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Designing waveforms with a Constant Modulus Constraint (CMC) to achieve desirable Slow-Time Ambiguity Function (STAF) characteristics is significantly important in radar technology. The problem is NP-hard, due to its non-convex quartic objective function and CMC constraint. Existing methods typically involve model-based approaches with relaxation and data-driven Deep Neural Networks (DNNs) methods, which face the challenge of dataimitation. We observe that the Complex Circle Manifold (CCM) naturally satisfies the CMC. By projecting onto the CCM, the problem is transformed into an unconstrained minimization problem that can be tackled using the CCM gradient descent model. Furthermore, we observe that the gradient descent model over the CCM can be unfolded as a Deep Learning (DL) network. Therefore, byeveraging the powerfulearning ability of DL and the CCM gradient descent model, we propose a Model-Adaptive Learned Network (MAL-Net) method without relaxation. Initially, we reformulate the problem as an Unconstrained Quartic Problem (UQP) on the CCM. Then, the MAL-Net is developed toearn the step sizes of allayers adaptively. This is accomplished by unrolling the CCM gradient descent model as the networkayer. Our simulation results demonstrate that the proposed MAL-Net achieves superior STAF performance compared to existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we try to design the joint waveform and passive beamforming within the context of dual-function radar–communication (DFRC) systems. Focusing on the intricate trade-off between stringent radar beampattern constraints and their desired performance, we introduce a novel manifold idea based on the alternating direction method of multipliers (ADMM) framework. Specifically, our proposed method, named DFRC-MA, could address the challenge of constant modulus waveform design in a multiple-input–multiple-output (MIMO) DFRC system. Firstly, our methodology begins by formulating the reference waveform to achieve an optimal radar beamforming pattern. Subsequently, we define the DFRC optimization problem to mitigate the multi-user interference (MUI) under the constant modulus constraint. Through a series of simulations, we evaluate the efficacy of DFRC-MA, where the integrated waveform designed by DFRC-MA exhibits superior performance over some prevalent ones. [ABSTRACT FROM AUTHOR]

We tackle the issue of designing a transmit beampattern for multiple-input multiple-output (MIMO) radar while considering its coexistence with wireless communication systems. Our goal is to design a beampattern that can steer the mainlobe and regulate its gain level toward the desired direction. The significant challenge lies in concurrently enforcing the gain constraint along with the constant modulus constraint on the radar waveform. In our work, we propose a novel approach that entails solving a series of constrained quadratic programs to achieve constant modulus at convergence. Additionally, we demonstrate that each problem in the sequence admits a closed-form solution, ensuring analytical tractability. We assess the effectiveness of our proposed Mainlobe and Interference Control (MAIC) algorithm against state-of-the-art MIMO beampattern design techniques, illustrating that MAIC attains the desired gain level while mitigating interference energy in undesired areas.

Optimizing the energy spectrum density (ESD) of a transmitted waveform can improve radar performance. The design of a time–domain constant–modulus signal corresponding to the transmitted waveform ESD is practically important because constant–modulus signals can maximize transmission power and meet the hardware requirements of radar transmitters. Here, we present a time–domain signal design under dual constraints of energy and constant modulus. The mutual information (MI)–based waveform design method is used to design transmitted waveform ESD under the energy constraint. Then, the bacterial foraging optimization algorithm (BFOA) is proposed to design the time–domain constant–modulus signal. We use minimum mean square error (MMSE) in the frequency domain as the cost function. The BFOA monotonously decreases the MMSE with increasing iterations, which makes the ESD of the time–domain constant–modulus signal close to the MI–based optimal waveform ESD. The simulation results indicate that the proposed algorithm has advantages, including insensitivity to initial phases, rapid convergence, smaller MI loss, and MMSE compared with the iterative reconstruction algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we investigate non-orthogonal multiple access (NOMA) scheme in millimeter wave (mmWave) communication to serve nonclustered multiple users. We explore a low complex design of an analog beamforming weight vector and the power requirement of users aiming to minimize the total power targeting to satisfy the spectral efficiency (SE) requirements of all users. We propose a low complex constant modulus analog beamforming (CMAB) algorithm, where we first reduce the number of signal to interference plus noise ratio (SINR) constraints, which is attained from the order of equivalent channel gain of users. Then, the nonconvex constraint of constant modulus (CM) is relaxed and semi-definite programming (SDP) is used to solve the problem. Obtained weight vector and power for all users are optimal since the rank of positive semi-definite (PSD) matrix is one. Later, CM constraint is included. Simulation results show that the proposed algorithm requires less power with minimum complexity compared to the existing research, digital beamforming NOMA and time division multiple access (TDMA) for the same SE requirements. [ABSTRACT FROM AUTHOR]

