一种基于半定松弛规划的到达角定位方法

针对基于到达角的目标辐射源定位系统,提出了一种基于半定松弛规划的定位方程求解方法。主要思想是将噪声元素添加为有用参数,以增加定位方程凸优化的灵活性。先将目标定位的初始非凸二次优化问题转化为非凸半定优化问题,然后松弛到凸优化问题,再对凸优化问题进行求解作为初始复杂问题的近似解,从而得出目标位置估计。文中采用计算机仿真结果证明了这种解法的有效性。     

基于半定松弛的长码DSSS信号扩频波形估计

针对非合作通信中的长码DSSS信号,提出了一种基于半定松弛的扩频波形估计方法,并在确定信号模型下推导了扩频波形估计的CRB.首先推导了长码DSSS信号扩频波形的极大似然估计,由于该极大似然估计为非凸的组合优化问题,提出通过松弛约束条件将其转化为具有多项式计算复杂度的半定规划问题,实现对该极大似然估计问题的近似求解.仿真表明本文提出方法性能优于现有方法,并随着信噪比的提高逐渐逼近CRB.     

一种基于二阶锥规划的新时差定位算法

针对传统时差定位算法在量测噪声较大情况下定位性能不佳的缺点,提出了一种基于二阶锥规划的新时差定位算法.该算法通过凸松弛和引入惩罚项,将难以求解的用户位置最大似然估计问题转换为一个易于求解的二阶锥规划问题,并将松弛问题的最优解作为用户位置的初始估计,利用传统的泰勒级数展开法得到最终定位结果.仿真给出了不同基站数目及量测噪声下算法的定位性能.仿真结果表明,在量测噪声较大的情况下,新算法的定位精度仍可以逼近理论克拉美罗下限,而且算法中惩罚因子的选取范围易于确定.     

半定规划的非单调信赖域算法研究

半定规划是线性规划的一种推广,是一个非光滑的凸优化问题。文中利用半定规划的最优性条件将半定规划问题转化为一个非线性可微的方程组,然后将这一方程组转化为一个无约束优化问题。因此求解半定规划问题就转变为求解无约束优化问题,最后用非单调的信赖域算法求解此问题,即避免了重复计算子问题,且降低了运算次数,同时也证明了此算法的收敛性。     

基于半定松弛的时差定位系统优化布站算法

在时差定位系统中,观测站与目标的几何位置关系对定位精度有着重要影响。针对传统布站方法只适用于规则布站区域的不足,本文提出了一种新的可用于不规则布站区域内的近似最优布站算法。该算法所遵循的最优准则是使系统对目标的定位误差椭球体积下限达到最小,通过离散化布站区域将最优布站问题等价为一个组合优化问题,并采用半定松弛方法将难以求解的组合优化问题变换为一个易于求解的半定规划问题,从而得到规定布站区域内的优化布站方案。计算机仿真结果表明,该算法既可以用于规则布站区域也适用于不规则布站区域。     

基于目标容量的网络化雷达功率分配方案

针对现有网络化雷达功率资源利用率低的问题,该文提出一种基于目标容量的功率分配(TC-PA)方案以提升保精度跟踪目标个数.TC-PA方案首先将网络化雷达功率分配模型制定为非光滑非凸优化问题;而后引入Sigmoid函数将原问题松弛为光滑非凸优化问题;最后运用近端非精确增广拉格朗日乘子法(PI-ALMM)对松弛后的非凸问题进行求解.仿真结果表明,PI-ALMM对于求解线性约束非凸优化问题可以较快地收敛到一个稳态点.另外,相比传统功率均分方法和遗传算法,所提TC-PA方案可以最大限度地提升目标容量.     

