无线通信系统中的几个典型参数估计问题
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摘要
最近二十年，无线通信发展迅速，不仅用户数量急剧增加，而且单个用户的业务需求和数据传输量也迅速增长。为此，增加通信系统的系统容量是无线通信的关键问题。众所周知，在无线通信系统中阵列天线可以提供比单天线更大的信道容量而不需要增加信号带宽和发射功率。另外它们还能提供对移动终端的定位、跟踪等服务。这些优点使阵列天线成为第三和第四代移动通信系统中的关键技术之一。为实现阵列天线的这些优点，需要在接收端进行空时信号处理，而这通常要求空时无线信道状态信息和阵列流型已知。本文着重研究基站装有阵列天线时上行空时无线信道估计问题和阵列天线参数校准问题。具体来说，本文的主要贡献概括如下：
1.在上行空时无线信道估计问题中，针对传统子空间投影信道估计方法不能充分利用用户数据的缺陷，提出了一种基于空时信号子空间投影的信道估计算法。该算法用空时信号模型来描述信道估计问题，然后根据最大似然（ML）准则，推导出基于空时信号子空间投影的信道估计方法。在此基础上，利用信道缓变特性，我们将算法推广得到多时隙的空时信号子空间投影算法。另外，还推导了信道估计的克拉美-罗界。仿真结果表明，算法的信道估计性能优于现有的子空间投影方法。
2.在上行空时无线信道估计问题中，通过利用译码器反馈的软比特信息，提出了基于软信息的信道估计算法。该算法将未知的数据比特与其软信息间的误差描述为附加噪声，改进了接收信号模型，并将模型中的附加噪声近似为高斯分布，由此得到最大似然准则下的信道估计问题。然后，对最大似然估计问题进行近似，分别得到最小二乘问题和半正定规划问题，其中前者求解复杂度较低而后者估计性能较好。另外，将基于软信息的信道估计方法和空时信号子空间投影方法相结合可以进一步提高信道估计性能，最后推导了基于软信息的信道估计的克拉美-罗界。仿真结果表明所提算法信道估计性能较好，其相应turbo系统的误码率（BER）性能逼近信道已知时的BER性能。
3.在阵列幅相误差的有源校准问题中，针对均匀线阵（ULA）中不存在和存在未知互耦的情况，分别提出了基于最大似然准则的凸优化校准方法和块坐标轮换下降校准方法。算法考虑到幅相误差有上界且边界信息已知，并在最大似然准则中加入这一边界约束，由此改进大噪声环境中的校准性能，使校准误差低于无约束条件下的克拉美-罗界。
4.提出了均匀线阵中存在未知互耦时的ML波达方向（DOA）估计算法。该算法通过迭代求解以下两个子问题来获得DOA的估计值：互耦系数已知时的DOA估计问题和DOA已知时的互耦系数估计问题。针对这两个问题，分别提出了基于平方和以及半正定规划的ML DOA估计算法和基于ML准则的半正定松弛方法。因为所提方法基于ML准则，所以能够估计相关信号源的DOA，且其性能逼近克拉美-罗界。
Over the last two decades, the field of wireless communications has been devel-oping at an explosive rate. The number of users has not only increased dramatically,but the business type and the amount of data transmission of each user are also growingfast. Therefore, increasing the capacity of the current communication systems is a keyproblem in wireless communications. It is well known that antenna arrays can providemore channel capacity for wireless communication systems than single antenna withoutany extra signal bandwidth or transmission power. They can also supply locating andtracking services to mobile terminals. These merits make the antenna array one of thekey technologies in the third and fourth generation of mobile communication systems.To reveal the potential of the antenna arrays, space-time signal processing is necessaryat the receiver which usually needs not only the information of the space-time wirelesschannel but also the accurate array manifold. This dissertation focuses on the uplinkspace-time wireless channel estimation problems and antenna array parameter calibra-tion problems in systems where the base stations are equipped with antenna arrays. Themain contributions of this thesis are shown as follows:
1. In the uplink space-time wireless channel estimation problem, a space-time signalsubspace projection based channel estimation algorithm is proposed. Comparedwith the traditional signal subspace methods, the proposed method can better uti-lize the received signals corresponding to the user data. We formulate the channelestimation problem using a space-time signal model, then derive the space-timesignal subspace projection method in the context of maximum likelihood (ML)criterion. Furthermore, using the slowly-varying features in channels, we ex-tend the algorithm to obtain a multi-slot space-time signal subspace projectionalgorithm. In addition, the Cramer-Rao bound for channel estimation is derived.Simulation results show that the space-time signal subspace projection methodoutperforms the existing subspace projection methods.