Abstract Excitation amplitude control is a critical issue regarding the shaped beam synthesis of array antennas. Ideally, excitations can have the same amplitude, and the desired beam can be achieved only by changing the phases. This method is called constant modulus synthesis, which can reduce the complexity of array antennas and is more conducive to the feeding, but it is really difficult to realize. In this paper, the authors derive a novel constant modulus beam synthesis algorithm, which uses the linear fractional semidefinite relaxation to relax the constant modulus constraints. Simulation results show that this method is stable and can maintain the excitation modulus while realizing the shaped beam.

Outstanding beamforming performance of the Multiple-Input Multiple-Output (MIMO) radar can be achieved by deploying a large number of active antenna elements. Nonetheless, this will significantly increase power consumption, circuit complexity and hardware cost. These problems can be overcome by utilizing low-resolution Digital-to-Analog Converter (DAC) components. However, MIMO radar waveforms designed under the condition of infinite-resolution DACs are usually inapplicable to systems with low-resolution DACs. Therefore, under the constraints of discrete phases, this paper proposes a MIMO radar constant modulus waveform design method based on Integrated Sidelobe-to-Mainlobe Ratio (ISMR) minimization. The Dinkelbach algorithm is first used to convert the objective function with quadratic fractional form into a subtraction form. Then, the alternating direction penalty method is employed to solve the nonconvex constant modulus discrete phase constraint problem. Finally, by comparison with other methods through numerical simulations, the behavior of the transmit beampattern and the performance of ISMR are analyzed, and the effectiveness of the method is verified.

We study the transmit waveform optimization problem in multiple-input-multiple-output (MIMO) dual-function radar-communication (DFRC) systems. A penalty-based formulation is adopted where engineering concerns on radar and communication are integrated in a weighted manner. We transform the original problem into an unconstrained formulation and propose a novel waveform synthesis algorithm via combination of multiple algorithm updates. The combination operation experimentally reaches a better objective value than without. We develop two combination strategies and invent a shrinkage-expansion line search method for monotonicity maintenance. Numerical experiments show that the proposed algorithm suffices to generate constant modulus waveforms which achieve radar and communication purposes. • Constant modulus waveform synthesis in dual-function radar-communication systems. • Shrinkage-expansion line search method to maintain objective monotonicity. • Provably convergent algorithm reaching an experimentally lower objective. • Two strategies for descent direction combination: binary and probabilistic. [ABSTRACT FROM AUTHOR]

Abstract Unimodular waveforms with good correlation properties are desired for multiple‐input‐multiple‐output radar to achieve an increased transmitting/receiving virtual aperture. In this study, a new optimisation framework is introduced to design waveforms with good correlations. It is shown that many existing waveform design problems can be incorporated into this framework. Since the considered problem is in general highly non‐linear and non‐convex, an iterative optimisation method based on majorisation‐minimisation is developed. By carefully devising the surrogate function, the only requirement is to deal with a series of simple problems, which have closed‐form solutions. The proposed algorithm can be implemented via fast Fourier transform and hence is computationally efficient. In addition, the proposed algorithm is extended to deal with spectral constraints. Numerical results demonstrate the efficiency of the proposed algorithm compared with the state‐of‐the‐art techniques.

