NC-OFDM系统导频优化设计研究
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摘要
非连续OFDM(NC-OFDM)是IEEE802.22标准中物理层的主要数据传输模式。与传统的OFDM技术相比,其可用子载波具有非连续分布的特点,这给它的各种关键技术带来了新的挑战。导频设计是决定应用于CR的NC-OFDM系统性能的关键因素之一,NC-OFDM系统的本质虽然是OFDM,但是由于NC-OFDM可用频谱的非连续和动态变化特性,所以已有的面向固定使用频谱的OFDM系统的研究成果不能够照搬使用,需要对其进行必要的改进、完善和创新。传统的OFDM系统中的等功率等间隔导频序列是最优的,但在NC-OFDM系统中,由于可用频谱的非连续性,以及为保证授权用户(PU)干扰容限所引起的各子载波／子信道上的功率限制,应用于NC-OFDM系统的最优导频的功率和位置均呈现非均匀分布的特点。获取子载波非连续及子载波功率受限情况下NC-OFDM系统的最优导频设计规则,能够降低导频设计的计算复杂度,适应认知NC-OFDM系统导频图案需要动态变化的要求,并最大化地改善系统误码率性能。
本文以凸优化理论为工具,对NC-OFDM系统的导频优化设计问题进行研究。主要包括以下三个方面：
1.采用凸变换方法研究NC-OFDM系统导频优化设计问题；
NC-OFDM系统导频最优化设计的数学模型中,由于优化变量取值集合的非连续性,导致该优化问题是一个非凸优化问题,无法通过数值计算的方法获得最优解,必须寻求某种凸映射的方法解决上述非凸难题,才能利用成熟的凸优化工具对导频设计的可行解进行深入的研究。
首先建立NC-OFDM系统导频设计的多目标优化问题,分别在单PU和多PU通信环境提出解决导频优化设计非凸问题的凸变换方法,从而可以采用凸优化工具研究NC-OFDM系统的导频优化设计。这也是以后各章导频优化设计的基础。除此之外,本章针对单PU通信环境提出适合NC-OFDM系统的一种次优导频图案设计；然后分析多PU通信环境NC-OFDM系统载波功率分布特点,提出基于重要导频的次优导频设计。
2.研究子载波功率受限的导频位置优化设计问题；
当不同SU短距离通信时,一般只需对发射信号进行小功率放大即可满足信道传输要求,此时发射信号处于系统中功率放大器的线性区,不需要考虑HPA非线性带来的失真。因此理想HPA特性下NC-OFDM系统的导频优化设计要满足子载波总功率限制条件,以及子信道的功率分布限制,以保证自身系统的高性能和PU通信的可靠性。本文首先建立认知NC-OFDM系统PU干扰温度分析模型,并把PU干扰温度限制转化为子信道发射功率限制；在此基础上,建立满足子载波总功率限制以及子信道功率限制条件下的功率分配最优化问题,运用Lagrange乘子法得到其最优解,即同时满足PU通信可靠性和SU自身性能要求的最优子载波/子信道功率分布；然后,建立子信道功率受限的导频位置优化问题,并对该优化问题进行松弛求解,从理论上推导出最优导频位置与子载波功率的关系式、不同导频位置距离的函数关系以及初始导频的选择规则。所得结论可用于解决子载波功率受限时的最优导频位置选择问题。
3.研究HPA非线性干扰受限的导频位置优化设计问题。
当不同SU远距离通信或信道较差时,往往需要对发射信号进行大功率放大以满足系统性能的要求。此时动态范围较大的NC-OFDM信号经过HPA后将产生严重的带内失真和带外频谱泄露,影响自身性能,并对PU造成严重干扰。此时NC-OFDM系统的导频设计需要考虑HPA非线性的影响。
首先建立NC-OFDM系统带外功率泄漏和PU频带干扰功率的数学模型,定量计算NC-OFDM系统中HPA非线性引起的PU频带干扰,并建立以PU频带干扰功率等于PU干扰容限为目标函数的一个非线性规划问题,通过优化求解得到PU干扰容限与HPA非线性参数、保护载波数量、PU频带占用率之间的约束关系,称此约束关系为HPA非线性干扰限制；然后推导导频辅助非线性信道估计的MSE闭合式,并建立满足HPA非线性干扰限制的导频优化设计数学模型；最后运用数值分析的方法得到HPA非线性干扰限制下的最优导频位置。
本文从NC-OFDM系统导频优化设计问题的凸变换求解、子载波功率受限以及考虑HPA非线性三个角度展开深入研究,给出适用于NC-OFDM系统的最优以及次优导频设计方法,从而完善和提高NC-OFDM系统接收机的信道估计性能,优化系统误码率性能,为认知无线电技术的应用提供理论依据和技术基础。
Noncontinuous orthogonal frequency division multiplexing (NC-OFDM) modulation technique is one of main data transmission mode for IEEE802.22, and its available subcarriers have the characteristics of non-continuous distribution compared with traditional OFDM systems, which brings new technical challenges. Especially, the pilot design is one of the key issues that has to be solved in order to improve the performance of NC-OFDM systems in cognitive radio context. Because of the noncontinuous and dynamic characteristics of available spectrums, it is necessary to modify, improve or/and innovate the existing research of OFDM systems. In traditional OFDM systems, equi-powered and equi-spaced pilots are optimal, however, for satisfying primary users(PUs)'interference constrains, the optimal pilots of NC-OFDM systems will be non-uniform with available subcarriers' limited power distribution and non-continuous spectrums. The proposed pilot optimization design rules under the above two conditions can reduce the computation complexity of pilot designs, adapt to the requirements of dynamic pilot pattern, and maximize the BER performance.
