fanyibishe

Abstract—In this paper, we propose a novel and efficient relay selection protocol based on geographical information for cluster-based cooperative wireless sensor networks (WSNs).
摘要：本文中，我们对于基于集群的协作无线传感网络(WSNs)提出了一种新型高效基于地理信息
的中继选择协议。

Multihop transmission is realized by concatenation of single cluster-to-cluster hops, where each cluster-to-cluster scheme forms the simplified cooperative network that consists of a single source destination pair and a set of available relays.
多跳传输是由单个集群对集群的跳通过级联来实现，其中每个集群到集群方式形成了由单个源目标对
和一组可用中继的简化协作网络。

With the relay selection mechanism, the source in each cluster-to-cluster hop selects an optimum relay to execute the cooperative diversity transmission via the simple adaptive decode-and-forward (DF) strategy.
这种中继选择机制，在每个集群到集群跳源通过简单的自适应解码转发（DF）策略选择最佳中继来执行
协作分集传输

The proposed relay selection protocol is designed for minimum symbol error probability (SEP) at the destination by utilizing only geographical information among nodes as selection criteria.
我们提出的中继选择协议被设计为最小误码率（SEP）在目的节点作为选择标准中仅使用地理信息。

In particular, such geographical information is often available during network initialization, and its state required to be maintained is minimum.
特别是，这样的地理信息通常可用在网络初始化，并且其需要维持的状态为最小。

Therefore, the proposed protocol can efficiently perform relay selection without complicated procedures that examine out the optimum relay by channel estimations, and hence it reduces significantly the computational complexity and is applicable to a fast-varying environment.
因此，该协议能够有效地执行中继选择而没有像检查出的最佳中继信道估计这么复杂的过程，因此它显著降低了计算复杂度，适用于快速变化的环境。

Simulation results demonstrate the proposed relay selection protocol can efficiently improve the system performance and outperform the random relay selection protocol in terms of symbol error probability.
仿真结果验证了所提出中继选择协议可以有效地提高系统的性能并且在误码率方面优于随机中继选择协议。

Keywords—Cooperative wireless sensor networks; relay selection
protocols; decode-and-forward (DF); symbol error probability (SEP)
关键字：协作无线传感网络；中继选择协议；解码转发；误码率；

I. INTRODUCTION
Wireless sensor networks (WSNs) consist of a large amount of sensor nodes deployed over a certain wide area, where the sensor nodes are required to be low-cost and low-power devices for long lifetime requirements.
一、引言

无线传感器网络（WSN）由大量部署在一定的范围内的具备使用寿命长，低成本和低功耗器件的传感器节点所组成。

One very challenging task in WSNs due to the limited resources is to develop efficient and scalable protocols meeting the demands for different network functions, such as transmission, routing, and scheduling protocols. Furthermore, affected by physical channel impairments, sensor energy constraints are the main factor that limits the system performance of WSNs.
一种在，由于无线传感器网络中资源的限制，一个极具挑战性的任务是开发满足不同的网络功能的高效和可扩展的协议，如传输，路由和调度协议。此外，限制无线传感器网络的系统性能的主要因素还有物理信道损耗和传感器能源的约束。

Recently, cooperative diversity techniques [1] have been proposed to enhance the system performance without increasing hardware complexity. In cooperative networks, nodes are allowed to collaborate with each other to provide spatial diversity gain at the destination. Considering more than one available relays, Sadek et al. [2] introduced a multi-node cooperative transmission protocol with arbitrary N-relay nodes, in which full diversity order can be achieved.
近来，协作分集技术（文献[1]）已经提出了以提高系统的性能，而不会增加硬件的复杂性。在协作网络中，节点可以互相协作，以提供空间分集增益的目的。考虑到多个可用中继器，Sadeket 等人（文献[2]）提出了一种多节点协作传输协议与任意N个中继节点，其中全分集阶数已经被实现。

However, employing multiple relays may substantially provide high-order cooperative diversity, but it leads to more waste of bandwidth while increasing difficulty in time and carrier synchronization among nodes.
然而，采用多重中继可能会大大提供高阶协作分集，但它会导致带宽比较浪费，同时增加节点之间的困难在时间和载波同步方面。