The paper presents a modified Constant Envelope Multiplexing with Intermodulation Construction (CEMIC) technique for multiplexing signals within a single frequency band. A constant envelope signal is necessary to operate a transponder at maximum efficiency. This paper proposes a novel scheme to incorporate backwards compatibility constraints into the cost function of the existing CEMIC scheme to minimize changes in the onboard navigation system and ground receivers. The proposed scheme maximizes multiplexing efficiency by optimizing signal power sharing as per system requirements. Simulation results indicate that the proposed scheme provides 0.1% to 13.7% better efficiency than the existing CEMIC scheme, depending upon the case severity. Furthermore, the power distribution and phasing of the individual intermodulation constituent signals are optimized to minimize intra-system and inter-system interference. As a result, the proposed scheme facilitates frequency coordination with GNSS service providers. The paper also discusses the hardware performance of the proposed scheme’s composite signal. [ABSTRACT FROM AUTHOR]

Excitation amplitude control is a critical issue regarding the shaped beam synthesis of array antennas. Ideally, excitations can have the same amplitude, and the desired beam can be achieved only by changing the phases. This method is called constant modulus synthesis, which can reduce the complexity of array antennas and is more conducive to the feeding, but it is really difficult to realize. In this paper, the authors derive a novel constant modulus beam synthesis algorithm, which uses the linear fractional semidefinite relaxation to relax the constant modulus constraints. Simulation results show that this method is stable and can maintain the excitation modulus while realizing the shaped beam. [ABSTRACT FROM AUTHOR]

The phase-only null beamforming synthesis is widely used in communication, radar, and sonar. Due to the phase-only constraint (constant modulus constraint), the problem is nonconvex and NP-hard. The existing methods mainly solve the problem in an indirect way, by relaxing the problem to a more tractable form. Nevertheless, these methods either need huge computational cost or degrade the performance. To break the tradeoffs between the performance and computational complexity, a direct method is proposed without relaxation. In the proposed method, the problem is first transformed into an unconstrained problem on a complex circle manifold. Then, by deriving the gradient descent direction and the step size, a Riemannian manifold optimization-based conjugate gradient algorithm is derived to obtain the direct solution for the transformed problem. Compared with the existing methods, the proposed method can achieve 4 dB null gain reduction and 1 magnitude complexity decreasing. [ABSTRACT FROM AUTHOR]

The transmit beampattern design with constant modulus (CM) constraint is a key technical issue in Multiple-Input Multiple-Output (MIMO) radar system. The problem is non-convex and direct solution is impossible in general, due to the CM constraint. Usually, most existing methods indirectly solve this problem by relaxing it to a more tractable form. These methods usually either degrade the performance due to relaxation or consume expensive computational cost. Different from the relaxation methods, a direct method is proposed to solve the non-convex problem without relaxation. In the proposed method, the original problem is first converted to an Unconstrained Quadratic Lagrange Multiplier Problem (UQLMP) over the non-convex complex circle manifold. Then, by efficiently finding the descent direction and step size to ensure the objective function to be non-increasing, a novel Manifold Optimization-based Conjugate Gradient (MOCG) approach is derived to directly solve UQLMP. Compared with current methods, the proposed method has better performance in terms of nulling depth. [ABSTRACT FROM AUTHOR]

Unimodular waveforms with good correlation properties are desired for multiple‐input‐multiple‐output radar to achieve an increased transmitting/receiving virtual aperture. In this study, a new optimisation framework is introduced to design waveforms with good correlations. It is shown that many existing waveform design problems can be incorporated into this framework. Since the considered problem is in general highly non‐linear and non‐convex, an iterative optimisation method based on majorisation‐minimisation is developed. By carefully devising the surrogate function, the only requirement is to deal with a series of simple problems, which have closed‐form solutions. The proposed algorithm can be implemented via fast Fourier transform and hence is computationally efficient. In addition, the proposed algorithm is extended to deal with spectral constraints. Numerical results demonstrate the efficiency of the proposed algorithm compared with the state‐of‐the‐art techniques. [ABSTRACT FROM AUTHOR]

