Sparse Channel Estimation Aided Federated Learning Assisted Non-Terrestral Network

Various channel estimation methods have been proposed for shallow underwater communication channel with sparse channel type. A matching pursuit (MP), which is one of typical sparse channel estimation methods, can detect dominant components of sparse channel sequentially as a portion of matching. Mean squared error of MP, however, converges to fixed value even though signal-to-noise ratio (SNR) increases. This paper proposes a minimum mean squared error (MMSE) estimation method with constant false alarm (CFAR) detection for sparse channel estimation. Unlike MP, the mean squared error of the proposed method decreases as SNR increases and is lower than that of conventional MMSE estimators on the sparse channel. Experimental results show that the proposed method estimates sparse underwater communication channel efficiently.

MMP-DCD-CV based sparse channel estimation algorithm for underwater acoustic transform domain communication system

Sparse channel arises in a number of applications in wireless communications such as channel estimation and signal processing. There is growing evidence that physical wireless channels exhibit a sparse structure, and channel sparsity has been even considered as a nature of channels in many recent research works. However, there still lacks a good measure of channel sparsity, and mostly the assumptions that channel is sparse or non-sparse are based on intuitive analysis without measurement validation, which leads to some contradictions. In this article, based on channel measurement data, it is pointed out that a widely-used assumption, that wireless channels can be considered to be sparse, has pitfalls. Without loss of generality, the measurements are conducted in an urban scenario with different degrees of channel multipath richness. The channel degrees of freedom, diversity measure, and the Ricean K factor are used to evaluate channel sparsity, and they are found to have fairly high accuracy of measuring degrees of channel sparsity. It is also observed from measurements that the degree of channel sparsity is not steady and a sparse channel may change to non-sparse within a short time/distance observation window. Moreover, sparse and non-sparse based channel estimators are evaluated based on the measurements and the performances are analyzed. The results show that a sparse channel estimator cannot guarantee stable estimation accuracy even in channels with a high degree of sparsity, and considerable performance degradation will occur if a channel changes to non-sparse, which actually often happens in realistic communication scenarios and should be carefully considered in performance analysis. Some sparse channel related technical issues are also discussed in the article.

This paper studies the pilot design for compressed sensing (CS)-based sparse channel estimation in multi-input–multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. To improve the performance of estimating multiple jointly sparse channels, based on the assumption that the modulus of the pilot symbol at each pilot carrier position is equal to a constant, the pilot is currently allocated by means of lowering the sensing matrix’s total coherence (TC). However, according to the block compressed sensing (BCS) theory, the recovery ability of the sensing matrix is determined by the block coherence (BC) and subblock coherence (SC), which should be as small as possible. Therefore, we propose a novel scheme, which designs the pilot by simultaneously minimizing the TC, BC, and SC of the sensing matrix to improve the channel estimation accuracy. We first formulate the jointly sparse channel estimation as a block sparse signal recovery problem, and the pilot allocation problem is comprised of allocating the pilot index for each transmitter and allocating the pilot symbol at each carrier. Then, we derive the error bound of BCS-based channel estimation, where the pilot symbols bear any value. Finally, a novel sequential joint criterion design (SJCD) method is proposed to design pilots with a joint criterion, where the pilot pattern and pilot power are designed by BC and TC, respectively. Simulation results show that, compared with existing algorithms, the proposed algorithm can achieve a better channel estimation performance in terms of normalized mean square error (NMSE) and bit error rate (BER).

This paper addresses the effective sparse channel estimation based on the most significant taps (MST) selection with high spectral efficiency and moderate computational complexity for orthogonal frequency division multiplexing (OFDM) systems. The main goal of this paper is to obtain an efficient time domain threshold and achieve the channel estimation performance approaching the least squares (LS) method with exact sparsity (exact number of non-zero channel taps) without using prior knowledge of both channel statistics and noise standard deviation. Firstly, classical LS method is used to get an initial channel impulse response (CIR) estimate. Then a novel effective threshold, estimated from the noise coefficients of the initial estimated CIR, is proposed. Finally, the obtained threshold is used to select the most significant taps. Simulations show that the proposed method is able to achieve good channel estimation performances for sparse channel within a comparatively wide range of sparsity with small number of pilots and moderate computational complexity.

Compressive sensing (CS) techniques have been shown to enhance the performance of sparse channel estimation. This paper addresses CS-based sparse channel estimation in practical systems where the measurements are quantized to a finite number of bits. In these systems, quantization introduces two kinds of errors into the CS framework: quantization errors and saturation errors. To combat the effect of quantization error on estimating the sparse channel, a new complex-valued cost function is formulated based on the quantization model. To minimize this cost function, a multi-bit iterative hard thresholding algorithm is proposed. The channel estimate performance is evaluated by modeling the quantization error as white Gaussian noise. Our simulation results quantify the number of bits needed for our proposed quantized CS-based sparse channel estimate to achieve satisfactory performance.

