CN117082476A - A C-V2V massive MIMO multicast and unicast robust collaborative transmission method - Google Patents
A C-V2V massive MIMO multicast and unicast robust collaborative transmission method Download PDFInfo
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Abstract
Description
技术领域Technical Field
本发明涉及一种C-V2V大规模MIMO多播和单播鲁棒协同传输方法,尤其涉及一种行驶车辆网络中通信使用的C-V2V大规模MIMO蜂窝网多播和车辆通信对单播场景下对于基站和车辆发送端的不完美信道统计信息鲁棒的协同传输方法。The present invention relates to a C-V2V massive MIMO multicast and unicast robust cooperative transmission method, and in particular to a C-V2V massive MIMO cellular network multicast and vehicle communication used in a moving vehicle network for communication, which is robust to the cooperative transmission of imperfect channel statistical information of a base station and a vehicle transmitter in a unicast scenario.
背景技术Background Art
随着5G通信技术的发展以及业务的多样性需求,车辆-车辆(V2V)和车辆-网络(V2N)通信在近几年取得了快速发展。为满足未来V2V通信应用需求,需要深度挖掘利用空间无线资源,大幅提升V2V无线通信的频谱利用率和功率利用率。因此,把大规模MIMO系统引入V2V通信中成为一个非常有潜力的解决方案。在车辆接收端配置大规模天线阵列(数十根以上),以深度挖掘利用空间维度资源,成为未来V2V无线通信的发展趋势之一。With the development of 5G communication technology and the diversified needs of services, vehicle-to-vehicle (V2V) and vehicle-to-network (V2N) communications have achieved rapid development in recent years. In order to meet the future needs of V2V communication applications, it is necessary to deeply tap and utilize spatial wireless resources and greatly improve the spectrum utilization and power utilization of V2V wireless communications. Therefore, introducing large-scale MIMO systems into V2V communications has become a very potential solution. Configuring large-scale antenna arrays (more than dozens) at the vehicle receiving end to deeply tap and utilize spatial dimension resources has become one of the development trends of future V2V wireless communications.
在C-V2V大规模MIMO系统中,由于存在更高的移动速度和更快的信道衰落,需要进行更加频繁的信道信息获取操作,这会导致导频开销大大增加。在导频资源受限的情形下,瞬时信道状态信息的获取变得较为困难,基站侧和各V2V通信对的发送端并不总能知道高质量的瞬时CSI。并且在大规模MIMO系统的实际应用中存在很多挑战,如功率放大器非线性、收发机I/Q失衡、量化误差等,同时由于存在信道估计误差和信道老化等因素,基站端和各V2V通信对的发送端通常无法得到完美的CSI。考虑一个C-V2V大规模MIMO下行链路,研究C-V2V大规模MIMO下行链路传输中对基站端和V2V发送端处的不完美CSI鲁棒的预编码设计和多播单播协同传输。本发明给出了一种C-V2V大规模MIMO多播和单播鲁棒协同传输方法。In the C-V2V massive MIMO system, due to the higher mobile speed and faster channel fading, more frequent channel information acquisition operations are required, which will greatly increase the pilot overhead. In the case of limited pilot resources, it becomes more difficult to obtain instantaneous channel state information, and the base station side and the transmitter of each V2V communication pair cannot always know the high-quality instantaneous CSI. In addition, there are many challenges in the practical application of large-scale MIMO systems, such as power amplifier nonlinearity, transceiver I/Q imbalance, quantization error, etc. At the same time, due to factors such as channel estimation error and channel aging, the base station side and the transmitter of each V2V communication pair usually cannot obtain perfect CSI. Considering a C-V2V massive MIMO downlink, the precoding design and multicast-unicast coordinated transmission that are robust to imperfect CSI at the base station side and the V2V transmitter in the C-V2V massive MIMO downlink transmission are studied. The present invention provides a C-V2V massive MIMO multicast and unicast robust coordinated transmission method.
发明内容Summary of the invention
发明目的:针对上述技术的不足之处,提供一种C-V2V大规模MIMO多播和单播协同传输方法,该传输方法对于基站端和V2V发送端处的不完美CSI鲁棒,在各种典型移动场景下均能得到较好的增益。Purpose of the invention: To address the deficiencies of the above-mentioned technologies, a C-V2V large-scale MIMO multicast and unicast collaborative transmission method is provided, which is robust to imperfect CSI at the base station and the V2V transmitter, and can obtain good gain in various typical mobile scenarios.
