Digital Signal Processing 19 (2009) 990–997

www.elsevier.com/locate/dsp

System performance analysis of situation awareness messagingusing narrow-band multi-user detection

Mark Rice ∗, Tim Giles, Michael Peake

DSpace Pty Ltd., Innovation House, First Avenue, Mawson Lakes, Technology Park, SA 5095, Australia

Available online 25 September 2007

Abstract

This paper is concerned with enhancing situation awareness messaging using narrow-band multi-user detection techniques.Situation awareness messaging involves sending short packets of situation update data. Low latency is an important requirement.This paper focuses on using satellite communications which have a substantial propagation delay. These factors favour the use ofa random access system such as Aloha. The main draw back of these systems is low channel utilisation. The capacity of an Alohasystem using multi-user detection is analysed is this paper. The capacity is substantially improved by using multi-user detectors.Furthermore the distribution of user powers experienced at the ground station enhances the performance of a system based onmulti-user detection.© 2007 Elsevier Inc. All rights reserved.

1. Introduction

Situation awareness messaging systems are receiving a greater focus recently as they play a critical role in reducingthe rate of fratricide in modern warfare [1]. Satellite communications is the natural solution in this application becauseof its wide area coverage and reliability. When short low latency messaging is required an Aloha [2] random accessmultiple access layer or similar is typically used. Aloha suffers from low channel utilisation. A conflict resolutionalgorithm [3] can increase the channel utilisation but at the expense of latency. Enhancements to the physical layersomewhat improve the situation, such as code division multiple access (CDMA) Aloha [4]. Parallel interferencecancellation (PIC) [5] is proposed to improve the physical layer. PIC with strong coding performs extremely wellso here it is modelled by the multi-user channel capacity [6]. In most radio Aloha systems the packets arrive withdifferent powers as a result of differing propagation paths. This is often the case in satellite systems however thereceived power difference is due to the transmitters being located at different locations within the spot beam of thesatellite. A wide distribution of user powers can be a disadvantage in CDMA systems however a multi-user detector(MUD) benefits from the differences.

The analysis in this paper considers multi-user detection, possibly narrow-band, Aloha and distributed receivedpacket powers.

* Corresponding author. Fax: +61 8 8260 8141.E-mail addresses: mark.rice@dspace.com.au (M. Rice), tim.giles@dspace.com.au (T. Giles), michael.peake@bigpond.com (M. Peake).

1051-2004/$ – see front matter © 2007 Elsevier Inc. All rights reserved.doi:10.1016/j.dsp.2007.09.007

M. Rice et al. / Digital Signal Processing 19 (2009) 990–997 991

2. System analysis

2.1. Random access system

Consider an Aloha random access scheme where a large pool of users occasionally wish to transmit a short packetof information. Each user transmits without consideration of the traffic already on the channel. The reception of thepacket may be unsuccessful as a result of co-channel interference from other users transmitting packets simultane-ously. All unsuccessful packets are backlogged for later retransmission. The traffic intensity as experienced by thechannel is called the offered load γ and is the sum of the traffic intensity from new packets λ and the backlog.A slotted system is assumed and the number of packets i simultaneously offered to the channel follows a Poissondistribution (1)

Pi(γ ) = e−γ γ i

i! . (1)

In the standard analysis [2] it is assumed that if two messages are present on the channel then there is a collisionand neither are received. We define a throughput ξi indicating the throughput achieved as a result of i packets beingsimultaneously offered to the channel. In the standard case ξ1 = 1 and ξi = 0, ∀i � 2. The relationship between offeredload γ and total throughput Ξ is given by the equation

Ξ(γ ) =i=∞∑i=1

ξiPi(γ ). (2)

If the system is in a steady state then the total throughput Ξ is equal to the traffic intensity from new packets λ. TheCapacity of the Aloha channel is given by the maximum value of the throughput Ξ over all values of offered load γ ,which is e−1 for the standard slotted Aloha system. In operation the new traffic load is kept well below the capacityin order to keep the latency low, however increasing the capacity will generally increase the operational traffic load.

