(N,B)-Connected Ad Hoc Networks
Reducing the waste of the limited battery power in exchanging cluster maintenance messages is one of the important issues in designing clustering algorithm for the wireless ad hoc networks.
Analyses show that this can be achieved by reducing the number of generated clusters and the variance of the number of cluster members. By assigning critical node (the only neighbor of boundary node) the highest weight (or priority) to be selected as a clusterhead, we show that the number of cluster maintenance overheads is reduced by the proposed Distributed Clustering Algorithm with Critical Node First (DCA/CNF) based approaches. As a consequence, the limited battery power is conserved and the organized network architecture is power efficient.
III. 研究方法研究方法研究方法 研究方法
Part I: Phase Noise Estimation in OFDM and OFDMA Uplink Communications
OFDM transmission technique has been adopted in several wireless communication standards for its capability of combating channel multipath fading with relatively low complexity while providing high spectral efficiency in comparison to single carrier transmission. An OFDMA system divides the available subcarriers into groups, called subchannels, and assigns one or multiple subchannels to multiple users for simultaneous transmission. Signals from different users are overlapping in frequency domain but occupying different subcarriers, the orthogonality among subcarriers prevents multiple access interference (MAI) among users.
On the other hand, OFDM is tremendously more sensitive to carrier frequency offset and phase noise than single carrier systems [1] because the orthogonalities among OFDM subcarriers will be destroyed so that common phase error (CPE) and inter-carrier interference (ICI) will appear. OFDMA inherits from OFDM the weakness of being more sensitive to both of them than single carrier multiple access systems. Furthermore, because of the multiple phase noise of multiuser, phase noise will be more detrimental to uplink OFDMA systems if not carefully compensated [2].
Various methods to suppress phase noise in OFDM systems have been proposed in the literature [3]-[5]. However, they are specifically suitable for dealing with single phase noise. To mitigate multiple phase noise in OFDMA uplink, unavoidably, the adopted subcarrier assignment scheme needs to be taken into account since it affects the amount of MAI in the system. Two major subcarrier assignment schemes: subband-based and interleaved [6] are examined. The former divides the whole bandwidth into small continuous subbands, each user is assigned to one or several subbands. In the latter, subcarriers assigned to different users are interleaved over the whole bandwidth. An example of both schemes is illustrated in Fig. 1.
Fig. 1. Illustration of subband-based and interleaved subcarrier assignment schemes [16]
Part II: Characterizing The Wireless Ad Hoc Networks by Using The Distance Distributions
Wireless ad hoc network has been recognized as one of the possible solutions to realize the dream of pervasive computing 0-0 especially when nodes are within the dead zone, an area where the exiting fixed infrastructures are unavailable, since nodes in the wireless ad hoc network can self-organize and operate without the help of the existing infrastructures. By using the multihop forwarding scheme, nodes in the wireless ad hoc networks exchange messages with other nodes that are not directly connected. Possible examples of the wireless ad hoc networks are tactical military applications, disaster recovery operations, exhibitions or conferences.
However, due to the random deployment of the wireless ad hoc networks, the deployed network topologies are also random. As a result, some criterions are commonly used to characterize the random organized network. In this part, we specifically focus on the following three criterions:
the optimum transmission range to organize a wireless ad hoc network and the node degree and the connectivity of the organized network. Since the power of the nodes in the wireless ad hoc networks are mainly provided by the batteries, the optimum transmission range (or the critical transmission range) provides us how to power efficiently assign the transmission range either homogeneously or non-homogeneously so that the organized wireless ad hoc network is connected 0-0. The degree of a node is defined as the number of neighbors that are directly connected with 00 and is widely used as an index of the connectivity of the organized wireless ad hoc networks 0. The network connectivity is one of the most important criterions used to characterize the organized wireless ad hoc networks 0-00-0. This is mainly because for the multihop forwarding scheme in the wireless ad hoc network to be applicable there must exists at least one path between any two nodes so that the messages can be hop-by-hop forwarded to the intended destination nodes. When we look into the three criterions, we find that they are highly related to the distances between the nodes. For example, if the distances between node pairs in the deployed wireless ad hoc networks are short, smaller transmission power is enough for each node to reach its neighbors and, thus, the battery power is conserved. Furthermore, if the transmission range is fixed, shorter distances between nodes result in the higher node degree and the better connectivity of the deployed wireless ad hoc networks. However, due to nodes in the wireless ad hoc networks are in nature randomly and independently distributed into the service area, the distance between any node pair is also random. Thus, it is necessary to study the
stochastic property of the distances between nodes. Only few related researches are found in the literatures. In 0, by using two different distributions, uniform and Gaussian, to deploy nodes into the service area, Miller analyzed the distributions of the distance between two nodes in the wireless ad hoc networks and found that similar distance distributions are obtained by using different models to distribute nodes. Thus, he concluded that using a simple model to distribute nodes would be enough for the analysis and simulation of the wireless ad hoc networks. To obtain the joint distribution, Miller presented an alternative approach to find the marginal cdf of the distance between node and a randomly selected reference node (RN) 0. Then, by employing the independence property, the joint cdf of the distances between nodes and a RN was obtained.