基于凸优化的宽带雷达波形优化方法

针对宽带雷达目标识别波形优化中多类目标方位和初相不确定问题,在高斯色噪声背景下提出一种基于凸优化的波形优化方法。该算法通过半正定松弛方法对目标识剐波形优化这个非凸问题进行近似求解,较好地解决了多类目标方位和初相不确定情况下的波形优化问题。仿真结果表明：该方法可以有效增加各类目标之间的可分性,从而提高目标识别性能。     

基于目标容量的网络化雷达功率分配方案

针对现有网络化雷达功率资源利用率低的问题,该文提出一种基于目标容量的功率分配(TC-PA)方案以提升保精度跟踪目标个数。TC-PA方案首先将网络化雷达功率分配模型制定为非光滑非凸优化问题;而后引入Sigmoid函数将原问题松弛为光滑非凸优化问题;最后运用近端非精确增广拉格朗日乘子法(PI-ALMM)对松弛后的非凸问题进行求解。仿真结果表明,PI-ALMM对于求解线性约束非凸优化问题可以较快地收敛到一个稳态点。另外,相比传统功率均分方法和遗传算法,所提TC-PA方案可以最大限度地提升目标容量。     

基于凸松弛优化的非规则子阵设计方法和性能对比北大核心CSCD

子阵技术是大型相控阵系统成本控制的关键手段,文中介绍了基于凸松弛优化的两类非规则子阵设计方法。首先,建立了子阵划分模型;然后,介绍了基于迭代凸松弛规划的求解方法和基于加权L_(1)范数迭代凸优化的求解方法,这两种方法均能实现子阵精确覆盖,但电性能和计算效率存在一定差异,可根据不同运用需求选择求解方法;最后,仿真实验验证了这两类设计方法的有效性和可行性。     

连续凸逼近加权自相关波形优化方法

针对雷达系统对距离向干扰抑制的需求，提出一种基于连续凸逼近的加权自相关恒模波形设计方法。由于原始问题的目标函数为不定二次型，无法直接求解，通过构造目标函数的上边界函数并对其最小化，获得原最小化优化问题的等效形式。同时，对非凸的恒模约束进行松弛处理，构建易于求解的凸优化模型。在此模型基础上，利用成熟优化工具对凸问题进行求解，并对最优解的幅度强制归一化得到恒模序列。通过数值仿真，将连续凸逼近算法与现有算法进行比较，验证了所提算法的可行性和快速收敛性。     

Efficient Design of Cosine-Modulated Filter Banks via Convex Optimization

This paper presents efficient approaches for designing cosine-modulated filter banks with linear phase prototype filter. First, we show that the design problem of the prototype filter being a spectral factor of $2M$th-band filter is a nonconvex optimization problem with low degree of nonconvexity. As a result, the nonconvex optimization problem can be cast into a semi-definite programming (SDP) problem by a convex relaxation technique. Then the reconstruction error is further minimized by an efficient iterative algorithm in which the closed-form expression is given in each iteration. Several examples are given to illustrate the effectiveness of the proposed method over the existing ones.      

多输入多输出雷达低旁瓣发射方向图优化算法

提出了一种基于波束域加权的低旁瓣方向图设计方法。综合考虑方向图匹配性能和发射阵元等功率作为约束条件,建立低旁瓣发射方向图优化模型,采用半正定松弛技术将优化模型转化为凸优化问题;对波束加权矩阵施加对偶约束,使得接收信号满足旋转不变性;利用高斯随机化方法对波束加权矩阵进行求解,得到原优化问题的最优解。仿真结果表明,算法能够保持期望主瓣形状并有效降低方向图旁瓣,提高到达角(DOA)的估计精确度和角度分辨力。     

Energy-Based Localization in Wireless Sensor Networks Using Second-Order Cone Programming Relaxation

Source localization in wireless sensor networks (WSNs) aims to determine the position of a source in a network, given inaccurate position-bearing measurements. This paper addresses the problem of locating a single source from noisy acoustic energy measurements in WSNs. Under the assumption of Gaussian energy measurement errors, the maximum likelihood (ML) estimator requires the minimization of a nonlinear and nonconvex cost function which may have multiple local optima, thus making the search for the globally optimal solution hard. In this work, an approximate solution to the ML location estimation problem is presented by relaxing the minimization problem to a convex optimization problem, namely second-order cone programming. Simulation results demonstrate the superior performance of the convex relaxation approach. More precisely, the new approach shows an improvement of 20 % in terms of localization accuracy when compared to the existing approaches at moderate to high noise levels. Simulation results further show comparable performance of the new approach and the state-of-art approaches at low noise levels.     