The user-centric cloud radio access network (C-RAN) is promising for significantly reducing the channel training overhead because only the intra-cluster channel state information (CSI) is required. However, the inter-cluster interference may degrade the network performance. To address this problem, we present a novel framework for the uplink of user-centric C-RANs where the interference cancellation is posed as a system of bi-unknown vectors linear equations. To solve this unusual system of equations, we propose a quasi-least squares (QLS) algorithm and analyze its robustness by exploiting the random matrix theory. We reveal the fact that QLS is very sensitive to the channel estimation error due to involving the inverse of an ill-conditioned matrix. It is well known that truncated singular value decomposition (TSVD) is an effective regularization scheme that can mitigate this ill-conditioning effect. Accordingly, we employ TSVD to further improve the robustness of QLS against the imperfect channel estimation. In addition, since the performance of the TSVD based algorithm strongly depends on the truncation parameter, a parameter-choice method using the constant modulus (CM) feature is also provided. Finally, simulation results are presented to examine the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

We consider the joint estimation of direction-of-arrival (DOA) and polarization of constant modulus (CM) signals based on an electromagnetic vector-sensor (EMVS) array. Two algebraic algorithms for canonical polyadic decomposition (CPD) with CM constraint are proposed in two scenarios, in which the source signals are fully and partially CM, respectively. The proposed algorithms use the analytic CM algorithm in the first step to calculate the source matrix, and then exploit the CPD structure of the data tensor to compute the remaining factor matrices, from which the DOA and polarization parameters can finally be obtained. Due to the algebraic nature, the proposed algorithms are faster and more stable than the optimization based algorithms, and can be used to effectively initialize the latter. We have shown that the proposed algorithms have more relaxed uniqueness conditions than unconstrained CPD, and thus can be applied in highly underdetermined cases where the number of source signals greatly exceeds that of the EMVSs. Simulation results are provided to illustrate the performance of the proposed algorithms.

In this article, we propose a new algorithm that designs a transmit beampattern for multiple-input multiple-output (MIMO) radar considering coexistence with other wireless systems. This design process is conducted by minimizing the deviation of the generated beampattern (which in turn is a function of the transmit waveform) against an idealized one while enforcing the waveform elements to be constant modulus and in the presence of spectral restrictions. This leads to a hard nonconvex optimization problem primarily due to the presence of the constant modulus constraint (CMC). In this article, we exploit the geometrical structure of CMC, i.e., we redefine this constraint as an intersection of two sets (one convex and other nonconvex). This new perspective allows us to solve the nonconvex design problem via a tractable method called iterative beampattern with spectral design (IBS). In particular, the proposed IBS algorithm develops and solves a sequence of convex problems such that constant modulus is achieved at convergence. Crucially, we show that at convergence the obtained solution satisfies the Karush–Kuhn–Tucker conditions of the aforementioned nonconvex problem. Finally, we evaluate the proposed algorithm over challenging simulated scenarios, and show that it outperforms the state-of-the-art competing methods. [ABSTRACT FROM AUTHOR]

Constant modulus algorithm (CMA) has been widely used in direction of arrival (DOA) estimation for constant modulus signals. However, CMA fails completely when dealing with array elements failure. In this paper we devise an algorithm to solve CMA fault-tolerance deficiency. The compensation of failed elements in 2D arrays is achieved by a Replace, Replicate, Reconstruct and Remove (4R) algorithm. The 4R-2D-CMA starts by replacing a failed-element signal by the nearest operating array element signal, then, after computing the covariance matrix, the corrupted rows and columns corresponding to failed elements in both elevation and azimuth are replicated from their Centro-symmetric counterparts to correct the covariance distortion. Replication step takes advantage of a special structure of two perpendicular Centro-symmetric arrays producing a Centro-Hermitian matrix. Afterwards, a 2D-CMA algorithm is used for decomposition to produce azimuth and elevation directions matrices. After decomposition, a linear phase correction is used before the covariance matrix is reconstructed. Finally, a second decomposition is used to obtain final DOAs. The number of constant modulus (CM) sources is estimated from a robust spectrogram analysis. Results for an SNR of −3 dB with 11% of elements failure show almost full recovery and hence prove the effectiveness of the novel approach. [ABSTRACT FROM AUTHOR]