The maximum value of λ = Ξ(γ ) occurs at a turning point so it can be found by solving the equation

dΞ

dγ= d

dγ

i=∞∑i=1

ξie−γ γ i

i! = 0. (3)

Equation (3) can be simplified to finding the roots of a polynomial in γ of degree M (4) where M is the maximumnumber of simultaneous packets for which some throughput can be achieved

i=M∑i=1

ξi

i!(iγ i−1 − γ i

) = 0. (4)

2.2. Uniformly distributed received packet powers

When a MUD is used a number of packets may be simultaneously detected. Quite sophisticated MUD algo-rithms [5] are now available so it is reasonable to use the multi-user Shannon capacity [6,7] to model the MUDperformance. Given a set of received powers E1, . . . ,EM the corresponding rates r1, . . . , rM are within the Shannoncapacity if all the capacity inequalities (5) are satisfied

rx < log2

(1 + Ex

N0

),

rx + ry < log2

(1 + Ex + Ey

N0

),

rx + ry + rz < log2

(1 + Ex + Ey + Ez

N0

),

...M∑

rm < log2

(1 +

∑Mm=1 Em

N0

). (5)

m=1

992 M. Rice et al. / Digital Signal Processing 19 (2009) 990–997

The channel bandwidth is normalised to 1 Hz and N0 is the noise spectral density in W/Hz.The equations above (5) represent the set of all combinations of the M received signals. Thus, the total number of

equations represented in (5) is

2M − 1 =(

M

1

)+

(M

2

)+

(M

3

)+ · · · +

(M

M

). (6)

In the case where all users transmit with the same rate and power, then the j th equation of (5) becomes

jr < log2

(1 + jE

N0

). (7)

In this simple case the capacity inequalities can be reduced to just one inequality

Mr < log2

(1 + ME

N0

). (8)

A single user detector (SUD) may also be able to detect multiple packets simultaneously, however the other packetsare regarded as interference by the receiver. This method can be thought of as conventional CDMA with the feasiblerate being defined in the equation

r < log2

(1 + E

N0 + (M − 1)E

). (9)

The capacity for standard Aloha, SUD, MUD and the scheduled access limit are plotted in Figs. 1 and 2. Thestandard Aloha is the case where only one packet can be received per slot. In the SUD and MUD cases the bit rate ofeach user is adjusted so that the maximum number of simultaneous packets M can be received. The Shannon capacityshows the limit of bit rate if the maximum number of users M transmitted continuously. The E/N0 values are a perpacket value, i.e., when more packets are transmitted simultaneously then there is more power available at the receiver.

In Fig. 2 the standard Aloha is shown against maximum number of packets however only one packet per time slotis allowed to pass through the channel in this case.

The SUD system does provide an improvement over the standard Aloha however when the E/N0 value becomeslarge there is no benefit because the mutual interference between users annuls any gain made by being able to transmitfrom more than 1 user simultaneously. The MUD does not have this limitation and is able to cancel the mutual

Fig. 1. System throughput versus E/N0 for a maximum of 4 simultaneous packets.

M. Rice et al. / Digital Signal Processing 19 (2009) 990–997 993

Fig. 2. System throughput versus maximum number of simultaneous packets for an E/N0 = 0 dB.

interference provided the Shannon capacity is not exceeded. At very low E/N0 values the mutual interference is nolonger significant and the MUD and SUD provide similar performance. Note that high E/N0 values correspond toa “narrow-band” waveform as the calculations have been normalised to 1 Hz. Naturally, if the data were scheduledthere would be a very high capacity as shown by the Shannon capacity line.

Increasing the capability of the MUD to receive more packets simultaneously has a positive effect on performance,(see Fig. 2). This can be explained by two factors: First, the more packets offered on the channel then the higherthe total received power. The second factor is the “sharpness” of the Poisson distribution (2). If the average numberof packets offered to the channel increases then the relative deviation in number of packets is reduced, thus theprobability of wasting time slots by transmitting too many or too few packets is reduced. It is, however, not a gooddesign to have an extremely high maximum number of packets. The complexity of the MUD receiver increases withnumber of simultaneous packets. Another concern may be that the optimum rate for each user is reduced as the numberof simultaneous packets increases and hence the messages are delayed on the physical layer so the low latency featuremay be lost.

2.3. Distributed received packet powers

In many radio systems the received power from each user varies. In a satellite system this is typically because theusers occupy different locations within the satellite’s receive antenna spot beam. The distribution of user power f (E)

given here is based on the antenna pattern of a circular aperture antenna [8] however the distribution for the satelliteor system concerned should be inserted. The theoretical antenna pattern A(θ) is

A(θ) =(

2J1(θ)

θ

)2

, (10)

θ = 2πr0 sin(φ), (11)

where φ is the angle from bore sight, r0 is the radius of the antenna aperture measured in wavelengths and J1 isa Bessel function of the first kind of order 1. For a geo-stationary satellite the angles φ are very small and it isa reasonable approximation to equate the distance from the centre of the spot beam d directly with the parameterθ ≈ 2πr0d/H , where H is the height of the satellite. It is assumed that the users are uniformly distributed in a circular

994 M. Rice et al. / Digital Signal Processing 19 (2009) 990–997

region around the centre of the spot beam with the edge at θ = θmax. The distribution of θ is fθ (θ) = 2θ/θ2max. The

user power distribution f (E) is

f (E) = −fθ

(A−1(E)

)dA−1(E)

dE. (12)

A−1(E) is the solution θ , to E = A(θ) where we are only interested in the range of 0 < θ < 3.8317, or betweenbore sight and the first null.

