Sparse channel estimation in OFDM systems by threshold-based pruning
TL;DR: A threshold-based procedure to estimate sparse channels in an orthogonal frequency division multiplexing (OFDM) system is proposed, derived by maximising the probability of correct detection between significant and zero-valued taps estimated by the least squares estimator.
Abstract: A threshold-based procedure to estimate sparse channels in an orthogonal frequency division multiplexing (OFDM) system is proposed. An optimal threshold is derived by maximising the probability of correct detection between significant and zero-valued taps estimated by the least squares (LS) estimator. Improved LS estimates are obtained by pruning the LS estimates with the statistically derived threshold.
Citations
More filters
TL;DR: The literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements, assuming the signals are assumed to be sparse in some transform domain or in some dictionary is reviewed.
Abstract: In this overview article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in some dictionary. Their sparsity patterns can change with time, although, in many practical applications, the changes are gradual. An important class of applications where this problem occurs is dynamic projection imaging, e.g., dynamic magnetic resonance imaging (MRI) for real-time medical applications such as interventional radiology, or dynamic computed tomography.
92 citations
Cites background from "Sparse channel estimation in OFDM s..."
..., [49]; and spars e channel estimation and data detection in orthogonal freque ncy division multiplexing (OFDM) systems [50]....
[...]
TL;DR: A very efficient semi-blind approach for the detection of most significant taps (MSTs) in sparse orthogonal frequency-division multiplexing (OFDM) channel estimation is developed and it is shown that the new MST detection algorithm can be extended for the estimation of multiple-input–multiple-output (MIMO)–OFDM channels.
Abstract: In this paper, a very efficient semi-blind approach for the detection of most significant taps (MSTs) in sparse orthogonal frequency-division multiplexing (OFDM) channel estimation is developed. The least square (LS) estimation problem of sparse OFDM channels is first formulated, showing that the key to sparse channel estimation lies in the detection of the MSTs. An in-depth study of the second-order statistics of the signal received through a noise-free sparse OFDM channel reveals the sparsity and other properties of the correlation functions of the received signal. These properties lead to a direct relationship between the positions of the MSTs of the sparse channel and the most significant lags of the correlation functions, which is then used in conjunction with a pilot-assisted LS estimation to detect the MSTs in a semi-blind fashion. It os also shown that the new MST detection algorithm can be extended for the estimation of multiple-input–multiple-output (MIMO)–OFDM channels. A number of computer-simulation-based experiments for various sparse channels are carried out to confirm the effectiveness of the proposed semi-blind approach.
66 citations
Cites methods from "Sparse channel estimation in OFDM s..."
...By exploiting the sparse structure of the channel, some improved channel-estimation algorithms have been developed for OFDM systems [10]–[12], [17], [20], [21] and code division multiple access systems [15], [16]....
[...]
TL;DR: This paper aims to approach the Minimum Mean Square Error (MMSE) channel estimation performance, while avoiding the need for a-priori knowledge of channel statistics (KCS), and introduces novel MSS strategies oriented towards instantaneous decimation, and windowed decimation (Average Energy Selection - AES).
Abstract: In this paper, OFDM data-aided channel estimation based on the decimation of the Channel Impulse Response (CIR) through the selection of the Most Significant Samples (MSS) is addressed. Our aim is to approach the Minimum Mean Square Error (MMSE) channel estimation performance, while avoiding the need for a-priori knowledge of channel statistics (KCS). The optimal set of samples is defined in the instantaneous and average senses. We derive lower bounds on the estimation mean-square error (MSE) performance for any MSS selection strategy. We show how MSS-based channel estimation can approach these MSE lower bounds. We introduce novel MSS strategies oriented towards instantaneous decimation (Instantaneous Energy Selection - IES), and windowed decimation (Average Energy Selection - AES). We also consider decimation via Threshold Crossing Selection (TCS), which we characterize analytically, to derive the optimum threshold in the minimum MSE sense. We also propose a sub-optimal method for threshold setting that does not require KCS. Finally, we provide numerical results in terms of both MSE estimation performance and Bit Error Rate (BER) of a coded OFDM system using the proposed channel estimators, to show that they indeed approach MMSE performance.
46 citations
Cites background or methods from "Sparse channel estimation in OFDM s..."
...β(2)Es/N0 (dB) M SE UNIFORM CHANNEL: LS TCS Kang et al [10] TCS Oliver et al [11] TCS SOT N̂t = 6 MMSE TU6 CHANNEL: LS TCS Kang et al [10] TCS Oliver et al [11] TCS SOT N̂t = 6 MMSE...
[...]
...THRESHOLD CROSSING SELECTION The TCS strategy for identifying the MSS set, which has been treated in [9], [10], [11], [15], [16], is based on the concept that only those samples which overcome a threshold ξ in absolute value are retained:...
[...]
...Even the criterion proposed in [11], which takes advantage of the KCS, is outperformed 0 5 10 15 20 10 −3 10 −2 10 −1 10 0...