Direct position determination (DPD) methods are known to outperform classical two-step localization methods under the condition of low signal-to-noise ratios and/or small number of snapshots. Additionally, they can directly exploit the prior knowledge of signal waveforms to achieve higher estimation accuracy. In this paper, we concentrate on the DPD method for locating multiple constant modulus (CM) sources based on a single moving receiving station. Both direction of arrival and Doppler frequency shift are used for source localization. First, a received array signal model with a small time delay that can incorporate the Doppler frequency information is formed. Subsequently, the corresponding maximum likelihood estimation criterion is established. An effective alternating minimization algorithm is developed to solve the optimization problem. Subsequently, we also derive the Cramér–Rao bound expressions for parameter estimation. It is proved that the CM property of the signals is useful in reducing the lower bound for location estimation. Simulation results demonstrate that the proposed method is asymptotically efficient. Moreover, it is also shown that the estimation accuracy of direct localization can be greatly increased if the CM characteristics of the radiated signals are adequately exploited. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of beampattern synthesis with sidelobe control using constant modulus weights. We specifically focus on two applications, i.e., notching and sidelobe-level (SLL) control (SLC). The considered problem is a challenging NP-hard due to the employed constant-modulus weights. Here, we convert the problem into an intermediate form by incorporating auxiliary variables and changing the form of the constant modulus. Then, we decompose the intermediate form into subproblems of single constraint each. Finally, we propose an iterative solution following the alternate direction method of multipliers (ADMM) and Proximal frameworks. The proposed solution solves the original problem by iteratively solving the subproblems in coordinated logical order. Importantly, it combines the convergence speed of ADMM and convergence property of Proximal methods. In addition, it always satisfies the constant modulus constraint. The solution has a significant contribution to mitigate interference using notching and to realize RadCom. Simulation results show that the proposed solution has a better performance in terms of computational speed, notching, and constant SLL than the previous works. [ABSTRACT FROM AUTHOR]

We present a novel convex-optimization-based solution to blind linear multiuser detection in direct-sequence code division multiple access systems. The solution is based on a convex low-rank approximation of the linearly constrained constant modulus cost function, thus guaranteeing its global minimization. Further, it can be cast as a semidefinite program, implying that it can be solved using interior-point techniques with polynomial time complexity. The solution is parameter free and is shown to be superior to existing solutions in terms of output signal-to-interference-plus-noise ratio and bit error rate, especially for a small number of samples. [ABSTRACT FROM AUTHOR]

Highlights • A novel convex-optimization-based low-rank approximation approach to the solutions of a family of problems involving constant modulus signals. • The family of problems includes the constant modulus and the constrained constant modulus, as well as the modified constant modulus and the constrained modified constant modulus. • These solutions are shown to constitute semidefinite programs (SDP), thus enabling efficient interior-point methods with polynomial time complexity. • The performance of the proposed solutions, is shown to be superior to existing blind beamforming methods. Abstract We present a novel convex-optimization-based approach to the solutions of a family of problems involving constant modulus signals. The family of problems includes the constant modulus and the constrained constant modulus, as well as the modified constant modulus and the constrained modified constant modulus. These solutions are shown to constitute semidefinite programs (SDP), thus enabling efficient interior-point methods with polynomial time complexity. The performance of the proposed solutions, demonstrated in several simulated experiments for the task of blind beamforming, is shown to be superior to existing methods. [ABSTRACT FROM AUTHOR]