The pilot optimization design of the NC-OFDM systems based on the convex optimization theory has been analyzed and summarized in this dissertation. The main contents include the following three aspects:
1. The pilot optimization design of a NC-OFDM system based on convex mapping has been studied.
Because of the discontinuity of the optimization variable set, the optimal pilot design is a non-convex optimization problem, which is very difficult to obtain the optimal solution by the numerical method. It is necessary to seek the convex mapping methods to this nonconvex problem, and then obtain the feasible solution by convex optimization tools.
Firstly, the pilot design of multi-objective optimization problem is found, the non-convex problem is solved by convex mapping in single PU scenarios amd more PU scenarios. Then we can obtain the optimal pilot pattern based convex optimization. The suboptimal pilot design in different Scenarios are also presented for reducing the computation complexity.
2. A optimization design of the pilot positions under a power constraint of available subcarriers has been studied.
In short-distance communication scenes beween different SUs, generally the lower power amplifier can meet the requiements of channel transmission, which presents linear characteristic and doesn't bring nonlinear distortion for NC-OFDM signals and out-of-band(OOB) interference. Assuming ideal HPA characteristics, the pilot optimization design only need to consider the total power constraint of available subcarriers and the sub-channel power constraints from PU interference constraints。
Under a total power constraint and sub-channel power constraints, the pilot optimization design is studied. Firstly, the mutual interference between SU and PU transmissions is analyzed and the PU interference temperature model is found. Mapping the PU interference temperature constraints into the sub-channels' transmission power constraints, the optimal subcarrier power allocation is obtained by the Lagrange method. Then, we reconstruct the pilot optimization design under the above available subcarriers'power allocation, and obtain the suboptimal soluton using a upper bound of the channel estion MSE instead of MSE. Theoretical analysis has shown that the suboptimal pilot positions is a function of the available subcarriers'powers and the distance between different pilots.
3. The optimization design of pilot positions under a HPA nonlinear interference constraint has been studied based on the analysis of nonlinear HPA.
For the poor channel conditions or long-distance communication between SUs, the high power amplifier(HPA) is neccssary to obtain higher signal power for meeting the requirements of NC-OFDM systems, however, large dynamic range of NC-OFDM signals after HPA will lead to serious in-band distortions and OOB spectrum leakages, the latter will increase the interference temperature in PU band. In this scene, it is necessary to consider the nonlineality of HPA for pilot optimization design.