To avoid these drawbacks, many recent studies focus on the issue of relay selection [3]-[5], i.e., choosing the best relay among the available relays when it has the best channel condition.
为了避免这些缺点，最近的许多研究集中于中继选择的问题（文献[3] - [5]），即，
选择可用中继之间的最佳中继时，它应具有最佳的信道条件。

In [3],the authors suggested the relay is the one closest to the destination, depending on its geographic position. However, it does not gain the advantage of spatial diversity.
在文献[3]中，作者提出的中继是一个最接近目的地，这取决于它的地理位置。然而，它并没有获得空间分集的优点。
In [4], two existing repetition-based cooperative strategies, called cooperative maximum ratio combining (C-MRC) and link adaptive regeneration (LAR), were considered to combine with relay selection respectively.
在文献[4]，现有的两个以重复型的协作策略，称为协作最大比合并（C-MRC）和链路自适应再生（LAR），被认为分别与中继选择相结合。
In [5], a channel-gain-based relay selection protocol was proposed, where the best relay is chosen according to an instantaneous metric. It has been proved that the both schemes of [4] and [5] can provide full or near full diversity order; however, they require a large amount of either channel estimations or Q-function computation and rely on strict coherent time intervals, which make it difficult to implement in realistic resource-constrained networks, such as wireless sensor networks. This motivated us to seek a practical and low-complexity relay selection protocol suitable for wireless sensor networks.
在文献[5]中，提出了一种以信道增益为基础的中继选择协议，其中最佳中继是根据瞬时度量选择。已被证明的是，文献[4]和[5]可以提供已满或接近满分集阶数的两种方案;但是，它们需要大量的任一通道估计或Q-函数的计算，并依靠严格一致的时间间隔，这使得它们难以在实际资源受限的网络，如无线传感器网络中实现。

In this paper, we propose a simple geographic-based relay selection protocol in wireless sensor networks, in which the best relay can be efficiently determined by using the geographical information among nodes. The proposed relay selection protocol is designed for minimum symbol error probability at the destination. In particular, such geographical information can be obtained during the network initialization, the state of which required to be maintained is minimum. Through the relay selection, the selected relay can provide the most reliable source-relay-destination link compared to the other possible relays. Interestingly, the derived selection criteria can be pth-order placement problem, which is a convex form and can be solved efficiently. The rest of this paper is organized as follows. Section II describes the network model of cluster-based cooperative WSNs with relay selection. In Section III we propose the relay selection protocol for every cluster-to-cluster transmission. Section IV provides an application of relay deployment based on the derived selection criteria. Section V shows the numerical simulation results. Finally, we give main conclusions and future work in Section VI.

在本文中，我们提出了在无线传感器网络中一个简单的基于地理信息的中继选择协议，其中最佳中继可以通过节点间的地理信息进行有效地确定。提出中继选择协议是专门被设计来实现到达目的节点的最小误码率。特别地，可以在网络初始化过程中获得这样的地理信息，并且其需要维持的状态量为最小。通过中继选择，所选择的中继和其他可能中继相比可以提供最可靠的源-中继-目的链路。有趣的是，衍生的选择标准可以是p阶布局的问题，这是一个凸形式并能有效地得到解决。本文的其余部分安排如下。第二节介绍了基于集群的协作无线传感器网络的网络模型与中继选择。在第三节中，我们为每个集群到集群传输提出了中继选择协议。第四部分提供中继部署的基础上衍生的选择标准的应用。第五节给出了数值模拟结果。最后，我们给出主要结论和后面第六节工作。

