Triple-receiver-based code protocol for unslotted DSISSMA packet-radio networks and its performance analysis

X.H. Chen N.C. Lim

Indexing terms: DSISSMA packet-radio networks, Protocol

~~ ______

Abstract: An unslotted DS/SSMA packet-radio protocol (the triple-receiver-based code (R’) protocol) suitable for code-division multiple- access (CDMA) wireless data networks is pro- posed. The communication between two data terminals is initiated by hand-shaking (request and acknowledgement stages) followed by data- packet transmission (pair-up stage), using the receiver-based signature codes for multiple- accessing. The two-dimensional continuous-time Markov chain was used to model and analyse the behaviour of the network. The analytical results show that a respectable improvement in throughput-delay performance can be achieved, applying the proposed protocol to unslotted DS/SSMA packet-radio networks, when com- pared to other reported code protocols.

1 Introduction

Direct-sequence spread spectrum multiple-access (DS/ SSMA) packet-radio systems allow users who transmit data in bursts to share a common radio channel, by making use of the following two techniques: that of transmitting only during times that a message is actively being sent, and that of transmitting messages simulta- neously with other users without necessarily causing mutually destructive interference, which is the case for single-channel ALOHA systems [l, 21. Therefore the DS/SSMA packet-radio network architecture is particu- larly suitable for wireless data networks, such as wireless local-area networks (LANs), and has become increasingly popular in implementing portable data networks in offices, factories, campuses etc. The wireless data net- works can sometimes save the unbearable costs associ- ated with complex cabling, due to moving terminals from one location to another, and provide easy access for mobile terminals to the networks. Apart from other unique features for spread-spectrum (SS) systems, the DS/SSMA packet-radio technology also provides the wireless data networks with the multipath-reuse capabil- ity, which is extremely important for the networks

0 IEE, 1995 Paper 19121 (EX), first received 18th May 1994 and in revised form 13th February 1995 X.H. Chen is with the Department of Electrical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 05 1 1 N.C. Lim is with Singapore Telecomms R e Ltd.. Singapore 0923

I E E Pix.-Commun., Vol. 142, No. 3, June 1995

located in urban areas or indoor environments, where severe multipath fading and shadowing may exist.

Various packet-radio network protocols and their per- formance analysis have been reported since the early 1970s. In 1975, Kleinrock and Tobagi proposed a carrier- sense multiple-access with collision detection (CSMA/ CD) protocol for narrow-band single-channel packet-radio networks [l]. They also worked on solving hidden terminal problems existing in the CSMA/CD pro- tocol, by introducing a busy tone (BT) in a separate BT channel for a busy user in the network [2]. From the 1980s. the DS/SSMA techniques were applied to packet- radio networks, to provide users with simultaneous access through code-division multiple access (CDMA). Raychaudhuri studied the random access CDMA net- works, by using Poisson, binomial and general packet- arrival models, and found that the use of multiple-access coding can provide utilisation-delay characteristics superior to that of ALOHA [3]. Polydoros and Silvester, in their paper published in 1987, proposed an analytical framework for the single-hop random access S S networks [4]. In 1988, Sousa and Silvester presented interesting analysis on various spreading code protocols for the SS networks [SI. In their paper, many important protocols, such as the common code, receiver-based code, transmitter-based code and their hybrid version proto- cols, were investigated. Abdelmonem and Saadawi applied the channel-load sensing technique to an S S packet radio network, and the effect of the CDMA threshold on network performance was studied [6]. In a paper written by Storey and Tobagi, the throughput for an SSMA packet-radio network considering BPSK modulation and Viterbi decoding was obtained [A. Morrow and Lehnert recently (in 1992) presented their work in studying bit-to-hit error dependence in a DS/SSMA radio network [8]. In our previous papers [9, lo], it was shown that the code sensing, combined with busy code broadcasting, can be employed to improve throughput-delay performance and stability of the

The authors wish to thank Prof. Juhani Oksman, Telecommunication Laboratory, Department of Electrical Engineering, University of Oulu, Finland, for his constructive discussions, encour- agement and support during the course of the research project. Financial support from the Academy of Finland and the National University of Singapore is also acknowledged gratefully.