Massive multiple-input multiple-output (massive-MIMO) is foreseen as a potential technology for future 5G cellular communication networks due to its substantial benefits in terms of increased spectral and energy efficiency. These advantages of massive-MIMO are a consequence of equipping the base station (BS) with quite a large number of antenna elements, thus resulting in an aggressive spatial multiplexing. In order to effectively reap the benefits of massive-MIMO, an adequate estimate of the channel impulse response (CIR) between each transmit–receive link is of utmost importance. It has been established in the literature that certain specific multipath propagation environments lead to a sparse structured CIR in spatial and/or delay domains. In this paper, implicit training and compressed sensing based CIR estimation techniques are proposed for the case of massive-MIMO sparse uplink channels. In the proposed superimposed training (SiT) based techniques, a periodic and low power training sequence is superimposed (arithmetically added) over the information sequence, thus avoiding any dedicated time/frequency slots for the training sequence. For the estimation of such massive-MIMO sparse uplink channels, two greedy pursuits based compressed sensing approaches are proposed, viz: SiT based stage-wise orthogonal matching pursuit (SiT-StOMP) and gradient pursuit (SiT-GP). In order to demonstrate the validity of proposed techniques, a performance comparison in terms of normalized mean square error (NCMSE) and bit error rate (BER) is performed with a notable SiT based least squares (SiT-LS) channel estimation technique. The effect of channels’ sparsity, training-to-information power ratio (TIR) and signal-to-noise ratio (SNR) on BER and NCMSE performance of proposed schemes is thoroughly studied. For a simulation scenario of: 4 × 64 massive-MIMO with a channel sparsity level of 80 % and signal-to-noise ratio (SNR) of 10 dB , a performance gain of 18 dB and 13 dB in terms of NCMSE over SiT-LS is observed for the proposed SiT-StOMP and SiT-GP techniques, respectively. Moreover, a performance gain of about 3 dB and 2.5 dB in SNR is achieved by the proposed SiT-StOMP and SiT-GP, respectively, for a BER of 10 − 2 , as compared to SiT-LS. This performance gain NCME and BER is observed to further increase with an increase in channels’ sparsity.

This paper is concerned with a challenging problem of channel estimation for amplify-and-forward cooperative relay based orthogonal frequency division multiplexing (OFDM) systems in the presence of sparse underwater acoustic channels and of the correlative non-Gaussian noise. We exploit the sparse structure of the channel impulse response to improve the performance of the channel estimation algorithm, due to the reduced number of taps to be estimated. The resulting novel algorithm initially estimates the overall sparse channel taps from the source to the destination as well as their locations using the matching pursuit (MP) approach. The correlated non-Gaussian effective noise is modeled as a Gaussian mixture. Based on the Gaussian mixture model, an efficient and low complexity algorithm is developed based on the combinations of the MP and the space-alternating generalized expectation-maximization (SAGE) technique, to improve the estimates of the channel taps and their location as well as the noise distribution parameters in an iterative way. The proposed SAGE algorithm is designed in such a way that, by choosing the admissible hidden data properly on which the SAGE algorithm relies, a subset of parameters is updated for analytical tractability and the remaining parameters for faster convergence Computer simulations show that underwater acoustic (UWA) channel is estimated very effectively and the proposed algorithm has excellent symbol error rate and channel estimation performance.

As the increasing requirement of channel capacity for next-generation mobile broadband communication systems, three-dimensional multiple-input multiple-output (3D MIMO) systems have been attracting much attentions in recent years. Accurate channel estimation is inevitably one of the most essential tasks for designing the 3D MIMO systems. This paper first studies the sparsity of 3D MIMO channel and then proposes a sparse channel estimation method based on Quantum Bacterial Foraging Optimization (QBFO) algorithm. Numerical simulations are conducted to confirm that the proposed algorithm can greatly improve estimation performance compared to traditional estimation algorithms.

Most existing downlink channel estimation methods rely on channel sparsity in the angular domain to reduce pilot overhead for massive multiple-input multiple-output (MIMO) systems. Compared with channel estimation methods based on predefined basis or offline dictionary learning, in this paper, we design an online two-timescale joint uplink/downlink dictionary learning and channel estimation (TTS-JDLCE) algorithm for dynamic scenarios, where the channel sparsity and angle reciprocity between uplink and downlink transmissions are both exploited to reduce the pilot overhead. The downlink channel estimation is constructed as a TTS stochastic optimization problem with a constraint coupled by the long-term dictionary and short-term sparse channel representations. Treating the dictionary as a learnable parameter, the proposed algorithm can capture dynamic spatial information for enhancing performance. By introducing a relaxed TTS primal-dual decomposition (PDD) framework, the original problem is decomposed into a long-term online dictionary learning subproblem and a family of short-term sparse channel estimation subproblems. Besides, the deep unfolding technique is employed to extract gradient information from short-term problems, which circumvents the non-closed form and non-convexity of long-term subproblem by constructing a convex surrogate problem. Finally, simulations show that the proposed method remarkably reduces the pilot overhead and achieves significant performance gains over various baselines.