II. NETWORK MODEL
Consider the network model in which relay selection is applied in the cluster-based cooperative wireless sensor network. As Fig. 1 depicts, the WSN is comprised of a fusion center and a set of distributed homogeneous sensors grouped into cooperative clusters, each of which elects a corresponding cluster head. The dash-dotted lines reveal the boundaries of the clusters, and the black-colored nodes denote the cluster heads. The transmission procedures that a sensor transmits its
data to the fusion center can be described as follows: First, a sensor shares the data to its cluster head. Next, the cluster head selects an optimum cooperating sensor within its cluster to collaboratively transmit the data to the neighboring cluster head. Finally, the cluster-based multihop transmission is
completed by concatenating this single-hop scheme, and the fusion center is the final destination.
二、网络模型
考虑到其中继选择是在基于集群的协作无线传感网络应用中的网络模型。如图1所描绘，无线传感网络是由一个决策中心和一组分成协作集群分布均匀的传感器，其中每一个选出相应的集群头。
点的连线表示出集群的边界，黑色的节点表示集群头。该传感器的传输过程及其数据传送到决策中心可以被描述为如下：

首先，传感器共享数据到集群头。接下来，集群头选择一个最佳的协作传感器在其集群内的传感器将数据传送协同向邻近的集群头。最后，基于集群的多跳传输是通过将这种单跳方案完成，并且决策中心是最终的目的地。

We can simplify the above-mentioned network model to the cluster-to-cluster scheme, where the transmission protocol is described as follows. In each cluster-to-cluster transmission, such single-hop scheme forms the simplified cooperative relay network, which consists of a single source (S)-destination (D) pair and N available relays (Ri, i = 1,…,N), depicted in Fig. 2. With the relay selection mechanism, the source cooperates with a selected relay Ri to transmit its data to the destination. In this paper, we assume that each node (either the sensor nodes or the fusion center) has single antenna operating over frequency-flat fading channels and can only either transmit or receive information at any time slot. Let hi,j denotes the fading coefficient of the channel from node i to node j. We assume the magnitude |hi,j| follows a Rayleigh distribution. Variances for Rayleigh fading are modeled using a σ_(i,j)^2∝ d_(i,j)^(-p) path loss model, where p denotes the path loss exponent and di,j represents the distance between node i and node j.
我们可以简化上述的网络模型的簇到簇方案，其中所述传输协议的描述如下。在每个簇到簇的传输，例如单跳方案形成简化的协作中继网络中，它由一个单一的源极（S）-目的地（D）一对与N个可用中继（RI，I = 1，...,N的），在图2中描绘。随着中继选择机制，源与选定的中继Ri相配合，它的数据传输到目的地。在本文中，我们假设每个节点（无论是传感器节点或决策中心）具有单个天线工作在频率平坦衰落信道中，只能要么在任一时隙进行发送或接收的信息。让hi,j，表示该通道从节点i到节点j衰落系数。我们假设的幅度|hi,j|，遵循瑞利分布。
方差为瑞利衰落是使用σ_(i,j)^2∝ d_(i,j)^(-p)的路径损耗模型，其中p表示路径损耗指数和二建模，j表示节点之间的距离i和结点j。

The cooperative diversity transmission under consideration is composed of two phases as follows. In the first phase, the source broadcasts its symbol x with transmission power Px to D and Ri, where the average power of x is normalized to be unity. The received signals at the destination and the selected
relay can be respectively expressed as
y_(S,D)= √(P_x ) h_(S,D) x+ n_(S,D) (1)
y_(〖S,R〗_i )= √(P_x ) h_(〖S,R〗_i ) x+ n_(〖S,R〗_i ) (2)
Where h_(S,D) and h_(〖S,R〗_i ) are the channel fading coefficients from S to D and S to Ri respectively, modeled as 2, , ~ (0, ) S D S D h CN  and 2 , , ~ (0, ) S Ri S Ri h CN ; the additive noise terms S,D n and S ,Ri n are circularly symmetric complex Gaussian random variables, assumed as , 0 ~ (0, ) S D n CN N and , 0 ~ (0, ) S Ri n CN N . Without loss of generality, we assume the noise terms have equal variance with N0 = 1. In the second phase, with the simple adaptive DF strategy [6], the selected relay decides whether to forward the decoded symbol to the destination. If the relay is able to decode the transmitted symbol correctly, it forwards the decoded symbol with the same transmission power Px to the destination, and if not, it remains idle. In practical scenarios, this ‘adaptive’ mechanism can be achieved based on an SNR threshold. If the SNR at the relay is greater than a certain threshold, the relay forwards; otherwise, it remains idle. Define the indicator function Ri I as follows:
I_(R_i )={█(1 ,if decodes the transmitted symbol correctly@0, otherwise.)┤