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DS/SSMS packet-radio networks. The busy-code broad- plexity is greatly reduced when compared with that for casting and sensing (BCBS) protocol allows collision-free the BCBS protocol [lo]. A terminal uses short burst-like operation of a network, at a price that two spreading hand-shaking packets for communication initiation

to outsde ~

networks

Fig. 1 Ofice wireless PC-link network using the R’ protocol

codes are needed for each user, and that the protocol may not be implemented easily for a network of relatively larger size. Furthermore, the BCBS protocol algorithm is complex in both receiver and transmitter algorithms, where simultaneous receiving and transmitting capability is required in each successful receiver. Therefore it requires rather costly receiver hardware to implement the protocol. In most practical applications, the excessive use of spreading codes in the network can also result in high CDMA noise level, owing to unperfected cross- correlation functions among the spreading codes, even though the unperfected cross-correlation was not con- sidered in the theoretical analysis presented in the papers.

In this paper, a nova1 code protocol for unslotted DS/SSMA packet-radio networks is proposed. It is called the triple-receiver-based code (R3) protocol, recognising the fact that the receiver-based codes should be utilised in the three stages of communication between two termin- als. In this protocol, the contentions among terminals are under control, and only one code is assigned to each user as the receiver-based code. The capability for a terminal to transmit and receive simultaneously is not required in this protocol, thus the hardware implementation com-

purpose. The hand-shaking packets consist of ‘request’ (REQ) and ‘acknowledgement’ (ACK) packets, both of which are encoded by receiver-based codes of the targets, but use different chip rates with a ratio of two. After hand-shaking is accomplished, the data packets will be followed from a source terminal to a target terminal using the higher chip rate. The reasons for using two chip rates for different packet transmission are given in Sec- tion 2. Because of its promising performance and rela- tively simple protocol algorithm, the R’ protocol is suitable for the wireless LANs, mobile data and other packet-radio networks implemented in an asynchronous, distributed and fully connected network geometry. A simple example for such applications is the wireless PC-link network for offices, as visualised by Fig. 1, in which many PCs equipped with radio-access adapter cards and antennas are connected by a common radio link, and are coordinated by the proposed R3 protocol. The connected PCs can communicate with each other, share the same laser printer or be routed to outside net- works through one interfacing terminal, which can be any one of the PCs in the network. This office wireless PC-link can provide a great flexibility whenever the

‘6 PAIR stage: A

Fig. 2

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Three communication stages between two term‘nals in the R’ protocol

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network needs reconfiguration, such as adding a few more terminals to the network or moving terminals from one place to another. Thus costly re-cabling is avoided.

quiet idle

I- t

A sends request packet to B by using receiver code of B

from B before time-out? than specified duration?

I 1

I A sends data packets to B I by usinq receiver code of B

Fig. 3 Transmitter algorithm for the R3 protocol

In order to analyse throughput-delay performance of the R3 protocol, a two-dimensional continuous-time Markov chain model is used in this paper. A state vector consisting of two elements, the number of successful pairs ( i ) and the number of waiting terminals (j), is introduced for the Markov chain. After solving for the state- occupancy probabilities, the network throughput and delay performance can be further evaluated.

2

In order to control the packet collisions, which exist excessively in many previously reported spreading code protocols [SI, the communication between two terminals in the R3 protocol will proceed in three stages, the request (REQ) stage, the acknowledgement (ACK) stage and the paired-up (PAIR) stage, which are shown in Fig. 2 for communication between two terminals A and B in the network.

Each terminal in the network is assigned only one unique signature code for addressing purposes. This sig- nature code of a terminal is never used by the terminal itself, but by other terminals to address packets to it. Therefore the code is called the receiver-based code [S, 9, lo]. In the REQ stage, as shown in Fig. 2, terminal A should use a signature code of B (rB) to send terminal B a short burst-like request packet. In the ACK stage, after decoding the REQ packet from A, which contains mainly the address information of A plus a packet head for syn- chronisation purpose, terminal B is able to know which terminal (A in this case) would like to communicate with it. Here it is assumed that each terminal keeps a ‘library’, which gives one-to-one correspondence between a ter- minal address and its signature code. Thus terminal B is able to choose the right signature code ( rA) to encode an ACK packet (it is also very short) to terminal A to confirm the reception of the REQ packet, and to inform A that B is ready to receive data packets from A. After

The R” protocol and its analytical model

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this hand-shaking process is accomplished, the terminal A will send data packets to terminal B by using the recei- ver code B (rB). When compared with the REQ and ACK packets, the length of data packets is relatively long. Therefore the communication between A and B will be dominated by a PAIR stage, in terms of the duration of time for different stages.

