 2D-RLS) adaptive filter is proposed for estimating an OFDM channel in frequency domain that makes use of the shift structure of the input data vector.
Abstract: In this paper a Fast Array Multichannel Two-Dimensional Recursive Least Square (FAM 2D-RLS) adaptive filter is proposed for estimating an OFDM channel in frequency domain. This filter makes use of the shift structure of the input data vector. Thus the computational cost of the classical RLS filter which is O(M
2) is reduced to O(M) for each iteration where M is the order of the filter. In order to ensure numerical stability in finite precision, we make use of array-based methods for implementing FAM 2D-RLS. The adaptive filters illustrated in the standard literature consist of a weight vector and desired data as a scalar. But in our scenario of OFDM channel estimation the weight is a matrix while the desired data are a vector. Hence the algorithm for the matrix form of FAM-2D RLS and its steady state equations are derived. Numerical stability, steady state and convergence performance are verified using MATLAB simulations.
Citations
More filters
TL;DR: Signal adaptive, multiple-clock-cycle hardware implementation (MCI) of an optimal (Wiener) filter for highly nonstationary two-dimensional (2D) FM signals estimation is developed and qualified as an optimal solution for wide range of practical implementations.
Abstract: Signal adaptive, multiple-clock-cycle hardware implementation (MCI) of an optimal (Wiener) filter for highly nonstationary two-dimensional (2D) FM signals estimation is developed here. It uses results of the space/spatial-frequency (S/SF) analysis in real-time processing of nonstationary 2D signals and is based on the correspondence of the filter's region of support to the local frequency (LF) of the filtered 2D signal and on the S/SF analysis-based LF estimation. The MCI approach helps the proposed design to minimize clock cycle time and to optimize critical design performances related to the hardware complexity, making it a suitable system for real-time and on-a-chip implementation. However, the major advantage of the proposed design is the ability to take variable (signal adaptive) number of clock cycles in different S/SF points within the execution. This property helps the design to optimize the execution time (the main drawback of the classical MCI approaches in comparison to the single-clock-cycle ones), but also to provide the highest quality LF estimation, high S/SF resolution, and a very efficient filtering of nonstationary 2D FM signals. In this way, it is qualified as an optimal solution for wide range of practical implementations. The implementation is verified by a field-programmable gate array (FPGA) circuit design.
16 citations
TL;DR: Variable (signal adaptive) number of clock cycles, taken within the execution in different S/SF points, provides this solution to retain the optimized time requirements, as well as high resolution, selectivity, and estimation quality of the corresponding recently proposed signal adaptive filtering solution.
Abstract: Multiple-clock-cycle, signal adaptive, and fully pipelined hardware design of the optimal (Wiener) space/spatial-frequency (S/SF) filter is developed in this paper. All implementation and verification details, as well as the extensive comparative analysis, are provided. The developed solution optimizes critical design performances related to the hardware complexity, in line with multiple-clock-cycle nature. Variable (signal adaptive) number of clock cycles, taken within the execution in different S/SF points, provides this solution to retain the optimized time requirements, as well as high resolution, selectivity, and estimation quality of the corresponding recently proposed signal adaptive filtering solution. However, as the major contribution, the fully pipelined implementation enables the developed design to additionally improve the time required for execution. The achieved improvement corresponds to a clock cycle per each S/SF point performed within the estimation that results in the significant comparative improvement in execution time of up to 50% in terms of S/SF points lying outside the local frequency of the estimated 2D frequency-modulated signal. The implementation is tested on a highly nonstationary multicomponent signal and is verified by a field programmable gate array circuit design.
7 citations
Cites background from "Fast Array Multichannel 2D-RLS Base..."
...To provide participation in the other control signals creation, [18], [34], the STFT_AT_Reg signal is generated (through a multiplier, an adder, and a comparator, Fig....
[...]
...Thus, as explicitly proven in [18], this procedure significantly improves calculation complexities of the state-of-the-art estimation algorithms, such as the algorithm from [4], as well as the 2D LMS and 2D RLS algorithms, [34]....
[...]
...[18], [34]....
[...]
25 Sep 2013
TL;DR: A low complexity adaptive channel estimation technique for OFDM based two-way relay systems based on the Decision Directed (DD) principle that considers the correlation of the channel frequency response in both time and frequency, while estimating the channel.