where Ri ,D h denotes the channel fading coefficient from Ri to D, modeled as h_(S,R_i ) ~ CN(0,σ_(S,R_i)^2 ) and n_(R_i,D) denotes AWGN, n_(R_i,D) ~ CN(0,N_0). Finally, the destination coherently combines the received
signals from the source and the selected relay, i.e., S ,D y and Ri ,D y , by using a maximum ratio combining (MRC) Consequently, the decoded symbol ˆx at the destination is given by where S denotes the cardinality of the -ary constellation. By invoking the performance analysis in [7],-------- (9)暂不翻译！

公式：
正在审议的协作分集传输是由两个阶段如下。在第一阶段中时，源广播的符号x，其中传输功率Px到D和Ri，其中x的平均功率被归一化，以成为统一。协作分集传输是由两个阶段如下。
在目标和所选择的接收的信号中继可分别表示为其中，S ,D h和S ,Ri h 为信道从S到D和S衰落系数到Ri，建模为n_(S,D) ~ CN(0,N_0)和 h_(S,R_i ) ~ CN(0,σ_(S,R_i)^2); 加性噪声项S,D n和S ,Ri n为圆对称复高斯随机变量，假设为 n_(S D) ~ CN(0,N_0) 和 n_(S,R_i ) ~ CN(0,N_0)。不失一般性，我们假设噪声项与n_0=1时方差相等。在第二阶段中，用简单的自适应解码转发策略（文献[6]），所选择的中继决定是否要将码元解码转发至目的地。如果中继能够将发送的码元进行正确解码，将解码码元以相同的发送功率Px转发到目的地，并且如果不是，就保持空闲。在实际情况下，这种“自适应”机制可以基于信噪比（SNR）阈值来实现。如果中继信噪比大于一定的阈值时，中继转发;否则，它仍然闲置。定义指标功能I_(R_i )如下:
I_(R_i )={█(1 ,if decodes the transmitted symbol correctly@0, otherwise.)┤

I_(R_i )={█(1 , 正确解码所传送的码元@0, 否则 .)┤

接下来，目的接收到的信号在第二阶段可以被描述为：
y_(R_i,D)= √(P_x I_(R_i ) ) h_(R_i,D) x+ n_(R_i,D)

其中h_(R_i,D)表示信道衰落系数从Ri到D，模型为h_(S,R_i ) ~ CN(0,σ_(S,R_i)^2)，和 n_(R_i,D) 表示
高斯白噪声（AWGN），n_(R_i,D) ~ CN(0,N_0)。最后，目标相干地组合从源和选择的中继所接收的信号，即，S，D y和日，D Y，通过使用最大比值合并（MRC）。------------------------------

III. RELAY SELECTION DESIGN FOR MINIMUM SEP
We assume that the distances between any two nodes in the network can be obtained by some well-known distance estimation methods, such as [8], during the network initialization. In this paper, we consider an ideal scheme in which the distance information is perfectly known.
三、中继选择设计最小误码率
我们假设网络中的任何两个节点之间的距离可以通过一些众所周知距离估计方法，
例如以下方式获得（文献[8]），在网络初始化期间。在本文中，我们考虑一个理想的方案，其中距离信息是完全已知的。

