This paper proposes a novel method for estimating the direction of arrival (DOA) in a time-modulated linear array (TMLA) based on the Golay-paired Hadamard (GPH) matrix. The objective is to address challenges presented by conventional TMLAs of limitations in the directional range due to the energy dispersion of radiation. To tackle this challenge, we construct a complete complementary set through the recursive derivation of the GPH matrix. From this set, we select mutually paired sequences that maintain an equal number of activated radio frequency switches, thereby designing an optimized time-modulated sequence. Theoretical analysis demonstrates that the proposed method can form an approximately flat sum beam across the entire spatial domain, thus facilitating an expansion of the directional measurement range. Furthermore, the DOA estimation is utilized by the multiple signal classification (MUSIC) algorithm. Simulation results validate the effectiveness of the proposed method. Specifically, the root mean square error is reduced by about$2.5^{\circ }$in the case of$\rm{SNR}$of$-10 \rm{ dB}$.

Accurate acquisition of channel state information (CSI) is essential for fully harnessing the potential of stacked intelligent metasurfaces (SIMs) in communication systems. In this paper, we address the channel estimation (CE) problem in SIM-based multi-user (MU) millimeter-wave (mmWave) near-field communication systems. To address the severe path loss and blockage in mmWave communication systems, many meta-atoms are typically integrated into each layer of the SIM. Then, the number of radio frequency (RF) chains at the base station (BS) is fewer than that of meta-atoms per layer, resulting in an underdetermined problem. Additionally, the increase in the number of meta-atoms in each layer expands the SIM’s near-field region, leading to the user equipment (UEs) being mostly situated in this region, necessitating precise modeling of the channel under the spherical wavefront assumption. To address these issues, we introduce a compressed sensing (CS)-based CE protocol to tackle the underdetermined problem. In contrast to the traditional CS-based estimation framework, we investigate a polar-domain channel representation to tackle the severe energy spread effect of the classical angular-domain channel representation in near-field communication systems. Specifically, we design a novel polar-domain transform matrix for uniform planar arrays (UPAs), thereby transforming the CE problem into a sparse recovery task of the paths’ support set and complex gains. To overcome the limitations of the sparse Bayesian learning (SBL) framework in tackling high-dimensional dictionaries, we propose a low-complexity polar-domain SBL (LCPD-SBL) algorithm, which significantly reduces computational complexity without compromising estimation accuracy. Numerical simulation results demonstrate that the proposed polar-domain transform matrix yields a better estimation accuracy than traditional angular-domain approaches. Additionally, the proposed LCPD-SBL algorithm can be faster than existing SBL methods by up to 4× while sustaining the same estimation performance.

Flexible intelligent metasurface (FIM) technology has emerged as a promising solution for enhancing wireless communication performance. In contrast to traditional rigid reconfigurable intelligent surfaces (RIS), an FIM consists of an array of electromagnetic (EM) elements, each capable of flexibly adjusting its position along the direction perpendicular to the surface to collaboratively morph the surface shape. In this paper, an optimization problem for maximizing the weighted sum-rate (WSR) in an FIM-aided multicell multi-user multiple-input single-output (MU-MISO) system is investigated. We jointly optimize the beamforming at the base station (BS), the phase shift matrix, and the FIM surface shape. To address this problem, we propose an efficient alternating optimization framework, where we employ the weighted minimum mean square error (WMMSE) method to reformulate the problem and the block coordinate descent (BCD) algorithm to iteratively update the variables. Specifically, we utilize the Riemannian Conjugate Gradient (RCG) algorithm to optimize the phase shift matrix, and the projected gradient descent (PGD) method to optimize the FIM surface shape. Additionally, the optimal beamforming vectors are obtained in closed form. Finally, simulation results demonstrate the superiority of FIM over conventional RIS in various scenarios.

Stacked intelligent metasurfaces (SIMs), emerging as a revolutionary programmable electromagnetic architecture, have demonstrated unprecedented capabilities in manipulating wireless propagation environments. However, the existing research on SIM-aided downlink communication does not consider the fairness among users. Therefore, this paper studies a SIM-aided hybrid analog-digital system, which aims to fairly guarantee the communication quality of each user while minimizing the transmission power. The hybrid system avails of a SIM for enhancing the communication channel with digital precoding to effectively suppress the interference between users. To this end, we formulate a transmit power minimization problem under quality-of-service constraints, solved by an efficient alternating optimization (AO) algorithm. Simulation results demonstrate that compared to conventional fully digital multiuser multiple-input single-output (MISO) systems, the proposed SIM-aided hybrid system requires 6.93 dBm less transmit power under the same signal-to-interference-plus-noise ratio (SINR) constraints for users. This work reveals the SIM’s powerful wave-based beamforming capabilities, providing effective solutions for energy-efficient networks with low hardware cost.