技术方案:为实现上述发明目的,本发明的C-V2V大规模MIMO多播和单播协同传输方法,在蜂窝网络中配置基站、多个蜂窝用户和多对V2V通信对,每个V2V通信对包含一个V2V-Tx和一个V2V-Rx,基站侧配备的天线个数为M,V2V-Tx配备的天线个数为N,蜂窝用户个数为K,V2V通信对个数为D,第k个蜂窝用户和第d个V2V-Rx分别配备Nk和Nd根天线,以分别表示蜂窝用户集合、V2V-Tx集合和V2V-Rx集合;Technical solution: To achieve the above-mentioned invention object, the C-V2V massive MIMO multicast and unicast coordinated transmission method of the present invention configures a base station, multiple cellular users and multiple V2V communication pairs in a cellular network, each V2V communication pair includes a V2V-Tx and a V2V-Rx, the number of antennas equipped on the base station side is M, the number of antennas equipped on the V2V-Tx is N, the number of cellular users is K, the number of V2V communication pairs is D, the kth cellular user and the dth V2V-Rx are equipped with N k and N d antennas respectively, so as to They represent the cellular user set, V2V-Tx set and V2V-Rx set respectively;
首先,蜂窝网络中的所有蜂窝用户和所有V2V-Rx分别向基站和匹配的V2V-Tx同时发送上行探测信号,基站和各V2V-Tx根据接收到的探测信号获取每个蜂窝用户和所有V2V-Rx的先验统计信道信息;First, all cellular users and all V2V-Rx in the cellular network send uplink detection signals to the base station and the matching V2V-Tx at the same time. The base station and each V2V-Tx obtain the prior statistical channel information of each cellular user and all V2V-Rx according to the received detection signals.
然后,在上行训练过程中所有蜂窝用户和V2V-Rx发送导频信号,基站和各V2V-Tx利用先验统计信道信息和接收到的导频信号进行信道估计,从而得到每个用户的后验统计信道信息,该后验统计信道信息包含信道均值和方差;Then, during the uplink training process, all cellular users and V2V-Rx send pilot signals, and the base station and each V2V-Tx use the prior statistical channel information and the received pilot signals to perform channel estimation, thereby obtaining the a posteriori statistical channel information of each user, which includes the channel mean and variance;
最后,基站和各V2V-Tx利用包含信道均值和方差的后验统计信道信息,通过MM算法和引入确定性等同进行低复杂度的鲁棒线性预编码,实施下行链路中的蜂窝网多播和V2V通信对单播的协同传输,使得协同传输的加权和速率最大化。Finally, the base station and each V2V-Tx use the a posteriori statistical channel information including the channel mean and variance, perform low-complexity robust linear precoding through the MM algorithm and introduce deterministic equivalence, and implement the coordinated transmission of cellular network multicast and V2V communication to unicast in the downlink, so as to maximize the weighted sum rate of the coordinated transmission.
优选的,在下行链路传输过程中,基站向所有蜂窝用户发送相同的信息,而每个V2V通信对中的V2V-Tx分别向相应的V2V-Rx发送不同的信息。Preferably, during downlink transmission, the base station sends the same information to all cellular users, while the V2V-Tx in each V2V communication pair sends different information to the corresponding V2V-Rx.
优选的,所述后验统计信道模型中引入时间相关系数,所述时间相关系数与蜂窝用户的移动速度有关,体现不同时间块之间的信道变化。Preferably, a time correlation coefficient is introduced into the posterior statistical channel model, and the time correlation coefficient is related to the moving speed of the cellular user and reflects the channel changes between different time blocks.
优选的,在所述的鲁棒预编码传输中,基站和各V2V-Tx根据蜂窝网多播和V2V通信对单播的协同传输加权遍历和速率最大化准则,进行蜂窝用户和所有V2V-Rx的线性预编码设计,包括如下步骤:通过迭代的方式给出加权和速率的最优解,输入值是前述上行探测得到的先验统计信道信息和上行训练得到的后验统计信道信息,输出值是最优预编码矩阵。本发明首次将MM算法和确定性等同应用于用于C-V2V预编码场景中。Preferably, in the robust precoding transmission, the base station and each V2V-Tx perform linear precoding design for cellular users and all V2V-Rx according to the weighted traversal and rate maximization criteria of the coordinated transmission of cellular network multicast and V2V communication to unicast, including the following steps: giving the optimal solution of weighted sum rate by iteration, the input value is the a priori statistical channel information obtained by the aforementioned uplink detection and the a posteriori statistical channel information obtained by uplink training, and the output value is the optimal precoding matrix. The present invention is the first to apply the MM algorithm and determinism to the C-V2V precoding scenario.
优选的,以协同传输加权遍历和速率为目标函数的原始优化问题无法直接求解,通过引进MM算法,找到了一个原始优化问题中目标函数的替代函数,从而构建出一个新的等价优化问题,该等价优化问题为凹二次优化问题,可以直接求解;由于和原优化问题是等价的,得到的最优解也即为原优化问题的最优解。Preferably, the original optimization problem with cooperative transmission weighted traversal and rate as the objective function cannot be solved directly. By introducing the MM algorithm, a substitute function for the objective function in the original optimization problem is found, thereby constructing a new equivalent optimization problem. The equivalent optimization problem is a concave quadratic optimization problem and can be solved directly. Since it is equivalent to the original optimization problem, the optimal solution obtained is also the optimal solution of the original optimization problem.
优选的,通过将所述凹二次优化问题中的速率替换为其确定性等同,来降低算法的计算复杂度。Preferably, the computational complexity of the algorithm is reduced by replacing the rates in the concave quadratic optimization problem with their deterministic equivalents.