There are two different types of collisions in the network, depending on the status of the target terminal, which may be transmitting or receiving. If a transmitter A sends a packet to another transmitter B, B can con- tinue transmitting without interruption and A should retry after a random delay. However, if transmitter A sends a packet to an existing successful receiver B, by using code r B , it will cause some trouble to B, since now two transmitters are sending packets to B using the same receiver-based code rB . These two different packets using the same spreading code will produce interference with each other at the same receiver B, if no appropriate mea- sures are taken. In order to resolve this problem, it is assumed here that an existing successful receiver (say B) can somehow lock to the previous transmitter (say A) which is addressing data packets to the receiver B, and B will not be interfered by other new attempting REQ packet transmitters (say C or others), which want to address packets to the receiver B using the same receiver- based code r B . One way to implement this lock mecha- nism at a receiver is by recognising the signal delay from a specific transmitter, since it is unlikely that two trans- mitters have exactly the same distance (thus the same delay) to the receiver they want to communicate with. In this way, any collisions happening in the network can be considered as the event that a new attempting transmit- ter addresses packets to a busy terminal (either a busy transmitter or a busy receiver), the existing successful ter- minals will remain in the same status (unaffected), and the new attempting transmitter should retry after a random delay.

The ‘lock mechanism’ can also be implemented in another way if the system satisfies the following two con- ditions

(a) The REQ and ACK packets are much shorter than that of the data packet followed

(b) The REQ packet will be sent at a chip rate only half of the normal rate used in sending the ACK and data packets

Under this circumstance, the damage caused by a colli- sion between a successful data (or ACK) packet receiver (A) and a new attempting REQ packet transmitter (B), aiming at A as its target, is greatly reduced or does not even exist if the cross-correlation function between a sig- nature code (the receiver code) and its 2-chip repeating version is under control. We call this technique ‘chip rate division multiple access’, and our recent study has revealed that it is not difficult to find a signature code family that possesses controllable cross-correlation func- tion between a code and its 2-chip repeating version. In this way, the terminals already engaged with each other in their ACK and data-packet transmission stage will lock to each other, even when other new attempting transmitters send the REQ packets to them using the same codes but different chip rates.

From Fig. 2 it can be seen that most collisions in the network are because terminal A sends a REQ packet to terminal B which is currently busy receiving an ACK or data packet from another transmitter, since A never knows the status of B until the time-out period used at

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terminal A ends. On the other hand, however, if the REQ packet in the lower chip rate can be received successfully, the terminals involved (A and B) are already well dedi-

by using receiver code B

by usinq receiver code A . . I

I I receive pockets from A 1 by using receiver code B

Receiuer algorithm for the R3 protocol Fig. 4

Fig. 5 Steady-state transition diagramfor the Markov chain

cated to each other by using the higher chip rate. There- fore they should be considered as ‘masked’ busy terminals to the other terminals, and will not be inter- fered with by others. The algorithms used by both trans- mitters and receivers are given in flow charts as shown in Fig. 3 and 4, respectively, in which terminal A is assumed to be a transmitter and terminal B a receiver.