As spectrum congestion intensifies in wireless communication, efficient spectrum utilization through advanced sensing techniques has become increasingly important. This paper proposes a joint carrier frequency and two-dimensional (2-D) Direction of Arrival (DOA) estimation algorithm with signal recovery, utilizing identical-delay channels and sub-Nyquist sampling rates with a Uniform Rectangular Array (URA). Compared to multi-coset structures, the proposed method places identical-delay channels only along the edges of the URA, eliminating the need for additional ADCs and reducing hardware cost. Moreover, by leveraging tensor techniques, the spatial structure of the array is preserved, and the parameter pairing problem is avoided, leading to higher precision in estimation. Simulation results demonstrate the superior performance of the proposed method.

Unmanned aerial vehicle (UAV) communication plays a pivotal role in achieving ubiquitous connectivity for the sixth-generation (6G) networks. Accurate and real-time direction of arrival (DOA) estimation is crucial for beamforming in UAV communication systems. However, the existing high-precision DOA estimation algorithms encounter high computational complexity when being implemented on a UAV with the on-board signal processing constraints. To tackle this issue, a hybrid optical-electric neural network (HOENN) is utilized for DOA estimation, which is capable of generating angular spectrum based solely on amplitude observation. The proposed HOENN consists of two components: a stacked intelligent metasurfaces (SIM)-enabled diffractive neural network, which is mounted on UAV and can process signals in the wave domain at the speed of light with low energy consumption, and a fully connected layer for processing the received amplitude signal. Finally, the simulation results validate that the HOENN achieves significant performance gain compared to the conventional beamforming (CBF) method, albeit with its lower cost and RF-related power consumption.

Stacked intelligent metasurfaces (SIMs), composed of a multi-layered structure, have emerged as a powerful computing tool and analog signal processing platform for enabling task-oriented semantic communications (SemCom). However, SIMs lack nonlinear inference capabilities, thus motivating the emergence of the hybrid optical-electronic neural network (HOENN) that cascades a SIM and an electronic neural network (ENN). In this work, we investigate a disaster recognition taskoriented SemCom setting by leveraging the HOENN technology. Specifically, the HOENN is made of an optical neural network (ONN) using SIM mounted on an unmanned aerial vehicle (UAV) and a shallow ENN at the ground receiving station (GRS). The SIM automatically processes semantic information modulated on electromagnetic waves, with reduced energy consumption and ultrafast processing speed. At the GRS, the energy signals are processed by the shallow ENN to enhance the system's inference capability. The aim is to recognize the disaster according to the captured geomorphic images. To this end, we utilize a stochastic gradient descent algorithm to train the HOENN efficiently to minimize the cross-entropy between the recognized and actual semantics. Numerical results show that the HOENN surpasses the performance of using either ONN or ENN alone, achieving$\mathbf{9 7 \%}$recognition accuracy.

Accurate acquisition of channel state information is crucial for unlocking the potential of stacked intelligent metasurface (SIM)-assisted communication systems. This paper investigates the channel estimation (CE) problem in SIM-assisted multi-user (MU) millimeter-wave (mmWave) near-field communication systems. We aim to solve the underdetermined problem caused by the large-scale deployment of nearly-passive meta-atoms, where the number of antennas at the base station (BS) is smaller than the number of meta-atoms on the last layer of the SIM. Specifically, we first design a polar-domain transform matrix for uniform planar arrays (UPA) to convert the near-field channel into a polar-domain representation. Moreover, we leverage the channel sparsity in the polar domain and the sparse Bayesian learning (SBL) technique to recover the channel parameters. Additionally, a covariance-free expectation maximization (CoFEM) algorithm is introduced to reduce the computational complexity of the SBL. Numerical simulation results indicate that in SIM-assisted near-field mmWave communications, the algorithms based on the proposed polar-domain transform matrix outperform existing angular-domain approaches. Moreover, the CoFEM algorithm significantly reduces the computational complexity compared to SBL methods.