优选的,利用矩阵求逆引理,回避所述凹二次优化问题求解过程中的大维矩阵求逆,降低算法的计算复杂度。上面所述的MM算法、确定性等同、矩阵求逆引理,都属于优化预编码算法的工具,结果已经体现在最终给出的预编码算法步骤中使用到的迭代公式。在具体实施中,只需要运行给出的预编码算法即可。Preferably, the matrix inversion lemma is used to avoid the large-dimensional matrix inversion in the process of solving the concave quadratic optimization problem, thereby reducing the computational complexity of the algorithm. The MM algorithm, deterministic equivalence, and matrix inversion lemma described above are all tools for optimizing the precoding algorithm, and the results are reflected in the iterative formula used in the final precoding algorithm steps. In the specific implementation, it is only necessary to run the given precoding algorithm.
优选的,所述蜂窝用户和发送车辆用户的后验统计信道信息包含了信道均值和方差,在所有用户信道均值都为零的特殊场景下,基站和各V2V-Tx均采用波束域发送,即:基站进行多播信号发送时,最优发送方向应与基站协方差矩阵的特征矢量一致,而V2V链路中,单播信号的发送方向应与相应V2V-Tx的协方差矩阵的特征矢量一致。Preferably, the a posteriori statistical channel information of the cellular user and the transmitting vehicle user includes the channel mean and variance. In the special scenario where the channel means of all users are zero, the base station and each V2V-Tx adopt beam domain transmission, that is, when the base station sends a multicast signal, the optimal transmission direction should be consistent with the eigenvector of the base station covariance matrix, and in the V2V link, the transmission direction of the unicast signal should be consistent with the eigenvector of the covariance matrix of the corresponding V2V-Tx.
优选的,在所有用户信道均值都为零的特殊场景下,采用波束域传输时,将原协同传输加权和速率最优化问题简化为一个波束域功率分配最优化问题。预编码矩阵体现的信息是信号的发送方向和各个信号发送方向的发送功率,由于波束域传输中信号的发送方向已经确定,因此只要求得各方向上的最优发送功率,就能够得到预编码矩阵的最优解。Preferably, in the special scenario where the mean of all user channels is zero, when beam domain transmission is used, the original coordinated transmission weighted sum rate optimization problem is simplified to a beam domain power allocation optimization problem. The information reflected by the precoding matrix is the transmission direction of the signal and the transmission power of each signal transmission direction. Since the transmission direction of the signal in beam domain transmission has been determined, it is only necessary to obtain the optimal transmission power in each direction to obtain the optimal solution of the precoding matrix.
优选的,在所有用户信道均值都为零的特殊场景下,波束域功率分配最优化问题的求解算法中,大维矩阵求逆通过逐元素求逆的方式完成,从而大大降低算法的计算复杂度。在用户信道均值都为零的特殊场景下,由于优化问题由天线域转到了波束域,在原天线域涉及到求逆的大维矩阵,在波束域是对角矩阵,而对角阵的求逆非常简单,对各对角元素逐个求逆即可,从而规避了计算复杂度很高的大维矩阵求逆。在具体实施中按照给出的波束域预编码算法中的公式计算即可。Preferably, in the special scenario where the mean of all user channels is zero, in the algorithm for solving the optimization problem of beam domain power allocation, the inversion of the large-dimensional matrix is completed by inverting the element by element, thereby greatly reducing the computational complexity of the algorithm. In the special scenario where the mean of all user channels is zero, since the optimization problem is transferred from the antenna domain to the beam domain, the large-dimensional matrix involved in the inversion in the original antenna domain is a diagonal matrix in the beam domain, and the inversion of the diagonal matrix is very simple, and each diagonal element can be inverted one by one, thereby avoiding the inversion of the large-dimensional matrix with high computational complexity. In the specific implementation, it can be calculated according to the formula in the given beam domain precoding algorithm.
有益效果:Beneficial effects:
本发明提出的C-V2V大规模MIMO基站多播和V2V链路单播鲁棒协同传输方法考虑了信道估计误差、信道老化和空间相关所造成的影响,对多种典型移动场景具有普适性,并且显著提升了系统的频谱效率。所提出的最大化协同传输加权和速率的预编码设计方法大大减少了大维矩阵求逆的数量,能够以较低计算复杂度实现。通过对后验统计信道状态信息中的信道均值为零的特殊场景的进一步研究,将原速率优化问题等价转化为一个更简单的波束域功率分配问题,且算法中可以用逐元素求逆的方式解决大维矩阵求逆,从而大大降低算法的计算复杂度。本发明首次在C-V2V场景下,在后验统计信道模型中引入时间相关系数,体现了不同时间块之间的信道变化。The robust cooperative transmission method for C-V2V massive MIMO base station multicast and V2V link unicast proposed in the present invention takes into account the impact of channel estimation error, channel aging and spatial correlation, is universal for a variety of typical mobile scenarios, and significantly improves the spectrum efficiency of the system. The proposed precoding design method for maximizing the weighted sum rate of cooperative transmission greatly reduces the number of large-dimensional matrix inversions and can be implemented with lower computational complexity. Through further research on special scenarios where the channel mean in the posterior statistical channel state information is zero, the original rate optimization problem is equivalently transformed into a simpler beam domain power allocation problem, and the algorithm can solve the large-dimensional matrix inversion in an element-by-element inversion manner, thereby greatly reducing the computational complexity of the algorithm. For the first time, the present invention introduces a time correlation coefficient in the posterior statistical channel model in the C-V2V scenario, reflecting the channel changes between different time blocks.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明C-V2V大规模MIMO多播和单播鲁棒协同传输方法流程图。FIG1 is a flow chart of the C-V2V massive MIMO multicast and unicast robust cooperative transmission method of the present invention.