From the SEP expression in (7), it gives us an insight into the factors involving the system performance, aiding us in designing the relay selection. By rewriting (7) in terms of coding gain and diversity order, we have-------- use a repetition-based DF scheme.红色暂不翻译
误码率的表达式（7）协助我们深入了解系统性能和终极选择的因素。通过编码增益和分集阶数的条件重写表达式（7），
-----需要注意的是Δ，在这里，也表示协作的增益，因为中继只需使用一个重复型解码转发方案。
Our goal is to select the best relay to maximize the cooperation gain in (11) and, hence, minimize the SEP at the destination. Notice that the only term affecting the cooperation gain is
Xxx= xxxx（12）

where mi is called the selection metric for the relay i. Generally, with the knowledge of channel variances from the i-th relay to the source and the destination, we can choose the best relay by minimizing the metric mi over all possible i’s. However, it is impractical to do so in energy-limited WSNs since the channel variance estimation requires a lot of overheads, considerably difficult to be performed especially in a complex environment. In particular, when there are N available relays it is necessary to execute 2N variance estimations. To avoid the difficulty of variance estimations, we proposed a geographic-based scheme in which we replace the channel variances 2,
i j in (12) with the distance-dependent parameters , p i j d −. Thus, (12) becomes------
xxxx = xxxxx (13)
where i m′is treated as our selection metric, which indicates the SEP performance at the destination-- The smaller the metrics, the better the resulting SEP performance. Therefore, the best relay can be determined by the following criteria,
xxxx = xxxxx (14) .
我们的目标是选择最佳中继，以最大限度地提高（11）的协作增益，因此，尽量减小到达目的的误码率。需要注意的是，影响了协作增益的唯一项是mi称为每个中继i的选择量度。一般情况下，从第i个中继到源和目标通道方差的信息，我们可以通过最小化度量 mi 在所有可能的i个中选择最佳中继。然而，这么做是不切实际的在能源有限的无线传感网络中由于信道方差估计需要大量的开销，所以难在特别复杂的环境中进行。特别是，当有N个可用的中继时有必要执行2N次方差估计。为了避免方差估计的困难，我们提出了一种基于地理信息的方案，我们替换信道方差xxxx 用距离相关参数------------------------
Our basic idea is to transfer the difficult variance estimation problem to the simple distance estimation problem. The reason behind this approach is the node-distribution nature of relay networks, which implies the path losses and hence offers certain information on the channel qualities among nodes. In practical scenarios for wireless sensor networks, the path loss exponent p and the distance information can be obtained from some measured data during the network initialization. Such geographic-based protocol has the following advantages: low overhead to be required and minimum state to be maintained, which make it more robust to a fast-varying environment. Therefore, by utilizing only the distance information, the network can efficiently perform relay selection without complicated channel estimations so that the computational complexity can be reduced significantly. However, there is no denying that the proposed relay selection scheme can only achieve the diversity order of 2. The reason is that the proposed scheme can be viewed as a relatively long-term selection
scheme depending on the nodes distribution at that time, which is expected to improve the system performance via less information. In view of the tradeoff between the system complexity and the diversity order, our approach provides a simple and practical relay selection for those energyconcerned
networks that demand low-complexity schemes.
我们的基本思路是将困难的方差估计问题转移为简单的距离估计问题。这一处理方式背后的理由是中继网络中节点分配的本质，这暗示着该路径损耗和对节点之间的信道质量的某些信息。在无线传感器网络的实际情况下，路径损耗指数p和距离信息，可以在网络初始化过程中从一些测量数据中获得的。这种基于地理信息的协议具有以下优点：低开销和最小状态量维护，这使得它具备更强的鲁棒性在一个快速变化的网络环境中。因此，通过利用唯一的距离信息，网络可以有效地进行中继选择，没有复杂的信道估计，使得计算复杂度显著降低。然而，无可否认，我们提出的中继选择方案只能达到2分集阶数。其原因是，该算法可随时根据不同的节点分配，预计通过较少的信息提高系统的性能将被看作是一个相对长期的选择方案。考虑到系统的复杂性和分集阶数之间的权衡，我们的方法提供了一种简单实用的中继选择方案为那些能源关注要求低复杂度的网络。
The procedures of relay selection for each cluster-to-cluster transmission can be summarized as follows: First, each relay acquires the relative distances including S ,Ri d and Ri ,D d to calculate its own selection metric and then send it to the source. Here we assume that the path loss exponent is a known
parameter. Next, the source chooses the best relay as the one with the minimum metric and broadcasts a message to others to indicate which relay is going to cooperate with it.
中继选择为每一个集群到集群传输的过程可以概述如下：首先，每个中继获得的相对距离，包括xxx和xxx来计算自己的选择度量，然后将其发送到源。这里我们假定路径损耗指数是已知的参数。接着，源选择最佳的中继作为一个具有最小度量和广播一条消息给其他中继，指出哪个中继会与它协作。