Reconfigurable intelligent surface (RIS) technology holds immense potential for increasing the performance of wireless networks. Therefore, RIS is also regarded as one of the solutions to address communication challenges in high-mobility scenarios, such as Doppler shift and fast fading. This paper investigates a high-speed train (HST) multiple-input single-output (MISO) communication system aided by a RIS. We propose a block coordinate descent (BCD) algorithm to jointly optimize the RIS phase shifts and the transmit beamforming vectors to maximize the channel gain. Numerical results are provided to demonstrate that the proposed algorithm significantly enhances the system performance, achieving an average channel gain improvement of 15 dB compared to traditional schemes. Additionally, the introduction of RIS eliminates outage probability and improves key performance metrics such as achievable rate, channel capacity, and bit error rate (BER). These findings highlight the critical role of RIS in enhancing HST communication systems.

The increase in antenna apertures and transmission frequencies in next-generation wireless networks is catalyzing advancements in near-field communications (NFC). In this paper, we investigate secure transmission in near-field multi-user multiple-input single-output (MU-MISO) scenarios. Specifically, with the advent of extremely large-scale antenna arrays (ELAA) applied in the NFC regime, the spatial degrees of freedom in the channel matrix are significantly enhanced. This creates an expanded null space that can be exploited for designing secure communication schemes. Motivated by this observation, we propose a near-field dynamic hybrid beamforming architecture incorporating artificial noise, which effectively disrupts eavesdroppers at any undesired positions, even in the absence of their channel state information (CSI). Furthermore, we comprehensively analyze the dynamic precoder’s performance in terms of the average signal-to-interference-plus-noise ratio, achievable rate, secrecy capacity, secrecy outage probability, and the size of the secrecy zone. In contrast to far-field secure transmission techniques that only enhance security in the angular dimension, the proposed algorithm exploits the unique properties of spherical wave characteristics in NFC to achieve secure transmission in both the angular and distance dimensions. Remarkably, the proposed algorithm is applicable to arbitrary modulation types and array configurations. Numerical results demonstrate that the proposed method achieves approximately 20% higher rate capacity compared to zero-forcing and the weighted minimum mean squared error precoders.

Reconfigurable intelligent surface (RIS) have emerged as a transformative technology capable of reshaping wireless channels to significantly enhance the efficiency of wireless communication networks in a cost-effective manner. However, the prevailing RIS reflection coefficient optimization scheme presents a significant challenge due to its dependence on channel state information (CSI), which results in excessive pilot overhead and error propagation. To address this issue, this paper proposes a probability update (PU) based dynamic codebook for RIS-aided multiuser multiple-input single-output (MU-MISO) communication systems. Specifically, we implement a learning-from-training strategy that dynamically updates the codebook independently of CSI. This process involves assigning a probability vector to the RIS reflecting elements to generate the codebook, with subsequent iterative updates to the probability vector based on codebook training outcomes. Moreover, numerical results illustrate that the proposed scheme can effectively cater to diverse system by flexibly balancing the training overhead and system performance. Finally, despite channel estimation errors, the proposed scheme outperforms passive beamforming and the existing codebook schemes, while significantly reducing training overhead and implementation complexity.

With the increase of antenna aperture and the utilization of high frequencies, near-field communications (NFC) have emerged as a critical trend in next-generation wireless networks. This paper examines the security of NFC by designing a dynamic precoder for secure multi-user multiple-input single-output (MU-MISO) transmission, which boosts signal quality of legitimate users, while mitigating inter-user interference and distorting the signals for eavesdroppers at any undesired position. Utilizing the array response control (ARC) framework, we derive a closed-form expression of the dynamic precoder while satisfying power constraints. Furthermore, we analyze the key performance metrics of the closed-form dynamic precoder such as average signal-to-interference-plus-noise ratio (SINR), achievable rate, and secrecy capacity. The numerical results demonstrate that the proposed precoder leveraging the inherent spherical wavefront features in NFC significantly enhances the secure transmission performance across both angular and radial dimensions. Additionally, the proposed dynamic precoder can be readily applied to diverse modulation schemes and array configurations while maintaining low computational complexity.

This paper addresses key challenges caused by high sampling rates in wideband joint spectrum sensing applications. A joint Direction of Arrival (DOA) and frequency estimation algorithm is proposed by utilizing the Cross-Covariance Matrix (CCM) constructed from the outputs of an efficient undersampling array receiver with multiple elements, only one of which is connected with multiple time-delay branches. In contrast to previous autocorrelation-based methods, the proposed method reduces the impact of noise and doubles the maximum unit time-delay, resulting in improved estimation performance. Additionally, it does not impose restrictions on the number of array sensors and time-delay channels, which allows for more flexibility in the allocation of resources for the receiver. In the simulation, the proposed algorithm demonstrates outstanding performance.