We consider the design of constant-modulus probing waveforms to improve the spectral compatibility of radar systems with the congested radio frequency environments. We seek to synthesize radar probing waveforms with desired spectral shapes. We use a weighted least-squares fitting approach to formulate the spectral shaping problem. We introduce two algorithms to tackle the optimization problem we encounter. Both algorithms are devised based on cyclic approaches and have guaranteed convergence of the objective values. Moreover, the proposed algorithms can be implemented via fast Fourier transforms and, hence, are computationally efficient. Furthermore, we extend the proposed algorithms to deal with peak-to-average-power ratio and similarity constraints, which are desirable in some radar applications. Finally, we provide several numerical examples to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

We address the problem of designing a transmit beampattern for multiple-input multiple-output (MIMO) radar considering coexistence with wireless communication systems. The designed beampattern is able to manage the transmit energy in spatial directions as well as in spectral frequency bands of interest by minimizing the deviation of the designed beampattern versus a desired one under a spectral constraint as well as the constant modulus constraint. While unconstrained beampattern design is straightforward, a key open challenge is jointly enforcing the spectral constraint in addition to the constant modulus constraint on the radar waveform. A new approach is proposed in this paper, which involves solving a sequence of constrained quadratic programs such that constant modulus is achieved at convergence. Furthermore, we show that each problem in the sequence has a closed form solution leading to analytical tractability. We evaluate the proposed beampattern with interference control (BIC) algorithm against the state-of-the-art MIMO beampattern design techniques and show that BIC achieves closeness to an idealized beampattern along with desired spectral shaping. [ABSTRACT FROM AUTHOR]

This paper deals with the robust waveform design of multiple-input multiple-output radar to improve target detectability embedded in signal-dependent interferences. Two iterative algorithms with ensuring convergence properties are introduced to maximize the worst case signal-to-interference-plus-noise ratio (SINR) over steering matrix mismatches under the constant modulus and similarity constraints. Each iteration of the proposed algorithms splits the high-dimensional problem into multiple one dimensional problems, to which the optimal solutions can be found in polynomial times. Numerical examples are provided to assess the capabilities of the proposed techniques in comparison with the existing methods in terms of the SINR and the computational times for both the continuous and discrete phase cases of the probing signal. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of minimum peak sidelobe transmit beampattern design for colocated multiple-input multiple-output radar systems. Two new methods are proposed to achieve it via designing constant modulus (CM) waveforms directly: One is to maximize the ratio of the minimum mainlobe level to the peak sidelobe level (PSL) without specifying pattern masks, and another is to minimize PSL under the mainlobe ripple and unspecified waveform modulus constraints. The resultant optimization problems are difficult to solve due to the coupled numerator and denominator of the quadratic fractional programming problem formulation in the former and double-sided quadratic constraints and unknown waveform modulus in the latter. For the former, we decouple the numerator and denominator by equivalent transformation and introduction of boundary-type auxiliary variables in order that feasible methods are derived to tackle them independently and efficiently. For the latter, we simplify the coupled double-sided quadratic constraints on the same waveform vector into those on different single auxiliary variables to tackle the corresponding nonconvex optimization problem. Numerical examples show that the proposed algorithms can attain sufficient low peak sidelobe beampattern levels under the CM constraints. [ABSTRACT FROM AUTHOR]

This paper proposes a blind carrier frequency offset (CFO) estimation method for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems, using constant modulus signaling. The proposed scheme is based on a robust cost-function, which deviates from the common assumption that the channel frequency response slowly varies either in time or frequency domain. The proposed method adopts a cost-function similar to the Godard’s method for blind channel equalization. Using Monte Carlo simulations, the proposed method is shown to offer a superior performance compared to prominent existing methods, in a practical optical link scenario. Also, we show that the proposed cost-function can be approximated and expressed in a closed-form in such a way that the CFO estimate is obtained using only three trial values. [ABSTRACT FROM AUTHOR]