IV. AN APPLICATION: BEST RELAY DEPLOYMENT

On the basis of the proposed relay selection criteria, onemay raise an interesting question: “Where is the best position of the relay that provides the source and the destination with the best cooperative link in terms of the SEP performance?” We discuss this question in the following. Consider a single relay network in which the positions of the source and the destination are fixed; our task is to determine the position of the relay. The objective is to place the relay on some where such that the SEP at the destination is as small as possible. As we know, it is a typical relay deployment problem. To tackle this problem, we first make some assumptions and then give the mathematical formulation. We assume that the single-relay network is in R2. Let xS and xD ∈R2 represent the positions of the source and the destination respectively, both of which are fixed points. Also, we define a free point x ∈R2, which denotes the position of the relay. Thus, from (13) the best relay deployment problem can be formulated as follows,
xxxx= xxxx (15)

where f : R2 →R is the objective function. Note that (15) is a standard nonlinear facility location problem [9], which is convex and can be solved efficiently via iteration algorithms. In general, for a pth-order placement in (15), it should be solved numerically. In particular, for a quadratic placement,
i.e., p = 2 (in free space), (15) becomes a quadratic placement problem; it can be expressed as the unconstrained quadratic programming (QP) as follows:
xxxx= xxx (16).
Taking derivatives, we see that the quadratic placement problem has the analytical solution, given by
Xxxx= xxxx (17)
四、应用：最佳中继的部署
就拟中继选择标准的基础上，人们提出一个有意思的问题：“哪里是提供了源和目标与误码率的性能方面的最优的协同链路中继的最佳位置？”。下面我们讨论这个问题。考虑单个中继网络中的源和目的端的位置是固定的; 我们的任务是决定中继的位置。目标是将中继上使得误码率在目的端尽可能地小。我们知道这是一个典型的中继部署问题。为了解决这个问题，我们首先做一些假设，然后给出数学公式。我们假设单中继网络是R2。让XS和xD∈R2分别表示源和目的的位置，这两者都是固定的点。此外，我们定义了一个自由点x∈R2，它表示该中继的位置。
因此，从表达式（13）可以看出最佳中继部署问题可以如下规划：
Xxxx= xxxx（15）
其中f：R 2→R为目标函数。需要注意，表达式（15）是一个标准的非线性设备定位问题（文献[9]）它是凸的，可以通过迭代算法，有效的解决。在一般情况下，对于表达式（15）中第p阶的位置，应该进行数值求解。特别地，对于二次布局即p= 2（在自由空间），（15）变成一个二次布局问题; 它可以如下表示为无约束的二次规划（QP）：
Xxxx= xxxxx（16）
取导数，我们看到，二次布局问题有解析解，由下式给出：
Xxxx= xxxx (17)

Without loss of generality we normalize the distance between the source and the destination to unit length while placing the source at the origin and the destination (1, 0), then from (8) and (17) for QPSK modulation the best placement of the relay is at (0.6359, 0). It means that in free space the best
placement of the relay is on the line segment between the source and the destination, and the relay is closer to the destination than to the source (it also holds for general path loss exponent p).
不失一般性，我们规范化源和目的单位长度的距离而放置在原点处的源和目的坐标为（1,0），
然后与从表达式（8）和（17）可以得到，用于QPSK（四相移键控）调制的最佳位置中继是（0.6359，0）。这意味着，在自由空间中中继的最佳位置在源和目的地之间的线段上，而且中继是更靠近于目的而不是源（它也适用于一般的路径损耗指数p）。