Part III: On The Distance Distributions of The Wireless Ad Hoc Networks
Since nodes in wireless ad hoc networks may be randomly and independently spread over the entire service area, the resulting network topologies are diverse and, thus, the separation distance between any selected node pair can be regarded as a random variable. Many characteristics of the wireless ad hoc networks are related to the separation distances between node pairs. One of the most important characteristics for the wireless ad hoc network to be applicable is the connectivity of the organized network. The most common approach to achieve the network connectivity is to maximize the transmission range so that nodes are connected. However, when the power consumption is considered, the transmission range should be optimized to the separation distance to its nearest neighbor. Most of the connectivity related researches 0-0 are mainly based on the necessary condition that network is k-connected if the minimum node degree of a wireless ad hoc network is k 0. When the wireless ad hoc networks are operated in the ideal environment, the node degree can be easily obtained based on the pathloss model, i. e. the number of nodes within the predefined separation distances. However, in the shadow fading environment, given the separation distances between nodes and a common reference node (CRN), the node degree will dynamically change due to the random fluctuation of the signal strength. Thus, it is necessary to find the joint distance distribution between nodes and a CRN. In this part, we assume that nodes are uniformly and independently deployed within a square service area and the location of each
The first distance distribution we derived is based on the concept that if the Euclidean distance from a reference node to its k-th nearest neighbor is less than the transmission range of the reference node, the minimum degree of the node is k. The disadvantage of this distribution is that the prior knowledge of the order of the nearest neighbor of a reference node is required. To this
Since the obtained marginal cdf and pdf possess the independence property, they can be easily generalized to obtain the joint cdf and pdf. Only few related researches are found in the literatures. The distribution of the k-th nearest neighbor is also known as Nearest Neighbor Distribution (NND) in 00. In 0, by using two different distributions, uniform and Gaussian, to distribute the nodes, Miller analyzed the distributions of the Euclidean distance between two nodes in the wireless ad hoc networks and noted that the models used to distribute nodes generate very similar cdfs. Thus, he concluded that using a simple model to distribute nodes would be enough for the analysis and simulation of wireless ad hoc networks. To obtain the joint distribution, Miller presented an alternative approach to find the marginal cdf of the Euclidean distance between two nodes 0. Then, by employing the independence property, the joint cdf of the Euclidean distances between node pairs that have a common reference node was obtained. In the following analyses, we assume the number of nodes in the network is N and ignore the boundary effects.
Part IV: Organizing an Optimal Cluster-Based Ad Hoc Network Architecture by the Modified Quine-McCluskey Algorithm
When wireless nodes are in an area that is not covered by any existing infrastructure, one of the possible solutions to achieve the ubiquitous computing is to enable wireless nodes to operate in the ad hoc mode [1] and self-organize themselves into a cluster-based network architecture.
One of the general approaches to build up a cluster-based network architecture is to design an algorithm to organize wireless nodes into set of clusters. Within each cluster, a node is elected as a clusterhead (CH) to take responsible for the resource assignments and cluster maintenances.