图2为本发明方法适用的C-V2V大规模MIMO无线通信系统示意图。FIG2 is a schematic diagram of a C-V2V massive MIMO wireless communication system to which the method of the present invention is applicable.
具体实施方式DETAILED DESCRIPTION
下面将结合附图对本发明的具体实施例做进一步说明:The specific embodiments of the present invention will be further described below in conjunction with the accompanying drawings:
如图1和图2所示,本发明实施例公开的一种C-V2V大规模MIMO多播和单播鲁棒协同传输方法,在蜂窝网络中配置基站、多个蜂窝用户和多对V2V通信对,每个V2V通信对包含一个发送车辆用户(V2V-Tx)和一个接收车辆用户(V2V-Rx),基站侧配备的天线个数为M,V2V-Tx配备的天线个数为N,蜂窝用户个数为K,V2V通信对个数为D,第k个蜂窝用户和第d个V2V-Rx分别配备Nk和Nd根天线,以 分别表示蜂窝用户集合、V2V-Tx集合和V2V-Rx集合。As shown in FIG1 and FIG2 , an embodiment of the present invention discloses a C-V2V massive MIMO multicast and unicast robust cooperative transmission method, in which a base station, multiple cellular users and multiple V2V communication pairs are configured in a cellular network, each V2V communication pair includes a transmitting vehicle user (V2V-Tx) and a receiving vehicle user (V2V-Rx), the number of antennas equipped on the base station side is M, the number of antennas equipped on the V2V-Tx is N, the number of cellular users is K, the number of V2V communication pairs is D, the kth cellular user and the dth V2V-Rx are equipped with N k and N d antennas respectively, so that They represent the cellular user set, V2V-Tx set and V2V-Rx set respectively.
步骤如下:Here are the steps:
首先,蜂窝网络中的所有蜂窝用户和所有V2V-Rx分别向基站和匹配的V2V-Tx同时发送上行探测信号,基站和各V2V-Tx根据接收到的探测信号获取每个蜂窝用户和所有V2V-Rx的先验统计信道信息,即各用户的信道功率矩阵;First, all cellular users and all V2V-Rx in the cellular network send uplink detection signals to the base station and the matching V2V-Tx at the same time. The base station and each V2V-Tx obtain the prior statistical channel information of each cellular user and all V2V-Rx according to the received detection signals, that is, the channel power matrix of each user;
然后,在上行训练过程中所有蜂窝用户和V2V-Rx发送导频信号,基站和各V2V-Tx利用先验统计信道信息和接收到的导频信号进行信道估计,从而得到每个用户的后验统计信道信息,该后验统计信道信息包含信道均值和方差;Then, during the uplink training process, all cellular users and V2V-Rx send pilot signals, and the base station and each V2V-Tx use the prior statistical channel information and the received pilot signals to perform channel estimation, thereby obtaining the a posteriori statistical channel information of each user, which includes the channel mean and variance;
最后,基站和各V2V-Tx利用包含信道均值和方差的后验统计信道信息,通过MM算法和引入确定性等同进行低复杂度的鲁棒线性预编码,实施下行链路中的蜂窝网多播和V2V通信对单播的协同传输,使得协同传输的加权和速率最大化。Finally, the base station and each V2V-Tx use the a posteriori statistical channel information including the channel mean and variance, perform low-complexity robust linear precoding through the MM algorithm and introduce deterministic equivalence, and implement the coordinated transmission of cellular network multicast and V2V communication to unicast in the downlink, so as to maximize the weighted sum rate of the coordinated transmission.
下面结合具体系统模型对本发明实施例作进一步详细介绍。The embodiments of the present invention are further described in detail below in conjunction with a specific system model.