2. In the uplink space-time wireless channel estimation problem, a soft-based chan-nel estimation method is proposed by utilizing the soft bit information fed backfrom the decoder. The signal model is modified by formulating the differencesbetween the unknown user data and their soft information as additional Gaussiannoise. By using this modified model, an estimation problem based on the ML criterion is formulated. This ML estimation problem can be approximated eitherby a low complexity least square problem or by a semidefinite programming (S-DP) problem. In another method, we proposed to use the soft-based method andthe space-time signal subspace projection method in combination. At last, theCramer-Rao bound is derived for soft-based channel estimation methods. Sim-ulation results show that the proposed soft-based methods perform well and thecombination method works better such that the bit error rate (BER) of the turbosystem approaches the BER of the system using perfect channel state informa-tion.
3. In the active array gain/phase calibration problem, an SDP method for uniformlinear arrays (ULAs) with known mutual coupling matrix (MCM) and a blockcoordinate descent (BCD) method for ULAs with unkown MCM are proposedbased on the ML criterion. We add the constraint that array gain/phase errorscan be upper bounded by a known value in practice. This bound constraint canimprove the calibration performance and make the calibration error smaller thanthe CRB without bound constraint at high noise levels.
4. An ML direction of arrival (DOA) estimation algorithm is proposed for ULAswith unknown MCM. This algorithm obtains the DOA estimations by iterativelysolving the following two subproblems: DOA estimation problem with givenMCM and mutual coupling coefficients estimation problem with given DOA. Wesolve the first problem by a ML DOA estimation algorithm based on sum ofsquares (SOS) combined with SDP and the second problem by a semidefiniterelaxation (SDR) method. Based on the ML criterion, the proposed method canestimate the DOAs of coherent sources and approach the CRB.
1.在上行空时无线信道估计问题中，针对传统子空间投影信道估计方法不能充分利用用户数据的缺陷，提出了一种基于空时信号子空间投影的信道估计算法。该算法用空时信号模型来描述信道估计问题，然后根据最大似然（ML）准则，推导出基于空时信号子空间投影的信道估计方法。在此基础上，利用信道缓变特性，我们将算法推广得到多时隙的空时信号子空间投影算法。另外，还推导了信道估计的克拉美-罗界。仿真结果表明，算法的信道估计性能优于现有的子空间投影方法。
2.在上行空时无线信道估计问题中，通过利用译码器反馈的软比特信息，提出了基于软信息的信道估计算法。该算法将未知的数据比特与其软信息间的误差描述为附加噪声，改进了接收信号模型，并将模型中的附加噪声近似为高斯分布，由此得到最大似然准则下的信道估计问题。然后，对最大似然估计问题进行近似，分别得到最小二乘问题和半正定规划问题，其中前者求解复杂度较低而后者估计性能较好。另外，将基于软信息的信道估计方法和空时信号子空间投影方法相结合可以进一步提高信道估计性能，最后推导了基于软信息的信道估计的克拉美-罗界。仿真结果表明所提算法信道估计性能较好，其相应turbo系统的误码率（BER）性能逼近信道已知时的BER性能。
3.在阵列幅相误差的有源校准问题中，针对均匀线阵（ULA）中不存在和存在未知互耦的情况，分别提出了基于最大似然准则的凸优化校准方法和块坐标轮换下降校准方法。算法考虑到幅相误差有上界且边界信息已知，并在最大似然准则中加入这一边界约束，由此改进大噪声环境中的校准性能，使校准误差低于无约束条件下的克拉美-罗界。
4.提出了均匀线阵中存在未知互耦时的ML波达方向（DOA）估计算法。该算法通过迭代求解以下两个子问题来获得DOA的估计值：互耦系数已知时的DOA估计问题和DOA已知时的互耦系数估计问题。针对这两个问题，分别提出了基于平方和以及半正定规划的ML DOA估计算法和基于ML准则的半正定松弛方法。因为所提方法基于ML准则，所以能够估计相关信号源的DOA，且其性能逼近克拉美-罗界。
Over the last two decades, the field of wireless communications has been devel-oping at an explosive rate. The number of users has not only increased dramatically,but the business type and the amount of data transmission of each user are also growingfast. Therefore, increasing the capacity of the current communication systems is a keyproblem in wireless communications. It is well known that antenna arrays can providemore channel capacity for wireless communication systems than single antenna withoutany extra signal bandwidth or transmission power. They can also supply locating andtracking services to mobile terminals. These merits