3 Throughput-delay performance analysis

In order to numerically analyse the throughput-delay performance of an unslotted SS/CDMA data network adopting the R3 protocol, the two-dimensional continuous-time Markov chain is utilised to model the network behaviour. A two-variable state vector (i, j) is introduced for the Markov chain, where i is the number of successful communication pairs and j the number of the waiting terminals, which are defined as the terminals attempting to send packets to their targets which are busy at the moment. Therefore it is understood that i and j should satisfy the following inequalities all the time, 0 C i C N / 2 and 0 C j C N - 2i, where N stands for the total number of terminals in the network. The variables i

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and j can be used to fully determine the behaviour of the network. The most important parameter associated with the state vector (i, j) is the state-occupancy probability Ai, j ) , which tells how likely the network will stay in a given state after the network reaches equilibrium. If one can solve for all those state-occupancy probabilities, the network performance is known also. It can be shown that when the state vector (i, j) is used to describe the behav- iour of the network, the future behaviour of the system depends only on the current state of the system, and is independent of the previous ones. Therefore the network is Markovian. Furthermore, the network can always transfer from one state to another through finite tran- sition steps and with specific state transition rates at each step. This observation is extremely important, and allows us to employ the analytical methods for an ergodic Markov chain to simplify the throughput-delay per- formance analysis of the network considered in this paper.

Now let us turn to the network model of interest. The three different terminal states of the network (idle, suc- cessful and waiting states) are defined as follows:

Idle state: A terminal is said to be in idle state if it is neither receiving nor transmitting nor waiting to trans- mit.

Waiting state: A terminal is said to be in the waiting state when its desired target terminal is currently busy. A terminal is busy when it is either an active receiver or an active transmitter.

Successful state: A terminal is said to be in the successful state if it is either successfully transmitting a packet or successfully receiving a packet from a transmitter. A transmitter will enter the successful state only if it addresses to either an idle or a waiting terminal.

The following assumptions will be used for the network analysis:

(i) Terminals in the network communicate with each other with equal probability, and the network contains N terminals, each of which is assigned with a receiver-based code, which is perfectly orthogonal to the others, so that the cross-correlation noise is not considered. The perfect orthogonality assumption is popularly adopted in the lit- erature [3, 5, 61, because it enables us to concentrate on the negative effect on the network performance owing to the packet-collision problem, which is a main concern in any random access network. It is indeed an optimistic assumption and the network‘s performance will otherwise be slightly worse.

(ii) The packets are assumed to arrive at a terminal according to a Poisson process, with the mean packet- arrival rate equal to I packets per second.

(iii) As specified by a Poisson packet-arrival process, the probability that more than one packet arrives at a terminal is zero. The composite packet-generation process in the network should be also approximately a Poisson process (especially when N is large), with a mean of N1 packets per second [S, 61.

(iv) The average packet transmission time between two successful terminals is exponentially distributed with a mean l/u.

(v) A terminal will not transmit and receive simulta- neously.

(vi) No priority levels are assigned to the users in the network.

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(vii) When terminal A is addressing packets to termin- al B, if B is in either the idle state or the waiting state and there are no other terminals addressing packets to B simultaneously, the packets from A will always be cap- tured by B.

(viii) A waiting terminal will not stay in the waiting state for ever if the target terminal is busy for an unex- pected long time. A time-out policy is used for a waiting terminal to return to the idle state if the target is not available for an excessively long time. The average dura- tion for a waiting terminal to stay in the waiting state is assumed to be ten times longer than the mean packet transmission time l/u. Although an even longer time-out period may be used in the analysis, the obtained results from our analysis did not show any significant difference.

A steady-state transition diagram for the two- dimensional continuous-time Markov chain of the network is depicted in Fig. 5, where possible transitions between states are represented by arrow lines. In Fig. 5 the state (0, j) exists for only j = 0, since all terminals initially are free for pairing-up and collision is impossible. Let us concentrate on the state transitions around the state (i, j ) , where i and j satisfy the conditions specified by 0 < i < N / 2 and 0 < j < N - 2i. The state transition rates from one state to another are denoted by the capital letters A, E, C, D, E , F, G, H , X and Y , some of which may not exist for certain states (i. j ) . Take (0, 0) as an example, only state transition rates D and E exist. Most transitions among different states are in either horizontal or vertical directions. However, two downward diagonal transitions exist between the state pairs {(i - 1, j + I), (i, j ) } and { ( i , j ) , ( i + 1, j - l)}, which represent the situations where a transmitter sends the REQ packet to a waiting terminal forming a successful pair. The following text will be dedicated to numerical determination of the state transition rates among different states.