1、C-V2V大规模MIMO系统配置及通信过程1. C-V2V massive MIMO system configuration and communication process
在C-V2V大规模MIMO系统模型中,基站位于小区中心,所有的蜂窝用户和V2V通信对分布在该区域上,基站侧和V2V接收端配置包含数十个以上天线单元的天线阵列,大规模天线阵列可采用线阵列、圆阵列、板阵列或其它阵列结构。本实施例采用均匀线阵。各天线单元可采用全向天线或者扇区天线,当各天线单元采用全向天线、120度扇区天线和60度扇区天线时,各天线之间的间距可配置为1/2波长、波长和1个波长。各天线单元可采用单极化或多极化天线。通信采用时分双工传输模式。设基站侧配备的天线个数为M,V2V-Tx配备的天线个数为N,蜂窝用户个数为K,V2V通信对个数为D,第k个蜂窝用户和第d个V2V-Rx分别配备Nk和Nd根天线。以分别表示蜂窝用户集合、V2V-Tx集合和V2V-Rx集合。In the C-V2V large-scale MIMO system model, the base station is located in the center of the cell, and all cellular users and V2V communication pairs are distributed in this area. The base station side and the V2V receiving end are configured with an antenna array containing more than dozens of antenna units. The large-scale antenna array can adopt a linear array, a circular array, a plate array or other array structures. This embodiment adopts a uniform linear array. Each antenna unit can adopt an omnidirectional antenna or a sector antenna. When each antenna unit adopts an omnidirectional antenna, a 120-degree sector antenna and a 60-degree sector antenna, the spacing between each antenna can be configured to be 1/2 wavelength, wavelength and 1 wavelength. Each antenna unit can use a single-polarization or multi-polarization antenna. Communication adopts time division duplex transmission mode. Assume that the number of antennas equipped on the base station side is M, the number of antennas equipped on the V2V-Tx is N, the number of cellular users is K, the number of V2V communication pairs is D, and the kth cellular user and the dth V2V-Rx are equipped with N k and N d antennas respectively. They represent the cellular user set, V2V-Tx set and V2V-Rx set respectively.
此种情况下,C-V2V大规模MIMO多播和单播鲁棒协同传输过程包含以下三个步骤:In this case, the C-V2V massive MIMO multicast and unicast robust cooperative transmission process includes the following three steps:
i.信道探测:基站端和各V2V-Tx依据接收到的探测信号获取各蜂窝用户的先验统计信道信息。i. Channel detection: The base station and each V2V-Tx obtain the prior statistical channel information of each cellular user based on the received detection signal.
ii.信道训练:蜂窝用户和V2V-Rx周期性地发送导频给基站和对应的V2V-Tx。基站和各V2V-Tx利用先验统计信道信息和接收到的导频信号进行信道估计,获得各用户的后验统计信道信息,包括信道均值和方差。ii. Channel training: Cellular users and V2V-Rx periodically send pilot signals to the base station and the corresponding V2V-Tx. The base station and each V2V-Tx use the prior statistical channel information and the received pilot signal to perform channel estimation and obtain the a posteriori statistical channel information of each user, including the channel mean and variance.
iii.预编码传输:基站和各V2V-Tx利用所得的后验统计信道信息进行鲁棒线性预编码,实施下行链路中的蜂窝网多播和V2V通信对单播的协同传输。iii. Precoded transmission: The base station and each V2V-Tx use the obtained a posteriori statistical channel information to perform robust linear precoding and implement the coordinated transmission of cellular network multicast and V2V communication to unicast in the downlink.
2、先验统计信道信息2. Prior Statistical Channel Information
各用户的先验统计信道信息的获取由上行信道探测过程完成。假设时间资源被分为若干个时隙,每个时隙包含若干个时间块,并且每个时间块有T个符号。考虑信道在每个时间块内平坦衰落,即信道在一个时间块内保持不变,而在不同的相干时间块之间会发生变化。假设在每个时隙中,第一个时间块用于上行训练,剩余时间块用于下行数据传输。The acquisition of the prior statistical channel information of each user is completed by the uplink channel detection process. Assume that the time resource is divided into several time slots, each time slot contains several time blocks, and each time block has T symbols. Consider that the channel fades flat in each time block, that is, the channel remains unchanged in a time block, but changes between different coherent time blocks. Assume that in each time slot, the first time block is used for uplink training and the remaining time blocks are used for downlink data transmission.
令和分别表示时隙s中第n个时间块里基站到第k个蜂窝用户的下行链路信道,基站到第d个VRx的下行链路信道,第d'个VTx到第k个蜂窝用户的下行链路信道,和第d'个VTx到第d个VRx的下行链路信道,表达式如下:make and They represent the downlink channel from the base station to the kth cellular user, the downlink channel from the base station to the dth VRx, the downlink channel from the d'th VTx to the kth cellular user, and the downlink channel from the d'th VTx to the dth VRx in the nth time block in the time slot s, respectively. The expressions are as follows:
其中,和均为确定的酉矩阵,VM和VN分别表示M维和N维的DFT矩阵,和均为所有元素是非负值的确定矩阵,和均为元素服从独立同分布的复高斯随机矩阵(各元素均值为零,方差为1)。下标中为求简洁忽略了s。in, and are all definite unitary matrices, V M and V N represent the M-dimensional and N-dimensional DFT matrices respectively, and are all deterministic matrices whose elements are non-negative. and are all complex Gaussian random matrices whose elements are independent and identically distributed (mean of each element is zero and variance is 1). s is ignored in the subscripts for simplicity.