Real-Time Optimized Error Protection Assignment for Scalable Image and Video over Wireless Channels

A new error protection assignment scheme with applications to real-time wireless multimedia transmission is presented. The proposed scheme exploits the structure of scalable sources to ensure optimal assignment. This novel approach recasts the nonlinear optimization problem into a linear one, and then further remodels it into a discrete programming problem, thereby reducing the computational complexity dramatically. Furthermore, the proposed algorithm does not impose any requirement on the convexity of the source; i.e., it can equally be applied on a convex or nonconvex source. Results show that the described method facilitates a significant complexity reduction with respect to existing schemes, while exhibiting almost equivalent performance.     

杂波环境下共享频谱恒模波形设计

针对射频频谱环境愈发拥挤问题,深入研究了通过波形设计的手段实现频谱共享的问题。为紧密贴近工程实践,提出了一种新的方法设计恒定幅度信号的问题。该算法首先针对雷达发射端,提出雷达波形满足特定的时域与频谱要求,施加约束,然后考虑雷达接收滤波器接收杂波,以优化最大信干噪比建立优化问题模型,得到了一个非凸的分式规划问题模型。最后,利用分步优化方法分解为两个优化问题,并且将非凸问题松弛为可解的凸问题再利用高斯随机化方法得到优化信号,多次循环优化。仿真结果验证了该算法的有效性,该方法设计得到的探测信号能够实现频谱共存,而且信干噪比性能能够得到保证。      

Globally convergent edge-preserving regularized reconstruction: anapplication to limited-angle tomography

We introduce a generalization of a deterministic relaxation algorithm for edge-preserving regularization in linear inverse problems. This algorithm transforms the original (possibly nonconvex) optimization problem into a sequence of quadratic optimization problems, and has been shown to converge under certain conditions when the original cost functional being minimized is strictly convex. We prove that our more general algorithm is globally convergent (i.e., converges to a local minimum from any initialization) under less restrictive conditions, even when the original cost functional is nonconvex. We apply this algorithm to tomographic reconstruction from limited-angle data by formulating the problem as one of regularized least-squares optimization. The results demonstrate that the constraint of piecewise smoothness, applied through the use of edge-preserving regularization, can provide excellent limited-angle tomographic reconstructions. Two edge-preserving regularizers-one convex, the other nonconvex-are used in numerous simulations to demonstrate the effectiveness of the algorithm under various limited-angle scenarios, and to explore how factors, such as the choice of error norm, angular sampling rate and amount of noise, affect the reconstruction quality and algorithm performance. These simulation results show that for this application, the nonconvex regularizer produces consistently superior results.     

Improved design of unimodular waveforms for MIMO radar

This paper proposes a novel method of unimodular transmitting waveforms design for multiple-input multiple-output (MIMO) radar to strengthen the detection performance in the presence of clutter and white Gaussian noise. An improved iterative algorithm is put forward to maximize the signal-to-clutter-plus-noise ratio (SCNR) under the constant modulus constraint. During iterations, the optimization of unimodular waveforms with filters fixed is a nonconvex fractional quadratically constrained quadratic program problem, which is NP-hard and not able to be solved in polynomial time. An algorithm based on semidefinite programming relaxation combined with bisection and Gaussian randomization is introduced to provide the high-quality suboptimal solutions with a polynomial time computational complexity. The analysis on the approximation bound is given to prove the tightness of the semidefinite programming relaxation and so the correctness of the proposed algorithm. The simulation results show that the improved method is efficient in designing unimodular waveforms for MIMO radar to achieve a better SCNR performance.     

Energy‐Efficient Power Allocation for Cognitive Radio Networks with Joint Overlay and Underlay Spectrum Access Mechanism

Traditional designs of cognitive radio (CR) focus on maximizing system throughput. In this paper, we study the joint overlay and underlay power allocation problem for orthogonal frequency‐division multiple access–based CR. Instead of maximizing system throughput, we aim to maximize system energy efficiency (EE), measured by a “bit per Joule” metric, while maintaining the minimal rate requirement of a given CR system, under the total power constraint of a secondary user and interference constraints of primary users. The formulated energy‐efficient power allocation (EEPA) problem is nonconvex; to make it solvable, we first transform the original problem into a convex optimization problem via fractional programming, and then the Lagrange dual decomposition method is used to solve the equivalent convex optimization problem. Finally, an optimal EEPA allocation scheme is proposed. Numerical results show that the proposed method can achieve better EE performance.