Abstract: This paper introduces a low complexity adaptive channel estimation technique for OFDM based two-way relay systems. The adaptive filter used is known as Group Fast Array Multichannel 2D-Recursive Least Square (GFAM 2DRLS) filter. It has a computational complexity comparable to that of 2D-Normalized Least Mean Square (2D-NLMS) algorithm while maintaining the same convergence rate as the classic 2D Recursive Least Square (2D-RLS) algorithm. It considers the correlation of the channel frequency response in both time and frequency, while estimating the channel. In order to reduce the number of training data for time varying channel, the channel estimation is carried out based on the Decision Directed (DD) principle. It is assumed that the relay is capable of performing complex signal processing tasks. Hence the channel estimation is performed at the relay. Since the Channel State Information (CSI) is available at the relay, it could perform Multiple Input Multiple Output (MIMO) precoding of the transmitted data. Hence CSI is not required at the transmitting nodes. The convergence rate of GFAM 2D-RLS is compared with the existing 2D-NLMS algorithm and the computational complexity at each iteration is tabulated. Simulations are performed using MATLAB.
5 citations
01 Oct 2014
TL;DR: An adaptive channel estimation scheme for two-way relay with node capability and the effect of channel estimation error on performance of Adaptive OFDM (AOFDM) is analyzed for pedestrian A (pedA) channel.
Abstract: In this paper we introduce an adaptive channel estimation scheme for two-way relay with node capability. The adaptive filter used is called Block Fast Array Multichannel 2D-Recursive Least Square (BFAM 2D-RLS). The modulation used is Orthogonal Frequency Division Multiplexing (OFDM) and channel estimation is done in the frequency domain. The proposed channel estimator considers correlation of channel frequency response in both time and frequency domain. The computational complexity is calculated and convergence performance of the adaptive channel estimator is studied. This paper also introduces an AOFDM scheme for two-way relay systems. The effect of channel estimation error on performance of Adaptive OFDM (AOFDM) is analyzed for pedestrian A (pedA) channel. All computer simulations are performed using MATLAB ®.
1 citations
04 Jun 2013
TL;DR: This paper proposes a simple method to obtain the individual channel assuming that the estimate of combined channel is available and the general frame work provided can be used to implement other loading algorithms for two-way relay systems.
Abstract: In this paper we introduce the concept of Adaptive Orthogonal Frequency Division Multiplexing (AOFDM) for two-way relay systems. In order to implement AOFDM at the nodes, the Channel State Information (CSI) is required. Usually CSI is estimated and hence the effect of estimation error should be considered while implementing AOFDM. In the case of two-way relay, channel estimation at the nodes usually result in the overall channel between the source and relay. But for implementing AOFDM, we require the individual channel between node and relay. We propose a simple method to obtain the individual channel assuming that the estimate of combined channel is available. The loading algorithm used is the Levin-Campello loading algorithm. But the general frame work provided by us can be used to implement other loading algorithms for two-way relay systems.
1 citations
References
More filters
Book•
01 Jan 1986
TL;DR: In this paper, the authors propose a recursive least square adaptive filter (RLF) based on the Kalman filter, which is used as the unifying base for RLS Filters.
Abstract: Background and Overview. 1. Stochastic Processes and Models. 2. Wiener Filters. 3. Linear Prediction. 4. Method of Steepest Descent. 5. Least-Mean-Square Adaptive Filters. 6. Normalized Least-Mean-Square Adaptive Filters. 7. Transform-Domain and Sub-Band Adaptive Filters. 8. Method of Least Squares. 9. Recursive Least-Square Adaptive Filters. 10. Kalman Filters as the Unifying Bases for RLS Filters. 11. Square-Root Adaptive Filters. 12. Order-Recursive Adaptive Filters. 13. Finite-Precision Effects. 14. Tracking of Time-Varying Systems. 15. Adaptive Filters Using Infinite-Duration Impulse Response Structures. 16. Blind Deconvolution. 17. Back-Propagation Learning. Epilogue. Appendix A. Complex Variables. Appendix B. Differentiation with Respect to a Vector. Appendix C. Method of Lagrange Multipliers. Appendix D. Estimation Theory. Appendix E. Eigenanalysis. Appendix F. Rotations and Reflections. Appendix G. Complex Wishart Distribution. Glossary. Abbreviations. Principal Symbols. Bibliography. Index.