采用Gauss-Markov过程来表示不同时间块之间的信道变化,则第(n+1)个时间块中的信道矩阵有如下表达式:The Gauss-Markov process is used to represent the channel changes between different time blocks. The channel matrix in the (n+1)th time block has the following expression:
其中,和为时间相关系数。该系数与基站用户和车辆的移动速度有关,体现了不同时间块之间的信道变化,可用Jake自相关模型求得,即其中J0(·)为第一类零阶Bessel函数,vk为第k个蜂窝用户的移动速度,fc为载波频率,c表示光速。其他相关系数可由相同的方法求得。定义信道功率矩阵 in, and is the time correlation coefficient. This coefficient is related to the moving speed of base station users and vehicles, reflecting the channel changes between different time blocks, and can be obtained using the Jake autocorrelation model, that is, Where J 0 (·) is the first kind of zero-order Bessel function, v k is the mobile speed of the kth cellular user, f c is the carrier frequency, and c represents the speed of light. Other correlation coefficients can be obtained by the same method. Define the channel power matrix
则这些信道功率矩阵即为上行探测过程中基站和各VTx获得的先验统计信道信息。该先验统计信道信息属于长时统计特性,其变化与具体的应用场景有关,其典型统计时间窗是短时传输时间窗的数倍或数十倍,相关信息的获取也在较大的时间宽度上进行。假设信道样本数为S,且的第s个样本表示为可以得到样本协方差矩阵为 These channel power matrices are the a priori statistical channel information obtained by the base station and each VTx during the uplink detection process. This a priori statistical channel information is a long-term statistical characteristic, and its variation is related to the specific application scenario. Its typical statistical time window is several times or dozens of times the short-term transmission time window, and the acquisition of relevant information is also carried out over a larger time width. Assume that the number of channel samples is S, and The sth sample of The sample covariance matrix can be obtained as
由特征值分解可以得到则信道功率矩阵可由下式计算得到:By eigenvalue decomposition Can get Then the channel power matrix It can be calculated by the following formula:
3、后验统计信道信息3. A posteriori statistical channel information
由TDD通信中的信道互易性可知,下行链路的信道状态信息可由上行链路的训练过程求得。每个时隙中的上行训练在该时隙的第一个时间块进行,令表示上行训练中基站的接收矩阵,则According to the channel reciprocity in TDD communication, the channel state information of the downlink can be obtained by the uplink training process. The uplink training in each time slot is performed in the first time block of the time slot. represents the receiving matrix of the base station in uplink training, then
其中,和分别为第k个蜂窝用户和第d个VRx在第一个时间块内发送的上行训练矩阵,为元素服从独立同分布的加性高斯白噪声矩阵(各元素均值为零,方差为)。将接收矩阵矢量化,即in, and are the uplink training matrices sent by the kth cellular user and the dth VRx in the first time block, is an additive Gaussian white noise matrix whose elements are independent and identically distributed (the mean of each element is zero and the variance is ). will receive the matrix Vectorization, that is
令表示的协方差矩阵,则有make express The covariance matrix of
假设所有发送天线的导频序列正交,则给定时对的MMSE估计的表达式如下:Assuming that the pilot sequences of all transmitting antennas are orthogonal, we can get Time The expression of MMSE estimation is as follows:
其中,矩阵的元素定义为Among them, the matrix The elements are defined as
则可得Then we can get
其中,in,
最终可得如下表达式:Finally, we get the following expression:
其中,in,
和and
同样地,令表示上行训练中第d个VTx的接收矩阵,则Similarly, represents the receiving matrix of the dth VTx in uplink training, then
并且的协方差矩阵有如下表达式:and The covariance matrix of There are the following expressions:
的MMSE估计和估计误差的协方差矩阵分别为 The covariance matrices of the MMSE estimate and the estimation error are
和and
其中,in,
因此,可得如下表达式:Therefore, the following expression can be obtained:
其中,in,
和and
式(1),式(2),式(3)和式(4)即为基站和各VTx通过信道估计得到的后验统计信道信息,包含了信道均值和方差。对于任意的和基站和所有车辆通信对的发送端已知其对应的和其中和为信道探测过程中得到的先验统计信道信息。由式(1)-式(4)可以看出,所述的后验统计信道信息可被基站和各VTx利用先验统计信道信息和上行训练过程中接收到的导频信号所获取。Formula (1), Formula (2), Formula (3) and Formula (4) are the a posteriori statistical channel information obtained by the base station and each VTx through channel estimation, including the channel mean and variance. and The base station and the transmitters of all vehicle communication pairs know their corresponding and in and It can be seen from equations (1) to (4) that the a posteriori statistical channel information can be obtained by the base station and each VTx using the a priori statistical channel information and the pilot signal received during the uplink training process.