Multiple-input multiple-output (MIMO) radar systems allow each antenna element to transmit a different waveform. This waveform diversity can be exploited to enhance the beampattern design, in particular, effective management of radar radiation power in directions of interest. We address the problem of designing a beampattern for MIMO radar, which in turn is determined by the transmit waveform. While unconstrained design is straightforward, a key open challenge is enforcing the constant modulus constraint on the radar waveform. It is well known that the problem of minimizing deviation of the designed beampattern from an idealized one subject to the constant modulus constraint constitutes a hard nonconvex problem. Existing methods that address constant modulus invariably lead to a stiff tradeoff between analytical tractability (achieved by relaxations and approximations) and realistic design that exactly achieves constant modulus but is computationally burdensome. A new approach is proposed in our paper, which involves solving a sequence of convex equality constrained quadratic programs, each of which has a closed form solution and such that constant modulus is achieved at convergence. We further prove that the converged solution satisfies the Karush–Kuhn–Tucker optimality conditions of the aforementioned hard nonconvex problem. We evaluate the proposed successive closed forms (SCF) algorithm against the state-of-the art MIMO beampattern design techniques in both narrowband and wideband setups and show that the SCF breaks the tradeoff between desirable performance and the associated computation cost. [ABSTRACT FROM PUBLISHER]

In this paper, a new unsupervised carrier frequency offset (CFO) estimation method is proposed for orthogonal frequency division multiplexing (OFDM) systems using constant modulus constellations. Under the assumption that the channel variation is slow within two adjacent OFDM symbols, the influence of the channel on corresponding subcarriers of the two OFDM symbols will be the same. Utilizing this feature, a robust cost function is formulated based on covariance fitting criterion between two nearby OFDM symbols, and the CFO is estimated by minimizing this objective function. The mean square error (MSE) and bit error rate (BER) performance of the proposed covariance-fitting-based CFO estimation method is compared with that of the prominent conventional estimation schemes under noisy multipath channels with high delay spreads and Doppler spreads. The effect of channel length on the performance of the proposed estimator is also investigated. Based on Monte Carlo simulations, it is shown that the proposed method is robust under different channel conditions and provides more accurate CFO estimates. [ABSTRACT FROM PUBLISHER]

As for the single-channel overlapped signals, in which the modulation parameters of the component signals are identical or similar, it is still a great challenge to extract the component signals. Aiming at this problem, a single-channel blind source separation (SCBSS) algorithm, constrained by constant modulus, is proposed for the overlapped Gaussian minimum shift keying (GMSK) signals and this algorithm also applies to other overlapped signals with constant modulus (CM), such as binary phase shift keying (BPSK) signals and quadrature phase shift keying(QPSK) signals. By tracking the channels of the component signals, the algorithm can effectively estimate their symbol sequences. Simulation results show that the proposed algorithm can work more robustly and reduce the frame error rate (FER), comparing with the competing algorithms. [ABSTRACT FROM PUBLISHER]

Waveform design is a pivotal component of the fully adaptive radar construct. In this paper, we consider waveform design for radar space time adaptive processing (STAP), accounting for the waveform dependence of the clutter correlation matrix. Due to this dependence, in general, the joint problem of receiver filter optimization and radar waveform design becomes an intractable, nonconvex optimization problem, Nevertheless, it is, however, shown to be individually convex either in the filter or in the waveform variables. We derive constrained versions of a) the alternating minimization algorithm, b) proximal alternating minimization, and c) the constant modulus alternating minimization, which, at each step, iteratively optimizes either the STAP filter or the waveform independently. A fast and slow time model permits waveform design in radar STAP, but the primary bottleneck is the computational complexity of the algorithms. [ABSTRACT FROM PUBLISHER]

An unscented Kalman filter-based constant modulus adaptation algorithm (UKF-CMA) is proposed for blind uniform linear beamforming. The proposed algorithm is obtained by first developing a model of the constant modulus (CM) criterion and then fitting that model into the Kalman filter-style state space model by using an auxiliary parameter. The proposed algorithm does not require a priori information about the process noise and measurement noise covariance matrices and hence it can be applied readily. Simulation results demonstrate that the proposed algorithm offers improved performance compared to the recursive least square-based CM (RLS-CMA) and least-mean square-based CM (LMS-CMA) algorithms for adaptive blind beamforming. [ABSTRACT FROM AUTHOR]