16,062 citations
TL;DR: The analysis and simulation of a technique for combating the effects of multipath propagation and cochannel interference on a narrow-band digital mobile channel using the discrete Fourier transform to orthogonally frequency multiplex many narrow subchannels, each signaling at a very low rate, into one high-rate channel is discussed.
Abstract: This paper discusses the analysis and simulation of a technique for combating the effects of multipath propagation and cochannel interference on a narrow-band digital mobile channel. This system uses the discrete Fourier transform to orthogonally frequency multiplex many narrow subchannels, each signaling at a very low rate, into one high-rate channel. When this technique is used with pilot-based correction, the effects of flat Rayleigh fading can be reduced significantly. An improvement in signal-to-interference ratio of 6 dB can be obtained over the bursty Rayleigh channel. In addition, with each subchannel signaling at a low rate, this technique can provide added protection against delay spread. To enhance the behavior of the technique in a heavily frequency-selective environment, interpolated pilots are used. A frequency offset reference scheme is employed for the pilots to improve protection against cochannel interference.
2,627 citations
Book•
01 Jan 2003
TL;DR: This paper presents a meta-anatomy of Adaptive Filters, a system of filters and algorithms that automates the very labor-intensive and therefore time-heavy and expensive process of designing and implementing these filters.
Abstract: Preface. Acknowledgments. Notation. Symbols. Optimal Estimation. Linear Estimation. Constrained Linear Estimation. Steepest-Descent Algorithms. Stochastic-Gradient Algorithms. Steady-State Performance of Adaptive Filters. Tracking Performance of Adaptive Filters. Finite Precision Effects. Transient Performance of Adaptive Filters. Block Adaptive Filters. The Least-Squares Criterion. Recursive Least-Squares. RLS Array Algorithms. Fast Fixed-Order Filters. Lattice Filters. Laguerre Adaptive Filters. Robust Adaptive Filters. Bibliography. Author Index. Subject Index. AC
1,987 citations
25 Jul 1995
TL;DR: The authors present the MMSE and LS estimators and a method for modifications compromising between complexity and performance and the symbol error rate for a 18-QAM system is presented by means of simulation results.
Abstract: The use of multi-amplitude signaling schemes in wireless OFDM systems requires the tracking of the fading radio channel. The paper addresses channel estimation based on time-domain channel statistics. Using a general model for a slowly fading channel, the authors present the MMSE and LS estimators and a method for modifications compromising between complexity and performance. The symbol error rate for a 18-QAM system is presented by means of simulation results. Depending upon estimator complexity, up to 4 dB in SNR can be gained over the LS estimator.
1,647 citations
TL;DR: This work has implemented a decision feedback equalizer for all sub-channels followed by periodic block-type pilots and compared the performances of all schemes by measuring bit error rates with 16QAM, QPSK, DQPSK and BPSK as modulation schemes, and multipath Rayleigh fading and AR based fading channels as channel models.
Abstract: Channel estimation techniques for OFDM systems based on a pilot arrangement are investigated. Channel estimation based on a comb type pilot arrangement is studied through different algorithms for both estimating the channel at pilot frequencies and interpolating the channel. Channel estimation at pilot frequencies is based on LS and LMS methods while channel interpolation is done using linear interpolation, second order interpolation, low-pass interpolation, spline cubic interpolation, and time domain interpolation. Time-domain interpolation is obtained by passing to the time domain by means of IDFT (inverse discrete Fourier transform), zero padding and going back to the frequency domain by DFT (discrete Fourier transform). In addition, channel estimation based on a block type pilot arrangement is performed by sending pilots in every sub-channel and using this estimation for a specific number of following symbols. We have also implemented a decision feedback equalizer for all sub-channels followed by periodic block-type pilots. We have compared the performances of all schemes by measuring bit error rates with 16QAM, QPSK, DQPSK and BPSK as modulation schemes, and multipath Rayleigh fading and AR based fading channels as channel models.
1,551 citations