Many related algorithms have been proposed. The minimum connected dominating set (MCDS) approach [2] tries to obtain an optimum configuration to be the virtual backbone of the wireless ad hoc networks. However, it is shown to be an NP-hard [3] problem. The most feasible alternative is to find an approximated heuristic algorithm to obtain a sub minimum connected dominating set. The general idea among the related literatures is to select CHs based on some attributes of the networks. For example, the node degree, the link delay, the transmission power, the mobility, . . . , etc.. A detail survey of the clustering algorithms can be found in [4].
In viewing the previous works, we find that the minimization of the waste of the precious bandwidth and the limited battery power in exchanging the cluster maintenance overheads has not been well studied. Thus, based on the technique to select the optimum set of prime implicants in the Quine-McCluskey (QM) algorithm [5], we propose a Modified QM (MQM) clustering algorithm to organize the wireless ad hoc network into a cluster-based network architecture that requires the minimum number of cluster maintenance overheads.
Part V: A Clustering Algorithm to Produce Power-Efficient Architecture for (N,B)-Connected Ad Hoc Networks
Wireless ad hoc network is a self-organizing network that can be rapidly deployed and operated without the help of the existing infrastructure. Possible examples of the wireless ad hoc networks can be found in the tactical military applications, disaster recovery operations, exhibitions and conferences. Since there is no existing fixed infrastructure in the wireless ad hoc network, organizing the randomly deployed nodes into a virtual backbone turns out to be an
important design issue. One of the general approaches is to organize nodes into groups of clusters. Within each cluster, a node is elected as the local controller of that cluster and is called clusterhead (CH). Major advantages of this approach include frequency spatial reuse, smaller interference and the increase of system capacity.
Many related algorithms 0-0 have been proposed in the literatures. The minimum connected dominating set (MCDS) scheme 0 organizes the wireless ad hoc network into an optimum configuration. However, the problem to find the MCDS in a connected graph is shown to be NP-hard 0 and the problem to find the optimal CH set is an NP-complete problem 0. The general feasible alternative is to design an approximated heuristic algorithm to obtain a sub-optimal MCDS. The Degree-based clustering algorithms 0 are proposed to select CHs based on the degree of the nodes. The ID-based clustering algorithms 00 organize the cluster simply based on the node ID. Other approaches that are based on different node attributes can be found in 0-0.
Due to the security concerns of the transmitted messages or the limitations of the geography of the service area, some singular nodes must/may be deployed within the service area. For example, some nodes in the networks have only one neighbor and are called boundary nodes. The only neighbors of boundary nodes play an important role in providing connections from boundary nodes to the other nodes. In view of the previous algorithms, we find that the impacts of the boundary nodes on the design of clustering algorithm have not been well studied in the literatures. This part addresses how to organize wireless ad hoc networks with boundary nodes into a power efficient cluster-based network architecture. The power efficiency of a cluster-based network architecture in this part is related to the number of overheads that are required to maintain the organized cluster-based network architecture.
IV. MHz. There are 4 sub-channels in the system, each contains 13 subcarriers. Each active user uses one sub-channel and the configuration and frequency domain structure of each subchannel are identical. We denote N the number of pilot subcarriers in a sub-channel and it varies from 1 to p 4 in our experiments.
The channel response of each user is generated according the IEEE 802.11a channel model with root-mean-square delay spread equals to 50 ns. The channel coefficients are modeled as independent and complex-valued Gaussian random variables with zero-mean and an exponential power delay profile
assignment as illustrated in Fig. 1 are used. Each simulation point is conducted using 3 10⋅ 5 frames, each frame consists of 16 OFDM symbols.
Fig. 1 shows the symbol error rate (SER) performance of the two proposed CPE estimators in comparison with both no-phase-noise and no-phase-noise-correction cases with QPSK. Since the number of pilot subcarriers affects the spectrum efficiency and the capacity of an OFDMA system, N is set to 1 in the simulation generating these two figures. Fig. 1(a) refers to p sub-band based subcarrier assignment while Fig. 1(b) corresponds to interleaved subcarrier assignment.
First of all, the maximum likelihood (ML) approaches always have more improvement than least square (LS) ones, which is not surprising because the statistics of ICI term is taken into consideration. We can observe that when the number of active users increases, interleaved subcarrier assignment suffers more from the multiple-access interference because other active user’s signals are at nearer subcarriers.