In the context of perceiving spatial information, researchers extensively investigate the use of large-scale arrays due to their numerous advantages such as high precision and resolution, as well as increased degrees of freedom. However, large-scale arrays may be impractical in certain applications due to the prohibitive hardware cost. To address this bottleneck, a switch-element array structure composed of a switch network offers an appealing low-cost alternative by multiplexing the Radio Frequency (RF) chains. With this novel array architecture, we explore the direction-of-arrival (DOA) estimation problem and examine the inherent signal structures. Subsequently, two DOA estimation algorithms based on a dynamic-dictionary sparse representation are developed, namely the Jointly-Selected Orthogonal Matching Pursuit (JSOMP) algorithm and the Auxiliary Variable Joint Alternating Optimization (AVJAO) algorithm. The performance of the proposed algorithms is demonstrated through simulation results.

Stacked intelligent metasurfaces (SIM) represents an advanced signal processing paradigm that enables over-the-air processing of electromagnetic waves at the speed of light. Its multi-layer structure exhibits customizable increased computational capability compared to conventional single-layer reconfigurable intelligent surfaces and metasurface lenses. In this paper, we deploy SIM to improve the performance of multi-user multiple-input single-output (MISO) wireless systems with low complexity transmit radio frequency (RF) chains. In particular, an optimization formulation for the joint design of the SIM phase shifts and the transmit power allocation is presented, which is efficiently solved via a customized deep reinforcement learning (DRL) approach that continuously observes pre-designed states of the SIM-parametrized smart wireless environment. The presented performance evaluation results showcase the proposed method's capability to effectively learn from the wireless environment while outperforming conventional precoding schemes under low transmit power conditions. Finally, a whitening process is presented to further augment the robustness of the proposed scheme.

Intelligent surfaces represent a breakthrough technology capable of customizing the wireless channel cost-effectively. However, the existing works generally focus on planar wavefront, neglecting near-field spherical wavefront characteristics caused by large array aperture and high operation frequencies in the terahertz (THz). Additionally, the single-layer reconfigurable intelligent surface (RIS) lacks the signal processing ability to mitigate the computational complexity at the base station (BS). To address this issue, we introduce a novel stacked intelligent metasurfaces (SIM) comprised of an array of programmable metasurface layers. The SIM aims to substitute conventional digital baseband architecture to execute computing tasks with ultra-low processing delay, albeit with a reduced number of radio-frequency (RF) chains and low-resolution digital-to-analog converters. In this paper, we present a SIM-aided multiuser multiple-input single-output (MU-MISO) near-field system, where the SIM is integrated into the BS to perform beamfocusing in the wave domain and customize an end-to-end channel with minimized inter-user interference. Finally, the numerical results demonstrate that near-field communication achieves superior spatial gain over the far-field, and the SIM effectively suppresses inter-user interference as the wireless signals propagate through it.

This paper focuses on the wideband frequency invariant (FI) deterministic beamformer design problem for mitigating beam squint and presents a spatial response variation (SRV)-constrained array response control (ARC) synthesis approach. By regarding the SRV matrix as the covariance matrix of an extra virtual colored noise, we extend the ARC-based narrowband beampattern synthesis techniques to wide band FI scenarios. Furthermore, we introduce the FI maximum magnitude response (FI-MMR) based design principle, which maximizes the array magnitude response at the main-beam direction on the reference frequency. Based on this principle, we present an iterative FI beampattern synthesis algorithm under arbitrary array configurations. Simulation results show the effectiveness of the proposed algorithm in comparison with several popular FI beampattern synthesis techniques.

Reconfigurable intelligent surface (RIS) provides a new electromagnetic response control solution, which can reshape the characteristics of wireless channels. In this paper, we propose a novel environment-aware codebook protocol for RIS-assisted multi-user multiple-input single-output (MU-MISO) systems. Specifically, we first introduce a channel training protocol which consists of off-line and on-line stages. Secondly, we propose an environment-aware codebook generation scheme, which utilizes the statistical channel state information and alternating optimization method to generate codewords offline. Then, in the on-line stage, we use these pre-designed codewords to configure the RIS, and the optimal codeword resulting in the highest sum rate is adopted for assisting in the downlink data transmission. Thirdly, we analyze the theoretical performance of the proposed protocol considering the channel estimation errors. Finally, numerical simulations are provided to verify our theoretical analysis and the performance of the proposed scheme.