4、鲁棒预编码传输4. Robust precoding transmission
考虑时隙s中的多播和单播协同传输,令和分别表示时隙s中第n个时间块下行链路中基站发送的多播信号和第d个VTx发送的单播信号。假设和互不相关,且有如下统计特性:令表示第k个蜂窝用户接收到的信号,表示第d个VRx接收到的信号,则和分别有如下表达式:Consider the multicast and unicast coordinated transmission in time slot s, let and They represent the multicast signal sent by the base station and the unicast signal sent by the dth VTx in the downlink of the nth time block in time slot s. and They are uncorrelated and have the following statistical properties: make represents the signal received by the kth cellular user, represents the signal received by the dth VRx, then and The expressions are as follows:
和and
其中,和分别为基站和第d个VTx的预编码矩阵,和 in, and are the precoding matrices of the base station and the d-th VTx respectively, and
为加性高斯白噪声矢量。假设所有的蜂窝用户和VRx均已知瞬时信道状态信息和预编码矩阵。在对多播信号进行解码时,将对于第k个蜂窝用户的干扰与噪声之和is the additive white Gaussian noise vector. Assume that all cellular users and VRx know the instantaneous channel state information and precoding matrix. When decoding the multicast signal, the sum of the interference and noise for the kth cellular user is
视为最坏情况下的高斯噪声,相应的协方差为Assuming it as the worst-case Gaussian noise, the corresponding covariance is
同样地,第d个VRx在对单播信号进行解码时,干扰与噪声之和Similarly, when the dth VRx decodes the unicast signal, the sum of interference and noise is
也被视为最坏情况下的高斯噪声,其协方差为It is also regarded as the worst-case Gaussian noise, with a covariance of
假设第k个蜂窝用户已知第d个VRx已知在基站对所有蜂窝用户的多播传输中,基站发送的多播信号要被所有蜂窝用户解码。对于蜂窝链路,其可达遍历多播速率定义为Assume that the kth cellular user is known The dth VRx is known In a multicast transmission from a base station to all cellular users, the multicast signal sent by the base station must be decoded by all cellular users. For a cellular link, the achievable ergodic multicast rate is defined as
其中,第k个蜂窝用户的可达遍历多播速率为Among them, the achievable ergodic multicast rate of the kth cellular user is for
而对于V2V链路的单播传输,由第d个VTx发送的单播信号被同一通信对中相应的VRx解码。对于第d个VTx,其可达遍历单播速率可表示为For unicast transmission of V2V links, the unicast signal sent by the d-th VTx is decoded by the corresponding VRx in the same communication pair. For the d-th VTx, its achievable ergodic unicast rate can be expressed as
在协同传输中,将蜂窝用户的多播速率和V2V链路的单播速率的加权和作为目标函数,构造如下速率最优化问题:In cooperative transmission, the weighted sum of the multicast rate of cellular users and the unicast rate of the V2V link is used as the objective function, and the following rate optimization problem is constructed:
其中,η∈(0,1)为权重因子,Pc和分别为基站和第d个VTx的功率约束。接下来,我们的目标是找到能够最大化式(5)中加权和速率的预编码矩阵和 Among them, η∈(0,1) is the weight factor, P c and are the power constraints of the base station and the dth VTx respectively. Next, our goal is to find the precoding matrix that can maximize the weighted sum rate in equation (5): and
令f表示式(5)中的目标函数。令表示第i次迭代中一个预编码矩阵的不动点组合。定义和为Let f denote the objective function in equation (5). represents a fixed point combination of precoding matrices in the i-th iteration. Definition and for
定义函数g1为Define the function g1 as
其中,和为常数,且in, and is a constant, and
则g1为函数f在处的最小化函数。利用该函数可将预编码矩阵更新为Then g 1 is the function f in The minimization function at . This function can be used to update the precoding matrix to
式(6)中提供的极限点是式(5)中预编码矩阵的一个稳定点,且式(6)中的最优化问题是一个凹二次优化问题,它的最优解可由拉格朗日乘子法求得。定义其拉格朗日函数为The limit point provided in equation (6) is a stable point of the precoding matrix in equation (5), and the optimization problem in equation (6) is a concave quadratic optimization problem, and its optimal solution can be obtained by the Lagrange multiplier method. Define its Lagrangian function as
其中,λ,λ1,…,λD为拉格朗日乘子。由上式的一阶最优条件可得Among them, λ, λ 1 ,…,λ D are Lagrange multipliers. From the first-order optimal condition of the above formula, we can get
和and
令λo=0且可得最优解Let λ o = 0 and The optimal solution
采用同样的方法也可以求得最优解The same method can also be used to obtain the optimal solution
为了计算式(7)和式(8)的最优解,我们需要先求得 In order to calculate the optimal solution of equation (7) and equation (8), we need to first find
定义definition
然后可得如下表达式:Then we can get the following expression:
则有Then there is
和的第一部分可用同样的方法求得,但是它们的第二部分非常复杂且没有闭式表达,下面用确定性等同来解决这个问题。 and The first part of can be found in the same way, but the second part is very complicated and has no closed form expression. We will solve this problem by using deterministic equivalence.
和的确定性等同表达式如下: and The deterministic equivalent expression of is as follows:
或or
其中,in,
且和可由下列迭代等式得到and and It can be obtained by the following iterative equation
和and
则和的确定性等同如下:but and The certainty is equivalent to the following:
注意在每次对的计算中,有一个M×M的求逆过程在每次对的计算中,有一个N×N的求逆过程因此,当M和N的值非常大时,计算复杂度会急剧增加。由矩阵求逆引理,可将和重写为:Note that in each In the calculation of , there is an M×M inverse process In each pair In the calculation of , there is an N×N inverse process Therefore, when the values of M and N are very large, the computational complexity increases dramatically. According to the matrix inversion lemma, and Rewritten as:
通过式(17)和式(18),可以回避每次计算时的M×M求逆和计算时的N×N求逆,计算复杂度也随之大大降低。By using equations (17) and (18), we can avoid calculating The M×M inverse and calculation of The N×N inversion is performed, and the computational complexity is greatly reduced.