[...]
...TCS Oliver et al [11] an....
[...]
...While in [10] the threshold was set according to heuristics, in [11] a genie-aided approach was followed, based again on ideal TCS....
[...]
TL;DR: An adaptive channel estimation method based on Doppler prediction and time smoothing, whose decision-directed operation allows for reduction in the pilot overhead and an order of magnitude decrease in the bit error rate when the number of carriers is chosen optimally is proposed.
Abstract: In this paper, Alamouti space–frequency block coding, applied over the carriers of an orthogonal frequency-division multiplexing (OFDM) system, is considered for obtaining transmit diversity in an underwater acoustic channel. This technique relies on the assumptions that there is sufficient spatial diversity between the channels of the two transmitters, and that each channel changes slowly over the carriers, thus satisfying the basic Alamouti coherence requirement and allowing simple data detection. We propose an adaptive channel estimation method based on Doppler prediction and time smoothing, whose decision-directed operation allows for reduction in the pilot overhead. System performance is demonstrated using real data transmitted in the 10–15-kHz acoustic band from a vehicle moving at 0.5–2 m/s and received over a shallow-water channel, using quadrature phase-shift keying (QPSK) and a varying number of carriers ranging from 64 to 1024. Results demonstrate an average mean squared error gain of about 2 dB as compared to the single-transmitter case and an order of magnitude decrease in the bit error rate when the number of carriers is chosen optimally.
41 citations
Cites background from "Sparse channel estimation in OFDM s..."
...The LS data estimate (3) then reduces to d̂A2k(n) = 1 ∑ r E r 2k(n) CH2k(n)y A 2k(n) (6) Extraction of the transmit diversity gain through summation of individual channel’s energies, and simplicity of data detection without matrix inversion, form the essence of Alamouti processing....
[...]
TL;DR: A detailed survey on various existing denoising strategies, with a comparative discussion of these strategies is presented, to enhance the MSE performance using LS based techniques.
39 citations
References
More filters
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: A time-domain based channel estimation for OFDM system with pilot-data multiplexed scheme and simulation results show that proposed method achieves almost the same performance as DFT-based LMMSE method and better BER performance than the other methods while keeping less complexity.
Abstract: A time-domain based channel estimation for OFDM system with pilot-data multiplexed scheme is investigated. As an approximation to linear minimum mean square estimator (LMMSE), a time-domain based channel estimation is proposed where intra-symbol time-averaging and most significant channel taps selection are applied. The relation and differences of the proposed method to DFT-based LMMSE methods are discussed. The performances of the proposed method, DFT-based LMMSE method and the methods of Chini, Wu, El-Tanany and Mahmoud (see IEEE Trans. on Broadcasting, vol.44, no.1, p.2-11, 1998) and of Yeh and Lin (see IEEE Trans. on Broadcasting, vol.45, no.4, p.400-409, 1999) are evaluated in multipath fading channels. The simulation results show that proposed method achieves almost the same performance as DFT-based LMMSE method and better BER performance than the other methods while keeping less complexity.
289 citations
TL;DR: An improved discrete Fourier transform (DFT)-based channel estimation for orthogonal frequency division multiplexing systems is proposed and can improve the performance by deciding significant channel taps adaptively without requiring any channel statistical information.
Abstract: An improved discrete Fourier transform (DFT)-based channel estimation for orthogonal frequency division multiplexing systems is proposed. Conventional DFT-based channel estimations improve the performance by suppressing time domain noise. However, they potentially require information on channel impulse responses and may also result in mean-square error (MSE) floor due to incorrect channel information such as channel delay spread. In contrast, our purposed channel estimation can improve the performance by deciding significant channel taps adaptively without requiring any channel statistical information. Significant channel taps are detected on the basis of a predetermined threshold. The optimal threshold to reduce the MSE of the estimation is also derived, and it is confirmed by computer simulation. Simulation results demonstrate that the proposed algorithm can improve the MSE performance ~6.5 dB compared with the conventional DFT-based estimation, and the MSE floor is not observed in any channels.
178 citations
TL;DR: The proposed modified LS with sparse channel-estimation algorithm has a 5-dB lower mean square error in channel estimation when compared to the conventional approach, which translates to approximately 0.5 dB improvement in signal-to-noise ratio at the receiver.
Abstract: We describe an algorithm for sparse channel estimation applicable to orthogonal frequency division multiplexing systems. The proposed algorithm uses a least squares (LS) technique for channel estimation and a generalized Akaike information criterion to estimate the channel length and tap positions. This effectively reduces the signal space of the LS estimator, and hence improves the estimation performance as demonstrated using computer simulations. For example, the proposed modified LS with sparse channel-estimation algorithm has a 5-dB lower mean square error in channel estimation when compared to the conventional approach , which translates to approximately 0.5 dB improvement in signal-to-noise ratio at the receiver.
144 citations