As a promising non-password authentication technology, radio frequency (RF) fingerprinting can greatly improve wireless security. Recent work has shown that RF fingerprinting based on deep learning significantly outperforms conventional approaches. However, this superiority relies largely on using plenty of labeled data for supervised learning, whereas training deep neural networks on a small dataset generally falls into overfitting, resulting in performance degradation. Considering that it is often easier to obtain enough unlabeled data in practice, we leverage deep semisupervised learning for RF fingerprinting, which largely relies on a composite data augmentation scheme specifically designed for wireless communication signals, combined with two popular techniques: 1) consistency-based regularization and 2) pseudo-labeling. Experimental results on both simulated and real-world datasets demonstrate that our proposed method for semisupervised RF fingerprinting is far superior to other competing ones, and it achieves remarkable performance almost close to that of fully supervised learning, with a very limited number of examples available.

The user-centric cell-free network has emerged as an appealing technology to improve the wireless communication’s capacity of the Internet of Things (IoT) networks thanks to its ability to eliminate intercell interference effectively. However, the cell-free network inevitably brings in higher hardware cost and backhaul overhead as a larger number of base stations (BSs) are deployed. Additionally, severe channel fading in high-frequency bands constitutes another crucial issue that limits the practical application of the cell-free network. In order to address the above challenges, we amalgamate the cell-free system with another emerging technology, namely reconfigurable intelligent surface (RIS), which can provide high spectrum and energy efficiency with low hardware cost by reshaping the wireless propagation environment intelligently. To this end, we formulate a weighted sum-rate (WSR) maximization problem for RIS-assisted cell-free systems by jointly optimizing the BS precoding matrix and the RIS reflection coefficient vector. Subsequently, we transform the complicated WSR problem to a tractable optimization problem and propose a distributed cooperative alternating direction method of multipliers (ADMMs) to fully utilize parallel computing resources. Inspired by the model-based algorithm unrolling concept, we unroll our solver to a learning-based deep distributed ADMM (D2-ADMM) network framework. To improve the efficiency of the D2-ADMM in distributed BSs, we develop a monodirectional information exchange strategy with a small signaling overhead. In addition to benefiting from domain knowledge, D2-ADMM adaptively learns hyperparameters and nonconvex solvers of the intractable RIS design problem through data-driven end-to-end training. Finally, numerical results demonstrate that the proposed D2-ADMM achieves around 210% improvement in capacity compared with the distributed noncooperative algorithm and almost 96% compared with the centralized algorithm.

Reconfigurable intelligent surface (RIS) provides a new electromagnetic response control solution, which can proactively reshape the characteristics of wireless channel environments. In RIS-assisted communication systems, the acquisition of channel state information (CSI) and the optimization of reflecting coefficients constitute major design challenges. To address these issues, codebook-based solutions have been developed recently, which, however, are mostly environment-agnostic. In this paper, a novel environment-aware codebook protocol is proposed, which can significantly reduce both pilot overhead and computational complexity, while maintaining expected communication performance. Specifically, first of all, a channel training framework is introduced to divide the training phase into several blocks. In each block, we directly estimate the composite end-to-end channel and focus only on the transmit beamforming. Second, we propose an environment-aware codebook generation scheme, which first generates a group of channels based on statistical CSI, and then obtains their corresponding RIS configuration by utilizing the alternating optimization (AO) method offline. In each online training block, the RIS is configured based on the corresponding codeword in the environment-aware codebook, and the optimal codeword resulting in the highest sum rate is adopted for assisting in the downlink data transmission. Third, we analyze the theoretical performance of the environment-aware codebook-based protocol taking into account the channel estimation errors. Finally, numerical simulations are provided to verify our theoretical analysis and the performance of the proposed scheme. In particular, the simulation results demonstrate that our protocol is more competitive than conventional environment-agnostic codebooks.

This article presents an accurate phase response control (APRC) algorithm to realize directional modulation (DM), improving the physical layer security of Internet of Things (IoT) networks. Specifically, the concept of normalized array response control is developed to realize the phase response control, and the designed weight vector is constructed as the sum of an initial weight vector and an appended weight vector. The precondition of precise phase response control is theoretically derived, and a geometric interpretation of phase response adjustment is given. The APRC algorithm can derive an analytical solution to realize the precise phase response control and normalized magnitude response control jointly, and the computational complexity of the APRC algorithm is much lower than the existing approaches. Moreover, a flexible DM scheme based on the APRC algorithm is presented to realize the specific PSK symbol synthesis. Different from the existing works that are only feasible for the single direction PSK modulation design, the APRC algorithm is applicable for the more general multipath and quasistatic block Rayleigh channels. The synthesis results with fixed and random initial weights are illustrated to show the wide applicabilities of the APRC algorithm, and the bit error rate simulations are given to validate the APRC algorithm.