To improve the blind equalization performance for complex noncircular signals, the widely linear (WL) filtering theory is deeply analyzed. The paper takes advantage of simplicity and robustness of the constant modulus (CM) criterion to construct the reduced complexity widely linear blind equalizer. A reduced complexity widely linear recursive least mean square CM blind equalization algorithm is produced. The new algorithm directly uses the real and imaginary parts of received signals as input of the equalizer, thus obtains the full second-order information of the real and imaginary parts. The proposed scheme takes the real operation instead of complex operation and obtains the computational complexity which is just a few more than the traditional linear blind equalization algorithm and much less than the standard WL filter. Simulation results show that the new algorithm can simultaneously decrease the residual inter-symbol interference (ISI) and symbol error rate when compared with the traditional blind equalization algorithms. [ABSTRACT FROM AUTHOR]

Multiple-input multiple-output (MIMO) radar waveform diversity design has received much attention, but most of the existing waveforms lack a large time-bandwidth product and are difficult to be implemented by real-life hardwares. In this paper, we propose a large time-bandwidth product waveform diversity design scheme based on chirp rate diversity for MIMO radar. The proposed scheme can generate a large number of pseudo-orthogonal waveforms that have large time-bandwidth product, constant modulus, no range-Doppler coupling target response, good orthogonality, and Doppler tolerance. In addition, the waveforms are orthogonal on both transmit and receive. The waveform performance is in-depth analyzed with the correlation and ambiguity functions. Furthermore, the corresponding frequency demodulation in the receiver is also discussed. Numerical results validate the superiorities of the designed waveforms in MIMO radar applications. [ABSTRACT FROM PUBLISHER]

Based on the constant modulus criterion, a new Widely Linear (WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance for complex-valued noncircular signals. The new algorithm takes advantage of the WL filtering theory by taking full use of second-order statistical information of the complex-valued noncircular signals. Therefore, the weight vector contains the complete second-order information of the real and imaginary parts to decrease the residual inter-symbol interference effectively. Theoretical analysis and simulation results show that the proposed scheme can significantly improve the equalization performance for complex-valued noncircular signals compared with traditional blind equalization algorithms. [ABSTRACT FROM AUTHOR]

To reducing the degradation of the beamforming caused by the impulsive stable noise, a new constant modulus (CM) algorithm was proposed based on the maximum matching of the probability density functions between the desired signal and output signal inspired by the information adaptive learning. The Parzen kernel method was utilized for the probability density function estimation and the weight of the beamforming was updated by the stochastic steepest gradient. Computer simulations show that the proposed CM algorithm has higher output signal to interfere noise ratio and faster convergence than the conventional CM beamforming in stable distribution noise. [ABSTRACT FROM AUTHOR]

We consider the problem of channel estimation for amplify-and-forward (AF) two-way relay networks (TWRNs). Most works on this problem focus on pilot-based approaches which impose a significant training overhead that reduces the spectral efficiency of the system. To avoid such losses, we propose blind channel estimation algorithms for AF TWRNs that employ constant-modulus (CM) signaling. Our main algorithm is based on the deterministic maximum likelihood (DML) approach. Assuming M-PSK modulation, we show that the resulting estimator is consistent and approaches the true channel with high probability at high SNR for modulation orders higher than 2. For BPSK, however, the DML algorithm performs poorly and we propose an alternative algorithm that yields much better performance by taking into account the BPSK structure of the data symbols. For comparative purposes, we also investigate the Gaussian maximum-likelihood (GML) approach which treats the data symbols as Gaussian-distributed nuisance parameters. We derive the Cramer-Rao bound and use Monte Carlo simulations to investigate the mean squared error (MSE) performance of the proposed algorithms. We also compare the symbol-error rate (SER) performance of the DML algorithm with that of the training-based least-squares (LS) algorithm and demonstrate that the DML offers a superior tradeoff between accuracy and spectral efficiency. [ABSTRACT FROM PUBLISHER]