Fig. 2 illustrates how the performance of the proposed schemes changes with phase noise levels. The number of pilot symbols N is set to 1. The aim of the proposed schemes is to p
correct medium to small phase noise, i.e., for phase noise variance βTs less than10−4. It shows in Fig. 7 that when phase noise variance is greater than10−5, the OFDMA system suffers remarkable performance degradation. However, the proposed CPE estimation schemes provide significant performance improvement over no-phase-noise-correction case.
When phase noise variance is less than 10−5 for an OFDMA system employing QPSK, we can see the error floor of the proposed schemes. For this phase noise variance range, it is not necessary to take the CPE correction to correct multiple phase noise.
(a) Subband-based
(b) Interleaved
Fig 1. Symbol error rate v.s. SNR with QPSK, K=1 to 4 [16]
(a) Subband-based
Fig. 2. Symbol error rate v.s. phase noise variance with QPSK, K=1 to 4 [16]
Part II: Characterizing The Wireless Ad Hoc Networks by Using The Distance Distributions
Table 1 The Optimum Transmission Range for a 1-connected Wireless Ad Hoc Network
p=0.95 p=0.99
N=100 N=200 N=100 N=200
1
rop 155.33m 114.75m 171.22m 125.55m
Based on equation, the optimum transmission ranges to construct a 1-connected network r1op
in a 1000m×1000m square-shaped service area with the probability p=0.95 and p=0.99,
100
N= and N=200 are shown in Table 1. The probability of organizing a k-connected wireless ad hoc network in the ideal environment obtained in equation is shown in Fig. 1. This figure shows that the required transmission range R for N nodes in the ideal environment to organize a k-connected wireless ad hoc network is inverse proportional to N and proportional to k. For example, from TABLE 1 and Fig. 1, the transmission ranges 171.22m and 125.55m are required for a wireless ad hoc network with 100 and 200 nodes to be 1-connected with the probability 0.99. The probability of the wireless ad hoc network organized by N nodes in the shadow fading environment is k-connected as derived in equation is shown in Fig. 2. In this figure, the transmission range R is set to 300m which corresponds to a wireless ad hoc network organized by 100 nodes in the ideal environment is 3-connected with the probability greater than 0.9999 as shown in Fig. 1. With the same transmission range, Fig. 2 shows that as the channel variation is concerned, fewer nodes are required to achieve the same network connectivity and the number of nodes to achieve the required network connectivity is inverse proportional to the channel
Fig. 1. The probability of k-connected in the ideal environment.
0
Fig. 2. The probability of k-connected in the shadow fading environment.
Part III: On The Distance Distributions of The Wireless Ad Hoc Networks
0
cdf of the distance to th k-th nearest neighbor
N=100,k=1
Fig. 1. The cdf of the distance to the k-th nearest neighbor.
The distribution of the distance to the k-th nearest neighbor
In Fig. 1, we show the cdf of the separation distance obtained in equation to the 1st, 2nd and 3rd nearest neighbor for a wireless ad hoc network with 100 and 200 nodes deployed over a 1000m×
1000m square-shaped service area. This figure shows that the distance to the k-th nearest neighbor is inverse proportional to the number of nodes in the service area. Furthermore, this figure also shows that almost surely that the first nearest neighbor is within the Euclidean distance 120m and 82m for the number of nodes are 100 and 200 respectively.
0.0
Fig. 2. The cdf and pdf of the Euclidean distance between two random selected nodes.
The distribution of the distance between two random selected nodes
The pdf and cdf in equations with different separation distance are shown in Fig. 2. By differentiating equation, the most probable normalized separation distance between two random selected nodes is 0.478. This can also be found from Fig. 2 that the 0.478 separation distance corresponds to the maximum probability density. Besides, from the cdf curve in Fig. 2, we find that if the normalized transmission range is higher than 0.94, the probability for two random
The pdf and cdf in equations with different separation distance are shown in Fig. 2. By differentiating equation, the most probable normalized separation distance between two random selected nodes is 0.478. This can also be found from Fig. 2 that the 0.478 separation distance corresponds to the maximum probability density. Besides, from the cdf curve in Fig. 2, we find that if the normalized transmission range is higher than 0.94, the probability for two random