Fig. 3. pth-order relay placement
Fig. 3 shows the general cases for the pth-order relay placement using QPSK; it reveals the relationship between the best position of the relay in x-axis and the path loss exponent p over the range from 1.6 to 8.0. We see that the best position of relay is always closer to the destination than to the source, and it moves toward the middle point (0.5, 0) as the path loss exponent increases.
图3显示了一般情况下的使用QPSK的p阶中继放置; 它揭示了中继在x轴方向和最佳位置的路径损耗指数p比从1.6到8.0的范围之间的关系。我们看到，中继的最好的位置总是更接近目标而不是源，并移向中间点（0.5，0）随着路径损耗指数的增加。
V. SIMULATION RESULTS
We first consider the simplified cooperative relay network with N = 5 available relays, deployed in R2. We locate the source and the destination at the coordinates of (0, 0) and (1, 0) respectively, and randomly place the relays at the location displayed in the column (A) of TABLE I. We consider the
ideal scheme introduced in Section III and assume that the channel variances between any two nodes follow 2
, ,
p
i j i j ∝d −,
where p is the path loss exponent and is taken to be p = 3 in our simulations. The channel variance is normalized to be unity for unit distance. Throughout our simulations, we use QPSK modulation and assume that the fading channels are ssufficiently fast-varying such that the channel coefficients
keep constant only within every symbol interval.
五、仿真结果
我们先考虑简化的协作中继网络与N=5个可用中继，部署在R2网络。我们确定源和目的的坐标（0,0）和（1,0），分别随机放置中继在表I.的列（A）中显示的位置。我们介绍的第三节的理想方案，并假设信道的方差之间的任何两个节点遵循 xxxx 其中p是路径损耗指数，并取为p=3在我们的仿真过程。
From the column (A) of TABLE I, we can determine the distances from each relay to the source and the destination, which are known at the source, and then the corresponding selection metric for each relay can be determined by using (13), given in the column (B) of TABLE I. According to the
proposed selection criteria in (14), R5 turns out to be the best relay selection since it has the minimum selection metric.
从表I的栏（A）中，我们可以确定各个中继到源和目的的距离，这是已知的源，然后将相应的选择度量为每个中继可以通过使用表达式（13）来确定，在表一中的列（B）给出。根据表达式（14）提出的选择标准，R5真可谓是最好的中继选择，因为它具有最小的选择度量。
Fig. 4 depicts the SEP versus SNR performance of the above scenario, where SNR is defined as P/N0, and P is the total transmitted power fixed in each case. In Fig. 4, the performance of direct transmission from the source to the destination is provided as a benchmark for a non-cooperation
scheme. Fig. 4 shows that R5 is the best relay since it contributes to the minimum SEP at the destination. Moreover, Fig. 4 also reveals that the worse relay (leading to the worse SEP performance) corresponds to the larger selection metric in the column (B) of TABLE I. In other words, the simulation results are consistent with the proposed relay selection, that is, the smaller the selection metrics, the better the resulting SEP performance. Thus, we have demonstrated that by utilizing the geographical information, nodes in wireless sensor networks can efficiently perform relay selection to improve the SEP performance at the destination. In addition, we also compare the performance with a possible relay selection protocol, named random relay selection protocol, which means that the source randomly selects a cooperating relay without any information for each transmission. We see, in Fig. 4, that the
performance curve of the random selection scheme lies between the best and the worst selection. This is because each relay has the same opportunities to be selected so that the performance will be averaged over all the distributed relays.
