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Assignment Methods for Spatial Reuse TDMA

Jimmi Gronkvist Swedish Defence Research Establishment

Div. of Command & Control Warfare Tech. SE-58 1 11 Linkoping, Sweden

Abstract- Spatial reuse TDMA is an access scheme for multi-hop radio networks. The idea is to increase capac- ity by letting several radio terminals use the same time slot when possible. A time slot can be shared when the radio units are geographically separated such that small inter- ference is obtained. STDMA schedules can assign trans- mission rights to nodes or alternatively assign transmis- sion rights to links, i.e. transmitter/receiver pairs. Here we compare these two methods and determine which one is preferable. We show that only the connectivity of the network and the input traffic load of the network is needed in order to determine whether node or link assignment is preferable.

I. INTRODUCTION

We consider a radio network where a number of radio units are spread out in some terrain and where the mobility demands are moderate. If the received signal power is sufficient in re- lation to noise and interferences, it is assumed that any two radio units can communicate, i.e., establish a link. In a multi- hop network, the power consumption can be kept low and area coverage is achieved by letting messages be relayed over one or several intermediate nodes.

One problem in a radio network is the interferences caused by simultaneously transmitting nodes. These conflicts occur if the received signal is too weak in comparison with the in- terfering signals, An important issue is therefore to design access schemes that control the use of the channel. One used access scheme is time division multiple access (TDMA). For sparsely connected networks, however, this is usually ineffi- cient. To increase capacity one can instead use spatial reuse TDMA (STDMA), which is an extension of TDMA where the capacity is increased by letting several radio units share the same slot. An STDMA schedule describes the transmission rights for each time slot. In ad hoc networks with moder- ate mobility demands updates of an STDMA schedule can be managed [ 13.

Channel access STDMA for multi-hop packet radio net- works was formalized in [2]. A number of algorithms to gen- erate STDMA schedules have been proposed. Some of these algorithms assign transmission rights to nodes, i.e. a node can transmit to any of its neighbors. In other algorithms, transmis-

sion rights are assigned to links, in this case both transmitter and receiver node is determined in advance.

Example of node assignment algorithms can be found in [3, 41, and link assignment algorithms in [5]. Sometimes both versions of the algorithm have been proposed, node assigned [4] and link assigned [5] Furthermore, in [6] both link and node assignment algorithms are described. However, it has not been shown which approach that is preferable.

The main focus here is to determine for what situations link or node assignment is preferable. Our result suggests that the connectivity of the network and the input traffic are sufficient parameters for determining which approach that is preferable. Furthermore, link assignment achieves higher throughput than node assignment and the gain in throughput increases with the size of the network and decreases with increased connectivity.

We focus on point-to-point traffic. The question whether node or link assignment should be used is interesting essen- tially for point-to-point traffic. For broadcast or multicast traffic node assignment is intuatively preferable by common sense.

The node and link algorithms used are described in [7] and [8], respectively. Here we give a short description of these algorithms. The only differens between these algorithms is that they assign transmission rights to nodes and links, respec- tively. We use an interference based model of the network as suggested for STDMA scheduling in [9].

11. NETWORK MODEL

Here we describe the interference based model of a radio net- work that is used. The network is represented by a set of nodes V and the basic path-loss &(i , j ) between any two dis- tinct nodes (vi, wj), i # j . To simplify notation, we assume isotropic antennas.

For any two nodes, (vi, V j ) where vi is the transmitting node and vj # wi, we define the signal to noise ratio (SNR), rij, as follows

D

where Pi denotes the power of the transmitting node V i , Lb( i , j ) is the basic transmission path-loss between nodes vi and vj, and NR is the receiver noise. For convenience, we de- fine I'ii = 0 corresponding to the physical situation of a node not being able to transmit to itself.

0-7803-6534-8/00/$10.00 0 2000 IEEE

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We say that a pair of nodes (vi,vj) form a link, ( i , j ) , if the signal to noise ratio (SNR) is not less than a threshold, 70. That is, the set of links, IC, is defined:

K = {(i,j) : ru 2 To) . (2) For a set of links, K C K, we define the set of transmitting

nodes as follows:

VT(K) = {vi : (i,j) E K } . For any link, (2, j ) E K , we define the inteflerence:

Furthermore we define the signal to inteference ratio (SIR):

D.

