高速宽带无线通信系统中，由于符号间隔降低，导致信号到达接收端的各延时路径可分辨，从而带来多径效应且引入了频率选择性衰落。此信道是非时变的，然而一旦通信双方中的一方处于高速运动中，或者周围环境快速变化，产生的多普勒频移(fd)将引入时间选择性，从而形成时间频率双选择性信道，简称双选信道。日常生活中高速行驶的汽车、高铁与汹涌海平面上的船只等均是双选信道存在的典型场景，并且通信信号将遭遇相比较静态多径信道更严重的干扰与衰落。因此双选信道的信道估计与均衡技术引起了广泛的关注。
    本文旨在研究单载波系统下双选信道的信道估计与均衡算法，其主要研究内容与贡献包括：
1. 基于经典指数加权的最小递归二乘(EW-RLS)信道估计算法，针对多步骤且高复杂度的增益矩阵与估计误差方差矩阵的求解过程，本文提出了两种低复杂度的平方根卡尔曼滤波(SR-KF)与基于QR分解的EW-RLS(QR-EW-RLS)估计算法。两算法通过分解复杂公式与构造矩阵，并分别应用SR-KF滤波与QR分解一步求得更新过程中两个关键矩阵。最后，两算法同时将计算复杂度降低了一个数量级，并且保持了EW-RLS的优秀估计性能。
2. 基于联合信道估计与均衡的扩展卡尔曼滤波(EKF)的turbo均衡方案，本文提出了一种线性卡尔曼滤波(LKF)的turbo均衡算法。LKF通过将信道估计与均衡分开，应用QR-EW-RLS算法估计信道，摆脱了EKF方案中假设信道服从一阶自回归(AR)变化的约束，得到了更加准确的估计结果，进而提升了均衡性能。而且LKF的状态空间向量长度小于EKF，所以LKF不但获得了更好地误比特率(BER)性能并且降低了计算复杂度。
3. 基于LKF的一倍速率均衡方案，通过引入整数倍过采样技术，本文提出了一种单载波传输系统中基于整数倍过采样的线性时域卡尔曼均衡(OSC-LKF)算法。该算法的关键在于应用成型滤波器、信道信息与匹配滤波器构造矩阵，以此建立空间状态向量与接收信号的关系式，即观测方程。最后，相比较于LKF方案，OSC-LKF算法进一步提升了BER性能。
    最后通过计算机仿真，验证了各算法的可行性，并且对比分析了各算法的计算复杂度与性能表现。
 

In high-speed wideband wireless communication systems, due to the reduced symbol interval, several paths of signals with different path delays can be classified at the receiver, which caused multipath effects and introduced frequency selective fading. The channel is not time-varying. However, once each of the communication partners is in high-speed motion, or the surrounding environment changes rapidly, the resulting Doppler shift (fd) will introduce the time-selectivity, thus forming a time-varying and frequency selective fading channel, referred to as doubly selective fading channels. In our daily life, such as the high-speed cars, trains or ships on rough sea are typical sites for doubly selective fading channels.
And the communication signal will encounter more severe fading and interference than the static multipath channels. Therefore, the channel estimation and equalization schemes have attracted widespread attention to mitigate these influences.
This paper aims to investigate the channel estimation and equalization algorithms for single carrier systems over doubly selective fading channels, and the main research and contributions are concluded as follows:
1. Considering the classical exponentially weighted recursive least square (EW-RLS) channel estimation algorithm, with complicate solutions to obtain gain matrix and estimation error variance matrix, this paper proposes two kinds of low-complexity estimation algorithms. The square-root Kalman filtering (SR-KF) algorithm and the QR decomposition-based EW-RLS (QR-EW-RLS) algorithm. By decomposing formulas, constructing matrices and applying SR-KF filtering and QR decomposition respectively, the two key matrices are obtained in only one step. Finally, both the algorithms reduce the calculation complexity by a factor of level and maintain the excellent performance of EW-RLS.
2. Based on the turbo equalization scheme, the extended Kalman filtering (EKF), which jointly performs channel estimation and equalization, this paper proposes a linear Kalman filtering (LKF) algorithm. The channel estimation and equalization are separated in the proposed LKF. By applying the QR-EW-RLS channel estimation algorithm, the assumption that the channel follows the first-order autoregressive variation is abandoned, resulting more accurate estimation results. Thus the equalization performance is improved. Furthermore, the proposed LKF outperforms the EKF in bit error rate (BER) performance and reduces the calculation complexity as the length of state space vector is shorter than EKF.
3. Based on the non-oversampled single carrier system, where the proposed LKF operates in, this paper proposes a linear time-domain turbo equalization scheme for integrally oversampled single carrier systems (OSC-LKF). The key procedure of this algorithm is to investigate the measurement equation, which is the relationship between the state space vector and the received signals, by constructing three key matrices using the wave forming filter, the channel state information and the matched filter.
Finally, the comparisons of calculation complexity and BER performance are presented and the validity of the proposed schemes are illustrated by simulation results.