The transition rates at which a transmitter sends the REQ packet to an idle terminal are indicated by A and D in Fig. 5. The composite packet-arrival rate is given by the current number of idle terminals multiplied by the rate generated by one single terminal, which is equal to (N - 2i - j ) I , if the current state is (i, j). The probability that a terminal sends the REQ packet to an idle terminal is calculated as (N - 2i - j - 1)/(N - 1). Thus the tran- sition rate from (i, j ) to (i + 1, j) is given by

( N -;i: i - 1) D = l.(N - 2i - j )

Similarly, the transition rate from (i - 1, j) to (i, j ) is given bY

N - 2 ( i - l ) - j - l [ N - 1 A = l .[N - 2(i - 1) - j ]

The state transition from state (i, j) to state (i, j + 1) (transition rate B) occurs when a transmitter sends packets to a successful paired-up terminal (either a busy transmitter or a busy receiver), with the probability 2i/(N - 1). Thus the transition rate is calculated as

B = I ( N - 2 i - j ) - ( N T 1) (3)

Similarly, we have the state transition rate from state (i, j - 1) to state (i, j) as

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Since the average packet transmission time is assumed to be 1/14, the departure rate from the successful paired-up state to the idle state is given by E and H, respectively, which can be determined as follows

E = ( i + 1)u (5)

H = iu (6)

and

The transition from the state (i, j ) to the state ( i . j - 1) occurs when a waiting terminal leaves for the idle state. Given that the average time for a waiting terminal to stay in the state is ten times longer than the average packet transmission time, the transition rates from (i . j + 1) to (i. j ) and from (i, j) to (i, j - 1) should be

C = ( j + l )u / lO (7)

F = ju/lO (8)

and

If a transmitter wants to communicate with a busy ter- minal (either an active transmitter or an active receiver), it enters the waiting state, in which it also can monitor the channel for possible incoming REQ packets from other transmitters. If this waiting terminal is addressed by another transmitter, it can abort the waiting status right away, and become a successful receiver. This specifi- cation will not conflict with the assumption made earlier in this Section that a terminal cannot transmit and receive simultaneously, because a waiting terminal can sense the channel whenever it is not transmitting the REQ packets to the target terminal. Therefore the tran- sition rates of X and Y can be determined as follows

X = I [ N - 2(i - 1) - ( j + l)] - (;?l)

and

Y = I [ N - 2 i - j ] - ( N 1)

(9)

For an ergodic Markov chain in equilibrium, the tran- sition rates into any given state should be equal to the transition rates out of the state. This allows us to obtain an equilibrium equation of the Markov chain, from which the all state occupancy probabilities {p(i, j ) } (0 < i < N / 2 and 0 < j < N - 2i) can be solved by numerical methods in linear algebra. By examining the state (i, j ) in Fig. 5, we can set up the following equi- librium equation for the network

( E + D + Y + H + F)p(i, j )

= Ap(i - 1, j ) + Xp(i - 1, j + 1) + Ep(i + 1, j )

+ Cp(i, j - 1) + Cp(i, j + 1) (1 1) where i and j should take the values according to the inequalities 0 < i < N / 2 and 0 < j < N - 2i. By substi- tuting eqns. 1-10 into eqn. 11, a set of linear equations is obtained, with the state occupancy probabilities as the unknown variables. The number of linear equations (also the number of states) contained in eqn. 1 1 is determined by the index ranges for i and j , which are specified by 0 < i < N / 2 and 0 < j < N - 2i. For example, if N = 8, there are in total 25 linear equations embedded in eqn. 11. In general, there should be ( N + 2)’/4 equations in eqn. 11, where N is the number of terminals in the network. Therefore the number of equations in eqn. 11 increases almost with the square of N . Take N = 50 as an

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example, there will be 676 linear equations contained in eqn. 11. Therefore a great amount of computation is needed to study a large sized network. Among these (N + 2)2/4 equations, however, only [(N + 2)2/4] - 1 equations are independent. In order to solve (N + 2)2/4 state occupancy probabilities, eqn. 1 1 should be solved together with the probability conservation law which is given as follows

N12 N - 2 i

After solving for all state occupancy probabilities, we can use them to evaluate the network performance using the formulas given in the literature [6], where the average network throughput is defined by

N12 N - 2 i

which is actually the expectation of the number of suc- cessful communication pairs in the network. Therefore the average throughput normalised by the maximum number of terminal pairs is

which is called normalised throughput and is used more commonly than eqn. 13. If we define the average number of waiting terminals in the system as the 'backlog', which means exactly what the name suggests and is calculated by

then, by using Little's result [ll], which says, in queueing theory, that the average number of customers in a system is equal to the average time for each customer to stay in the system multiplied by the rate at which customers leave the system, we can have the normalised delay as follows

The eqns. 14 and 16 will be used to evaluate the throughput-delay performance of the network using the R3 protocol in the following Sections.