Firstly, a mathematical model for measuring the OOB radiation in NC-OFDM systems is presented, and the interference power in adjacent PUs' bands are computed in this dissertation. Based on this mathematical model, the HPA nonlinear interference constraint among HPA nonlinear parameter, the number of guard subcarriers, PUs' occupancy rate and PU interference temperature limits is obtained by solving the nonlinear programming (NLP) problem. Then, the closed expression of pilot-assisted channel estimation MSE consideringr the HPA nonlinearity is deduced, and the pilot optimaization design problem under a HPA nonlinear interference constraint is described and solved by the numerical method..
According to the exploration and study of these key technologies, we have shown some pilot optimization designs which can reduce the computational complexity and improve the channel estimation performance of a NC-OFDM system receiver, thereby, optimizing the BER performance and providing a theoretical and technical basis for a widely application.
本文以凸优化理论为工具,对NC-OFDM系统的导频优化设计问题进行研究。主要包括以下三个方面：
1.采用凸变换方法研究NC-OFDM系统导频优化设计问题；
NC-OFDM系统导频最优化设计的数学模型中,由于优化变量取值集合的非连续性,导致该优化问题是一个非凸优化问题,无法通过数值计算的方法获得最优解,必须寻求某种凸映射的方法解决上述非凸难题,才能利用成熟的凸优化工具对导频设计的可行解进行深入的研究。
首先建立NC-OFDM系统导频设计的多目标优化问题,分别在单PU和多PU通信环境提出解决导频优化设计非凸问题的凸变换方法,从而可以采用凸优化工具研究NC-OFDM系统的导频优化设计。这也是以后各章导频优化设计的基础。除此之外,本章针对单PU通信环境提出适合NC-OFDM系统的一种次优导频图案设计；然后分析多PU通信环境NC-OFDM系统载波功率分布特点,提出基于重要导频的次优导频设计。
2.研究子载波功率受限的导频位置优化设计问题；
当不同SU短距离通信时,一般只需对发射信号进行小功率放大即可满足信道传输要求,此时发射信号处于系统中功率放大器的线性区,不需要考虑HPA非线性带来的失真。因此理想HPA特性下NC-OFDM系统的导频优化设计要满足子载波总功率限制条件,以及子信道的功率分布限制,以保证自身系统的高性能和PU通信的可靠性。本文首先建立认知NC-OFDM系统PU干扰温度分析模型,并把PU干扰温度限制转化为子信道发射功率限制；在此基础上,建立满足子载波总功率限制以及子信道功率限制条件下的功率分配最优化问题,运用Lagrange乘子法得到其最优解,即同时满足PU通信可靠性和SU自身性能要求的最优子载波/子信道功率分布；然后,建立子信道功率受限的导频位置优化问题,并对该优化问题进行松弛求解,从理论上推导出最优导频位置与子载波功率的关系式、不同导频位置距离的函数关系以及初始导频的选择规则。所得结论可用于解决子载波功率受限时的最优导频位置选择问题。
3.研究HPA非线性干扰受限的导频位置优化设计问题。
当不同SU远距离通信或信道较差时,往往需要对发射信号进行大功率放大以满足系统性能的要求。此时动态范围较大的NC-OFDM信号经过HPA后将产生严重的带内失真和带外频谱泄露,影响自身性能,并对PU造成严重干扰。此时NC-OFDM系统的导频设计需要考虑HPA非线性的影响。
首先建立NC-OFDM系统带外功率泄漏和PU频带干扰功率的数学模型,定量计算NC-OFDM系统中HPA非线性引起的PU频带干扰,并建立以PU频带干扰功率等于PU干扰容限为目标函数的一个非线性规划问题,通过优化求解得到PU干扰容限与HPA非线性参数、保护载波数量、PU频带占用率之间的约束关系,称此约束关系为HPA非线性干扰限制；然后推导导频辅助非线性信道估计的MSE闭合式,并建立满足HPA非线性干扰限制的导频优化设计数学模型；最后运用数值分析的方法得到HPA非线性干扰限制下的最优导频位置。
本文从NC-OFDM系统导频优化设计问题的凸变换求解、子载波功率受限以及考虑HPA非线性三个角度展开深入研究,给出适用于NC-OFDM系统的最优以及次优导频设计方法,从而完善和提高NC-OFDM系统接收机的信道估计性能,优化系统误码率性能,为认知无线电技术的应用提供理论依据和技术基础。
Noncontinuous orthogonal frequency division multiplexing (NC-OFDM) modulation technique is one of main data transmission mode for IEEE802.22, and its available subcarriers have the characteristics of non-continuous distribution compared with traditional OFDM systems, which brings new technical challenges. Especially, the pilot design is one of the key issues that has to be solved in order to improve the performance of NC-OFDM systems in cognitive radio context. Because of the noncontinuous and dynamic characteristics of available spectrums, it is necessary to modify, improve or/and innovate the existing research of OFDM systems. In traditional OFDM systems, equi-powered and equi-spaced pilots are optimal, however, for satisfying primary users(PUs)'interference constrains, the optimal pilots of NC-OFDM systems will be non-uniform with available subcarriers' limited power distribution and non-continuous spectrums. The proposed pilot optimization design rules under the above two conditions can reduce the computation complexity of pilot designs, adapt to the requirements of dynamic pilot pattern, and maximize the BER performance.