This paper investigates sparse channel estimations to improve the performance of passive-phase conjugation (PPC) communications. PPC processing achieves pulse compression for time delayed arrivals at the receiver. This property is used for underwater communications with a reduced computational load. The channel estimation is required by PPC. In multipath channels, the sparse channel estimations can be used to improve the communication performance. The dominant arrivals are estimated by matching pursuit (MP) processing for PPC processing and the remained arrivals are treated as zeros. Using experimental data collected in a range dependent acoustic channel, MP processing is assessed in improving the performance of PPC communications.

The least mean p-power (LMP) is one of the most popular adaptive filtering algorithms. With a proper p value, the LMP can outperform the traditional least mean square \((p=2)\), especially under the impulsive noise environments. In sparse channel estimation, the unknown channel may have a sparse impulsive (or frequency) response. In this paper, our goal is to develop new LMP algorithms that can adapt to the underlying sparsity and achieve better performance in impulsive noise environments. Particularly, the correntropy induced metric (CIM) as an excellent approximator of the \(l_0\)-norm can be used as a sparsity penalty term. The proposed sparsity-aware LMP algorithms include the \(l_1\)-norm, reweighted \(l_1\)-norm and CIM penalized LMP algorithms, which are denoted as ZALMP, RZALMP and CIMLMP respectively. The mean and mean square convergence of these algorithms are analysed. Simulation results show that the proposed new algorithms perform well in sparse channel estimation under impulsive noise environments. In particular, the CIMLMP with suitable kernel width will outperform other algorithms significantly due to the superiority of the CIM approximator for the \(l_0\)-norm.

In this paper, equalization of channels with large delay spread but with few nonzero taps, such as those encountered in HDTV, are considered. Exploiting the sparse nature of the channel impulse response, we propose a decision feedback equalizer (DFE) which is based on a channel estimate obtained via a matching pursuit (MP) algorithm rather than the standard least squares (LS) channel estimate. It is shown that equalizers so designed result in a large performance gain. It is also shown that while truncation of the LS channel estimate to give a sparse channel estimate leads to some performance improvement, it falls well short of the MP-based DFE. In addition, an adaptive scheme which is intermediate in complexity between the LMS and RLS is presented for updating the sparse channel estimate in a time-varying environment. This adaptive algorithm outperforms the LMS.

Reconfigurable intelligent surface (RIS)-aided mmWave communication offers a promising approach to overcome the issue of severe signal blockage that limits the data rate of mmWave networks. However, joint base station beamforming and RIS phase shift (BF-PS) design presents great challenges not only because of the intricate relationship between the beamforming and phase shift matrices in determining the network sum-rate, but also due to the lack of accurate channel estimation when the number of RIS elements gets large. In this work, we study learning-based BF-PS design for RIS-aided mmWave networks under sparse channel estimation. Our main finding is that, under the practical constraint of pilot overhead for RIS channel estimation, learning-based BF-PS design can yield superior performance to that achieved by the conventional block-coordinate-descent (BCD) algorithm. This work provides an initial study of learning-based BF-PS design under the compressed-sensing framework for mmWave channel estimation. The proposed BF-PS design adopts an enhanced four-stage neural-network architecture that improves upon the existing two-stage design by utilizing outputs from earlier stages to form new features for later stages. The new four-stage design using hybrid beamforming (HBF) outperforms those of the two-stage design using either HBF or fully digital beamforming (DBF).

In this paper, a fast orthogonal matching pursuit (OMP) algorithm based on optimized iterative process is proposed for sparse time-varying underwater acoustic (UWA) channel estimation. The channel estimation consists of calculating amplitude, delay and Doppler scaling factor of each path using the received multi-path signal. This algorithm, called as OIP-FOMP, can reduce the computationally complexity of the traditional OMP algorithm and maintain accuracy in the presence of severe inter-carrier interference that exists in the time-varying UWA channels. In this algorithm, repeated inner product operations used in the OMP algorithm are removed by calculating the candidate path signature Hermitian inner product matrix in advance. Efficient QR decomposition is used to estimate the path amplitude, and the problem of reconstruction failure caused by inaccurate delay selection is avoided by optimizing the Hermitian inner product matrix. Theoretical analysis and simulation results show that the computational complexity of the OIP-FOMP algorithm is reduced by about 1/4 compared with the OMP algorithm, without any loss of accuracy.