4 Numerical results and discussions

Several important state occupancy probabilities for N = 8 versus normalised traffic load (p = l/u) are given in Figs. 6a-c, respectively, from which it can be found that the state occupancy probabilities with more paired- up terminals and less waiting terminals, such as p(4, 0) and p(3, 2), are quite high, and they increase as the offered traffic load increases. On the other hand, the state occupancy probabilities with less paired-up terminals and more waiting terminals, such as p(1, 6) and p(1, 5), have relatively low values, and they reach the peak points first, and then decrease rapidly as the offered traffic load increases. This implies the stable operation of the network with the R3 protocol, which will be seen more clearly later, even though the packet collisions still exist in the network using the R3 protocol.

The normalised throughput of networks of various sizes, N = 8, 20 and 50, is shown in Fig. 7, from which it is observed that the throughput for different-sized net-

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works is very close, because the throughput parameter used for the analysis is defined by eqn. 14 and has been normalised by the network size (N/2). From another

U 0 r c

c

normalised traffic lood 0

5r

0

I

0 2 4 6 8 10 normollsed traffic load

b

normalised traffic load

State probabilities against normalised tr&c load (N = 8) C

Fig. 6 P -e- do, 0 ) -+- dl, 0) -A- ~(4.0)

-0- dl.6) -x- ~ 4 3 . 2 ) -0- dl, I) b - + - d1.2) -A- dl.3) -0- dl .4) - x - dl,5) e -0- dl, I) -+- p(l, 2) -A- dl, 3)

01 0 2 4 6 0 10

normalised troffic lood

Fig. 7 Throughput against normalised trafic load -0- n = 8 -0- n = 2 0 - x - n - 3

point of view, it can also be said that the performance obtained for N = 8 is already very trustworthy for network performance evaluation and comparison pur- poses. Using a small N helps facilitate the analytical study of the network. The throughput performance for

IEE Proc.-Commun., Vol. 142, No. 3, June 1995

the proposed R3 protocol is very respectable, about 0.48 at p = 1 and about 0.75 at p = 10, which represent two different traffic load conditions (low and high).

The delay performance for various N against normal- ised traffic load is given in Fig. 8, from which it is found

0.2-

0

6

5

$ 3

2

1

0 0 2 4 6 8 10

normalised traffic load Fig. 8 Delay against normalised t r m c load -*- n = 8 -A- n = 2 0 -0- n = M

that the delay increases as the network size N increases for the same offered traffic load p. Since more terminals in the network mean a higher backlog K, which is not a normalised figure (it can be shown that K defined by eqn. 15 increases as N increases), if the normalised throughput is kept unchanged with N, the delay will certainly increase as N increases.

The curves of delay versus throughput for N = 8, 20 and 50 are shown in Fig. 9, 10, and 11, respectively. It is

0.8

3r

normal !sed throughput

Fig. 10 -*- n = U )

Delay against throughput for N = 20

very interesting to notice that, when the normalised traffic load p changes from 0 to 10, the networks of N = 8 and 20 are always stable, indicated by their posi- tive slopes in their curves in Figs. 9 and 10, respectively. However, when the network size N becomes 50, the curve of delay versus throughput contains a negative-slope portion, which indicates the unstable region of the network. Therefore the R3 protocol can only ensure a stable operation for a network of relatively small size, but

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not for a large network. In order to be used in a large network, some additional measured to avoid the colli- sions should be taken.