The pilot optimization design of the NC-OFDM systems based on the convex optimization theory has been analyzed and summarized in this dissertation. The main contents include the following three aspects:
1. The pilot optimization design of a NC-OFDM system based on convex mapping has been studied.
Because of the discontinuity of the optimization variable set, the optimal pilot design is a non-convex optimization problem, which is very difficult to obtain the optimal solution by the numerical method. It is necessary to seek the convex mapping methods to this nonconvex problem, and then obtain the feasible solution by convex optimization tools.
Firstly, the pilot design of multi-objective optimization problem is found, the non-convex problem is solved by convex mapping in single PU scenarios amd more PU scenarios. Then we can obtain the optimal pilot pattern based convex optimization. The suboptimal pilot design in different Scenarios are also presented for reducing the computation complexity.
2. A optimization design of the pilot positions under a power constraint of available subcarriers has been studied.
In short-distance communication scenes beween different SUs, generally the lower power amplifier can meet the requiements of channel transmission, which presents linear characteristic and doesn't bring nonlinear distortion for NC-OFDM signals and out-of-band(OOB) interference. Assuming ideal HPA characteristics, the pilot optimization design only need to consider the total power constraint of available subcarriers and the sub-channel power constraints from PU interference constraints。
Under a total power constraint and sub-channel power constraints, the pilot optimization design is studied. Firstly, the mutual interference between SU and PU transmissions is analyzed and the PU interference temperature model is found. Mapping the PU interference temperature constraints into the sub-channels' transmission power constraints, the optimal subcarrier power allocation is obtained by the Lagrange method. Then, we reconstruct the pilot optimization design under the above available subcarriers'power allocation, and obtain the suboptimal soluton using a upper bound of the channel estion MSE instead of MSE. Theoretical analysis has shown that the suboptimal pilot positions is a function of the available subcarriers'powers and the distance between different pilots.
3. The optimization design of pilot positions under a HPA nonlinear interference constraint has been studied based on the analysis of nonlinear HPA.
For the poor channel conditions or long-distance communication between SUs, the high power amplifier(HPA) is neccssary to obtain higher signal power for meeting the requirements of NC-OFDM systems, however, large dynamic range of NC-OFDM signals after HPA will lead to serious in-band distortions and OOB spectrum leakages, the latter will increase the interference temperature in PU band. In this scene, it is necessary to consider the nonlineality of HPA for pilot optimization design.
Firstly, a mathematical model for measuring the OOB radiation in NC-OFDM systems is presented, and the interference power in adjacent PUs' bands are computed in this dissertation. Based on this mathematical model, the HPA nonlinear interference constraint among HPA nonlinear parameter, the number of guard subcarriers, PUs' occupancy rate and PU interference temperature limits is obtained by solving the nonlinear programming (NLP) problem. Then, the closed expression of pilot-assisted channel estimation MSE consideringr the HPA nonlinearity is deduced, and the pilot optimaization design problem under a HPA nonlinear interference constraint is described and solved by the numerical method..
According to the exploration and study of these key technologies, we have shown some pilot optimization designs which can reduce the computational complexity and improve the channel estimation performance of a NC-OFDM system receiver, thereby, optimizing the BER performance and providing a theoretical and technical basis for a widely application.
引文
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