make the antenna array one of thekey technologies in the third and fourth generation of mobile communication systems.To reveal the potential of the antenna arrays, space-time signal processing is necessaryat the receiver which usually needs not only the information of the space-time wirelesschannel but also the accurate array manifold. This dissertation focuses on the uplinkspace-time wireless channel estimation problems and antenna array parameter calibra-tion problems in systems where the base stations are equipped with antenna arrays. Themain contributions of this thesis are shown as follows:
1. In the uplink space-time wireless channel estimation problem, a space-time signalsubspace projection based channel estimation algorithm is proposed. Comparedwith the traditional signal subspace methods, the proposed method can better uti-lize the received signals corresponding to the user data. We formulate the channelestimation problem using a space-time signal model, then derive the space-timesignal subspace projection method in the context of maximum likelihood (ML)criterion. Furthermore, using the slowly-varying features in channels, we ex-tend the algorithm to obtain a multi-slot space-time signal subspace projectionalgorithm. In addition, the Cramer-Rao bound for channel estimation is derived.Simulation results show that the space-time signal subspace projection methodoutperforms the existing subspace projection methods.
2. In the uplink space-time wireless channel estimation problem, a soft-based chan-nel estimation method is proposed by utilizing the soft bit information fed backfrom the decoder. The signal model is modified by formulating the differencesbetween the unknown user data and their soft information as additional Gaussiannoise. By using this modified model, an estimation problem based on the ML criterion is formulated. This ML estimation problem can be approximated eitherby a low complexity least square problem or by a semidefinite programming (S-DP) problem. In another method, we proposed to use the soft-based method andthe space-time signal subspace projection method in combination. At last, theCramer-Rao bound is derived for soft-based channel estimation methods. Sim-ulation results show that the proposed soft-based methods perform well and thecombination method works better such that the bit error rate (BER) of the turbosystem approaches the BER of the system using perfect channel state informa-tion.
3. In the active array gain/phase calibration problem, an SDP method for uniformlinear arrays (ULAs) with known mutual coupling matrix (MCM) and a blockcoordinate descent (BCD) method for ULAs with unkown MCM are proposedbased on the ML criterion. We add the constraint that array gain/phase errorscan be upper bounded by a known value in practice. This bound constraint canimprove the calibration performance and make the calibration error smaller thanthe CRB without bound constraint at high noise levels.
4. An ML direction of arrival (DOA) estimation algorithm is proposed for ULAswith unknown MCM. This algorithm obtains the DOA estimations by iterativelysolving the following two subproblems: DOA estimation problem with givenMCM and mutual coupling coefficients estimation problem with given DOA. Wesolve the first problem by a ML DOA estimation algorithm based on sum ofsquares (SOS) combined with SDP and the second problem by a semidefiniterelaxation (SDR) method. Based on the ML criterion, the proposed method canestimate the DOAs of coherent sources and approach the CRB.
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