b I

1 normolised throughput

Fig. 11 -*- n = 5 0

Delay against throughput for N = 50

The throughput and delay performance for various code protocols for the DS/SSMA packet-radio networks, such as the receiver-transmitter-based (R-T) spreading code protocol [SI, the receiver-based (R) spreading code protocol [SI and the BCBS protocol [lo], has been com- pared with the R3 protocol in Figs. 12 and 13. In order to

0.8

01 0 2 4 6 0 10

normalised traffic load

Fig. 12 Throughput comparison for different DSISSMA code proto- cols -x- Triple-R -A- R d e -+- BCBS -e R-T code

50r

normalised traffic load

Fig. 13 -x- Triple-R -A- R code -+- BCBS --t R-T d e

Delay comparison for different DSISSMA code protocols

make objective comparisons between the protocols, all data included in Figs. 12 and 13 were obtained using the same analytical method, the steady-state flow method suggested by Sousa and Silvester in Reference 5, which is a distinct method to the Markov chain method used in the previous Sections. It is easy to notice that the obtained results using the steady-state flow method are quite close to those obtained from the Markov chain method, although the throughput given at p = 10 is more

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conservative than that obtained from the Markov chain method. All the compared networks have the same size (N = 20). We can see from the comparisons that the R3 protocol undoubtedly outperforms all other protocols under any offered traffic conditions from p = 0 to p = 10.

5 Conclusions

In this paper, we have proposed and studied the R3 pro- tocol for DS/SSMA packet-radio networks. The throughput-delay performance of the protocol was analysed using the two-dimensional Markov chain model. The results show that the R3 protocol is prom- ising in terms of throughput and delay performance. The protocol is particularly suitable for the wireless data net- works, such as the wireless PC-link network shown in Fig. 1, which cover relatively small areas, although the protocol in principle can be applied to any distributed and asynchronous radio data networks using the DS/SSMA technique.

6 References

1 KLEINROCK, L., and TOBAGI, F.A.: ‘Packet switching in radio channels: Pt I - Carrier sense multiple access modes and their throughputdelay characteristics’, IEEE Trans., 1975, COM-23, (12), pp. 1400-1416

2 TOBAGI, F.A., and KLEINROCK, L.: ‘Packet switching in radio channels: Pt I1 - The hidden terminal Drohlem in carrier sense multiple-access and the busy-tone solution’, IEEE Trans., 1975, COM-23, (12), pp. 1417-1433~

3 RAYCHAUDHURI, D.: ‘Performance analysis of random access nacket switched code division multiole access svstem’. IEEE Trans.. ~. 1981, COM-29, pp. 895-901

4 POLYDOROS, A., and SILVESTER, J.A.: ‘Slotted random access spread spectrum networks: an analytical framework‘, IEEE J., 1987, SAC-5, (6), pp. 989-1002

5 SOUSA, E.S., and SILVESTER, J.A.: ‘A spreading code protocol for a distributed spread spectrum packet radio network‘, IEEE Trans. Commun., 1988,36, (3), pp. 272-281

6 ABDELMONEM, A.H., and SAADAWI, T.N.: ‘Performance analysis of spread spectrum packet radio network with channel load sensing’, IEEE J . Se/. Areas Commun., 1989.7, (1). pp. 161-166

7 STOREY, J.S., and TOBAGI, F.A.: ‘Throughput performance of an unslotted direct-sequence SSMA packet radio network’, IEEE Trans. Commun., 1989,37, (a), pp. 814-923

8 MORROW, R.K., and LEHNERT, J.S.: ‘Packet throughput in slotted ALOHA DS/SSMA radio systems with random signature sequences’, IEEE Trans. Commun., 1992,40, (7), pp. 1223-1230

9 CHEN, X.H., LIU, W.X., and OKSMAN, J.: ‘Use of code sensing technique in the receiver-based spreading code protocol and its per- formance analysis’, I E E Proc. I, 1992,139, (l), pp. 85-90

10 CHEN, X.H., and OKSMAN, J.: ‘Busy code broadcasting and sensing protocol for collision-free CDMA packet radio networks and its performance analysis’, IEE Proc. I, 1992, 139, (6). pp. 613- 619

1 1 KLEINROCK, L.: ‘Queueing system’, vol. 1 and 2 (John Wiley and Sons, 1975)

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