(3)

We assume that any two radio units can communicate a. packet without error if the SIR is not less than a threshold, 71. A schedule S is defined as the sets vt, for t = 1,2, ..., T , where T is the period of the schedule. The sets vt contain the nodes or links assigned time slot t . A schedule is considered to be conjlict free if equation ( 3 ) holds for all scheduled trans- missions.

Furthermore, we assume that a node cannot transmit more than one packet in a time slot and that a node cannot receive and transmit simultaneously in a time slot.

The Signal-to-interference criteria (3) gives the following

( 5 ) condition

I I K ( i , j ) 2 71 v ( i l j ) E K. If the above two conditions, (4) and (5 ) , hold for a set of

links K E IC, we say that the links in K can transmit simulta- neously.

Similarly we will state two necessary conditions for the sit- uation when all the nodes in a set V are allowed to transmit packages simultaneously. Let the neighbors Q(v) to a node v in V be the set of all nodes that have a link from v to itself. The neighbors are the nodes that v possibly can transmit a packet to. Similarly, let Q(V) denote the union of all neighbors of all nodes in V .

Thefirst condition is that two neighbors can not transmit at the same time. Another way to say this is that the sets V and Q(V) must be disjoint:

V n Q(v) = 0. (6) Let K ( V ) be the set of all links from the nodes in V to their neighbors in O(V) . Since all the links in K(V) must be possi- ble to use for transmission simultaneously, we state the second condition:

b q V ) ( i r j ) 2 71 for all (2, j ) E K ( V ) . (7) If the above two conditions, (6) and (7), hold for a set of

nodes V E V we say that the set of nodes can transmit simul- taneously.

IV. TRAFFIC CONTROLLED REUSE SCHEDULES 111. ASSIGNMENT METHODS

In a node assigned schedule, a node is allowed to transmit to any of its neighbors in its slot. If the schedule is to be conflict free this means that we have to guarantee that we will not have a conflict in any of the neighboring nodes. In link oriented assignment, the directed link is assigned a slot. A node can then only use this slot or transmission to a specific neighbor. In general this knowledge can be used to achieve a higher degree of spatial reuse. The effect is higher throughput.

In the following, we first describe the criterions needed for a set of links to be able to transmit simultaneously with suffi- ciently low interference level at the receiving nodes. Then, we do the same for a set of nodes.

We say that a link ( k , 1 ) is adjacent to link ( i , j ) E K iff {i, j } n {k, I} # 0. Furthermore we define Q(K) as the union of all adjacent links to the links in K . We assume that a node cannot transmit more than one packet in a time slot and that a node cannot receive and transmit simultaneously in a time slot. Alternatively, we say that a set of links K and the set of its adjacent links Q ( K ) must be disjoint:

K n Q ( K ) = 0. (4)

The relaying of traffic in multihop networks causes a consider- able variation of the traffic load on the links or nodes in a net- work. To achieve large capacities we have to use an efficient traffic controlled schedule to compensate for this problem.

In a traffic controlled schedule, links or nodes can use sev- eral slots, see [lo], according to the traffic load. We define hij as the number of slots allocated to link (i, j) within a frame in a schedule. The corresponding notation for node assignment is hi.

Note that the problem with varying traffic loads may be less severe in a node assigned schedule, since the variation of traf- fic is averaged over a node.

In our traffic model we assume point to point traffic, i.e., a packet entering the network has only one destination. Pack- ets enter the network at entry nodes according to a proba- bility function, p(v),v E V and packets exit the network at exit nodes. When a packet enters the network it has a desti- nation, i.e., an exit node from the network. The destination of a packet is modeled as a conditional probability function, q(ur(v), (tu, U) E V x V , i.e., given that a packet has entry node v, the probability that the packet's destination is w is q(z0lv). For simplicity we will assume a uniform traffic model,

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i.e., p ( v ) = 1 / N , and q(wlv) = 1 / ( N - 1 ) where N is the number of nodes, N = IV1.

Let X be the total traffic load of the network, i.e., the av- erage number of packets per time slot arriving to the network as a whole. The

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