图4描绘了误码率相对于上述方案中，其中SNR（信噪比）被定义为P/N0，在每一种情况下总发送功率P是固定的。在图4中，从源到目的直接传输性能是作为一个基准的非协作方案。图4示出了R 5是最好的中继，因为它有最小误码率到目的。此外，图4还表明，糟糕中继（导致较差误码率性能）对应于表I中的列（B）的更大的选择度量。换句话说，仿真结果与提出的中继选择方案一致的，即，较小的选择度量，能更好的获得误码率性能。因此，我们已经证明，通过利用地理信息，无线传感网络中的节点可以有效地进行中继选择，以改善误码率性能的在目的。此外，我们也与一个可能的中继选择协议，叫做随机中继选择协议做性能比较，这表示源随机选择一个协作中继为每个传输且无任何信息。我们可以从图4看到，该随机选择方案的性能曲线介于最好和最差的选择之间。这是因为每个已被选定的中继，以使性能将平均超过所有分布式中继在具备同等的机会时。
Next, without loss of generality, we consider the M-hop cluster-based wireless sensor network that concatenates M copies of the previous scheme. Likewise, we normalize the distance between the source and the final destination to be unity, where the source and the final destination are set at the coordinates of (0, 0) and (1, 0) respectively.
接下来，不失一般性，我们认为基于集群的M跳无线传感网络是将之前的方案复制M份的结果。同样，我们规范源和目的地之间的距离是统一的，其中源和最终的目的的坐标分别被设定为（0,0）和（1,0）。
We give the SEP performance comparison for the following three schemes: conventional multihop scheme (no cooperative diversity), multihop diversity scheme (i.e., the scheme discussed in Section II) with random relay selection protocol, and multihop diversity scheme with the proposed relay selection protocol. We set the number of hops as M = 2. Also, we take the direct transmission scheme as a benchmark for a scheme that has neither diversity gain nor multihop gain. Fig. 5 shows that the conventional multihop scheme has distinct multihop gain compared to the direct transmission, since it
reduces the effects of path loss. However, it has no cooperative diversity gain so that the slope of the SEP performance keeps unchanged. In the cases of the other two schemes, since they achieve the diversity order of 2 that leads to a deeper slope, they have better performance than the conventional multihop scheme. Furthermore, the performance of the multihop diversity scheme with the proposed relay selection outperforms the other two schemes. This is due to the fact that the proposed scheme has not only the diversity gain but also the maximum cooperation gain.
我们给出了以下三种方案误码率的性能比较：传统的多跳方式（无协作分集），多跳分集方案（即，在第二节中讨论的方案）与随机中继选择协议，以及与提出中继选择协议的多跳分集方案。我们设置跳数为M =2，同时，我们采取了直接传输方案为基准的方案，既没有分集增益也没有多跳增益。如图5示出，相对于直接传输传统的多跳方案具有明显的多跳增益，主要是因为它减少了路径损耗的影响。然而，它没有协作分集增益，使得误码率性能的斜率保持不变。在另外两个方案的情况下，因为他们实现分集阶数为2导致更深的斜率，它们比传统的多跳方式具备更好的性能。此外，多跳分集方案与提出的中继选择性能优于其他两个方案。这是因为，该方案不仅具有分集增益，但也是最大协作增益的事实。
VI. CONCLUSION
In this paper, the issue of relay selection for cooperative wireless sensor networks is discussed. We have proposed a new and efficient relay selection protocol based on the geographical information among nodes. Within our framework, the best relay is determined with the aim of providing the most
reliable source-relay-destination link in a simple manner. Simulation results show that after the network initialization, the proposed relay selection protocol can efficiently improve the system reliability without complicated channel estimations and is applicable in fast-varying channels. Furthermore, the proposed protocol can achieve better SEP performance compared with the random relay selection method. For practical schemes, the inherent distance estimation errors may be the main factor affecting the system performance, which are not yet taken into account in this paper. In our future work, we will assess and analyze the effects of such imperfect geographical information on the
proposed relay selection protocol.
六、结论
在本文中，我们对协作无线传感器网络中继选择的的问题进行了讨论。我们已经提出了一种基于节点间地理信息的一种新型高效中继选择协议。在我们的架构中，最好的中继是以简单的方式提供最可靠的源 - 中继器- 目的链路的目的来确定的。仿真结果表明，在网络初始化后提出的中继选择协议可以有效地提高系统的可靠性，而无需复杂的信道估计，且适用于快速变化的信道。此外，与随机中继选择方法相比，该协议能够保证更好的误码率性能。对于实际方案，固有的距离估计误差可能是影响系统性能的主要因素，这是本文中尚未考虑到的。在今后的工作中，我们将评估和分析就提出的中继选择协议，例如不完善地理信息的影响。

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