根据上述确定性等同的表达式,式(7)和式(8)的预编码更新表达式可重写为According to the above deterministic equivalent expressions, the precoding update expressions of equations (7) and (8) can be rewritten as
和and
下面给出所述C-V2V大规模MIMO鲁棒预编码算法的具体步骤:The specific steps of the C-V2V massive MIMO robust precoding algorithm are given below:
1)初始化:令i=0。随机生成满足功率约束的预编码矩阵初始值 1) Initialization: Set i = 0. Randomly generate the initial value of the precoding matrix that meets the power constraint
2)由式(9)计算和 2) Calculated by formula (9) and
3)利用步骤2的计算结果,根据式(11)计算和 3) Using the calculation results of step 2, calculate according to formula (11) and
4)利用步骤2和步骤3的计算结果,根据式(10)计算和根据式(17)和式(18)计算和根据式(14),式(15)和式(16)计算和 4) Using the calculation results of step 2 and step 3, calculate according to formula (10) and According to formula (17) and formula (18), and According to formula (14), formula (15) and formula (16), calculate and
5)根据步骤4的计算结果,由式(19)和式(20)更新预编码矩阵和令i=i+1。5) Based on the calculation result of step 4, update the precoding matrix by equation (19) and equation (20): and Let i=i+1.
6)重复步骤2到步骤5,直到相邻两次迭代得到的速率差达到预设的门限值。6) Repeat steps 2 to 5 until the rate difference between two adjacent iterations reaches a preset threshold.
5、信道均值为零时的预编码设计5. Precoding design when the channel mean is zero
对于任意的和当所有用户的信道均值都为零,即且For any and When the channel mean of all users is zero, that is, and
时,有 Sometimes, there are
其中,和为主对角元素非零、其余元素均为零的矩阵,和为置换矩阵。分别定义行矢量和如下:in, and is a matrix with non-zero main diagonal elements and zero elements elsewhere, and is a permutation matrix. The row vectors are defined as and as follows:
将置换矩阵和分别设置为使得和中的元素为降序排列。由于所有用户的信道均值都为零,可重写表达式如下:The permutation matrix and are set to make and The elements in are arranged in descending order. Since the channel mean of all users is zero, the expression can be rewritten as follows:
定义函数:Define the function:
以上所有函数的值均为对角矩阵,且All of the above functions evaluate to diagonal matrices, and
由以上表达式,可将和重写为From the above expression, we can and Rewrite as
其中,和均为对角阵,其值和预编码矩阵有关。in, and They are all diagonal matrices, and their values are related to the precoding matrix.
在所有用户的信道均值都为零时,波束域传输能够实现和速率的最大化,且引入确定性等同后,波束域传输仍然是所提出的协同传输加权和速率优化问题的最优解。此时,最优预编码器可重写为When the channel mean of all users is zero, beam domain transmission can maximize the sum rate, and after introducing deterministic equivalence, beam domain transmission is still the optimal solution to the proposed coordinated transmission weighted sum rate optimization problem. At this time, the optimal precoder can be rewritten as
即只需对和进行优化,原预编码设计问题简化为一个波束域功率分配最优问题。由上述表达式,预编码算法中可利用置换矩阵和对角阵的可交换性来简化计算,且在每一次的迭代过程中,大维矩阵求逆都可以通过逐元素的方式得到,这大大降低了算法的计算复杂度。式(24)和式(25)给出了迭代算法中需要的表达式如下:That is, only and The original precoding design problem is simplified to an optimal problem of beam domain power allocation. From the above expression, the precoding algorithm can use the commutativity of permutation matrix and diagonal matrix to simplify the calculation, and in each iteration process, the inversion of large-dimensional matrix can be obtained element by element, which greatly reduces the computational complexity of the algorithm. Equation (24) and Equation (25) give the expressions required in the iterative algorithm as follows:
和and
下面给出信道均值为零时C-V2V大规模MIMO波束域预编码算法的具体步骤:The specific steps of the C-V2V massive MIMO beam-domain precoding algorithm when the channel mean is zero are given below:
1)初始化:令i=0。生成初始值使得其中每个矩阵的主对角线元素值均为1,其他位置的元素均为0,再对这些矩阵进行归一化以满足功率约束值。1) Initialization: Set i = 0. Generate initial value The main diagonal element values of each matrix are all 1, and the elements at other positions are all 0, and then these matrices are normalized to meet the power constraint value.
2)由式(21)计算和 2) Calculated by formula (21) and
3)利用步骤2的计算结果,根据式(22)计算和 3) Using the calculation results of step 2, calculate according to formula (22) and
4)利用步骤2和步骤3的计算结果,计算式(24)中的各参数值。4) Using the calculation results of steps 2 and 3, calculate the values of the parameters in equation (24).
5)根据步骤4的计算结果,由式(25)更新矩阵令i=i+1。5) According to the calculation results of step 4, update the matrix by formula (25) Let i=i+1.
6)重复步骤2到步骤5,直到相邻两次迭代得到的速率差达到预设的门限值后,由式(23)得到最优预编码矩阵。6) Repeat steps 2 to 5 until the rate difference between two adjacent iterations reaches a preset threshold value, and then the optimal precoding matrix is obtained by equation (23).
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