Reconfigurable intelligent surfaces (RISs) are capable of enhancing the capacity of wireless networks at a low cost. In practical RIS-assisted communication systems, the acquisition of channel state information (CSI) and RIS reflection optimization constitute a pair of challenges. In this paper, a low-complexity channel estimation and passive beamforming design is proposed.First of all, we conceive a low-complexity framework for maximizing the achievable rate of RIS-assisted multiple-input multiple-output (MIMO) systems having discrete phase shifts at each RIS element. In contrast to existing solutions, the proposed arrangement partitions the channel training stage into several phases, where the RIS reflection coefficients are pre-designed and the effective superposed channel is estimated instead of separately training the source-destination and source-RIS-destination links. Based on this, the active beamformer can be designed at low complexity and the RIS reflection optimization is performed by selecting that one from the pre-designed training set which maximizes the achievable rate.Secondly, we propose novel techniques for generating the training set of RIS reflection coefficients. The theoretical performance of the proposed scheme is analyzed and compared to the optimal RIS configuration.Finally, our simulation results demonstrate that the proposed framework is more competitive than its existing counterparts when relying on imperfect CSI, especially for rapidly time-varying channels having short channel coherence time.

This paper presents a beampattern synthesis scheme based on the single-point array response control with minimum pattern deviation (SPARC-MPD) method. The central concept of SPARC-MPD stems from adaptive array theory, and a closedform expression of the designed weight vector is devised. Comparing to the state-of-the-art methods like the accurate array response control (A2RC) approach, the SPARC-MPD method addresses the pattern distortion issue. Moreover, the SPARC-MPD method can realize accurate magnitude response control at one single direction and minimize the pattern deviation at any other direction simultaneously, leading to a faster convergence speed. Simulation results show the effectiveness of the SPARC-MPD method and the efficiency of the pattern synthesis scheme.

Recently, dimensionality reduction for radiometric identification has attracted more attention. Previous research works generally considered dimensionality reduction and radio fingerprint classification separately, which resulted in poor performance. The reason is that the feature set after dimensionality reductions may not be suitable for classifier. In this letter, a new radiometric identification method based on combined optimization of dimensionality reduction and fingerprint classification is presented. The proposed method attempts to find an optimal dimension-reducing projection matrix by minimizing the classification error and maximizing the quadratic mutual information between the reduced low-dimensional features and the class label simultaneously. Since both the uncertainty of the true class label of the reduced low-dimensional features and the classification error of the classifier are considered, the proposed method can obtain better results in radiometric identification applications. Experiments on real data sets demonstrate that the proposed method not only outperforms the other methods with a higher accuracy of radiometric identification, but also has a better robustness against noises. The experimental results indicate that the proposed method can identify six emitters made by three different manufacturers with the classification accuracy over 95.08%.

The serial concatenated convolutional code (SCCC) structure of Turbo code shows excellent decoding performance in the region of moderate-to-high signal-noise-ratio (SNR), which has been widely applied to many fields, such as deep space communication and so on. So, the recognition of SCCC turbo code is very important in the cognitive radio and information interception. We firstly estimated the parameters of outer encoder by Gaussian elimination and Euclidean algorithm. Then, the proposed method exploits the invariance property between the original data and interleaved data. Parameters of interleaver can be estimated easily by calculating the correlation between the check bits and the data. The computer simulations show that the proposed method has good performance when errors exist in the interception data.

In this study, the problem of estimating the spreading waveform of long-code direct sequence spread spectrum (DSSS) signals is considered. A novel spreading waveform estimation method based on a missing data model is proposed. By showing that the long-code DSSS signal can be equivalently represented as a short-code DSSS signal with missing data, the spreading waveform estimation problem can be viewed as a low-rank matrix approximation problem with missing data that can be approximately solved by the existing optimisation methods. To evaluate the performance of the author's proposed estimator, the authors also derive the Cramer–Rao lower bound (CRB) on the mean square error of spreading waveform estimators. The simulation results demonstrate that the proposed estimator approaches the CRB and provides significant performance improvement compared with the existing estimators in the case of low signal-to-noise ratio situations.