If the packet from each user is received with a different power the capacity calculation is a little more involved,however the number of tests to be performed can be substantially less than that given in (6). The received powers aresorted such that E1 � E2 � E3 � · · · � EM−1 � EM . Note that for the set of equations in (5) involving n signals,where 1 � n � M , the following inequality holds

log2

(1 + E1 + E2 + · · · + En

N0

)< log2

(1 + E2 + E3 + · · · + En+1

N0

)

< log2

(1 + EM−n+1 + EM−n+2 + · · · + EM

N0

). (13)

The inequality (13) can be used to reduce the number of equations in (5). All users have the same data rate r

so all(Mn

)inequalities can be verified by applying the one equation with the smallest values of received power

E1,E2, . . . ,En. The MUD performance for all n ∈ {1,2, . . . ,M} can be verified by M equations, and equationsin (5) are reduced to the following:

r < log2

(1 + E1

N0

),

2r < log2

(1 + E1 + E2

N0

),

...

nr < log2

(1 + E1 + E2 + · · · + En

N0

),

...

Mr < log2

(1 +

∑Mm=1 Em

N0

). (14)

As an additional consideration there is the possibility of using the MUD to receive only k packets out of the M

packets transmitted. In this case the M–k discarded packets are regarded as extra noise by the MUD.Consider the case where (14) is not satisfied and the case where one packet is discarded. If the packet with power Ex

is chosen then an element of (14) becomes (15)

(n − 1)r < log2

(1 + E1 + E2 + · · · + En − Ex

Ex + N0

). (15)

The right-hand side of (15) is maximised by choosing the Ex with the lowest power, i.e., E1. By recursion it canbe seen that the packets to be discarded should be the packets received with the lowest power.

Now a capacity function C(E, r) is defined which returns the highest number of packets that can be simultaneouslydetected given received packet powers E. C(E, r) can be determined by evaluating the inequalities (16)

r < log2

(1 + EM−k+1

N0 + ∑m=M−km=1 Em

),

2r < log2

(1 + EM−k+1 + EM−k+2

N0 + ∑m=M−km=1 Em

),

...

M. Rice et al. / Digital Signal Processing 19 (2009) 990–997 995

nr < log2

(1 +

∑M−k+nj=M−k+1 Ej

N0 + ∑m=M−km=1 Em

),

...

kr < log2

(1 +

∑Mj=M−k+1 Ej

N0 + ∑m=M−km=1 Em

). (16)

C(E, r) can be determined by evaluating, at most, M(M − 1)/2 inequalities.Using the distribution of received power f (E) and the capacity function C(E, r) the throughput ξi can be deter-

mined. The throughput ξi is dependent on the rate r chosen for the transmitted packets,

ξi,r = r

∫E

F (E)C(E, r) dE, (17)

where E is Ri and F (E) = ∏i

m=1 f (Em) and ee < Em < ec. We define ee as the received power at the edge of thespot beam and ec as the received power at the centre of the spot beam. In the graphs shown f (E) is the distribution ofpowers for the new traffic. It would be more accurate to use the distribution of the powers of the offered traffic. It ispossible that the packets transmitted from near the beam centre are more often received than those transmitted fromthe beam edge hence the offered traffic may differ from the new traffic distribution. This is expected to be a secondorder effect and a correction could be added as a future refinement.

The best rate r needs to be selected given the received power distribution and maximum number of packets thatcan be simultaneously received by the MUD. Figure 3 shows how the individual user rate effects the capacity. Thevalue given in the legend is the power difference between the edge of the antenna beam and the centre ec/ee. The0 dB power difference case is equivalent to the uniform received powers case. The jagged shape of the 0 dB curve isexpected. The best rate is where all four packets can be simultaneously received. If the rate is increased above thislevel then only 3 packets can be simultaneously received and the capacity is instantly reduced, thus producing a step inthe curve. Steps can be noted for all the transitions in number of simultaneous packets 4 to 3, 3 to 2, 2 to 1 and 1 to 0.For the cases involving a received power distribution then there is no distinct rate marking the transition between 4and 3 simultaneous packets, for example.

Fig. 3. System capacity versus individual user rate with E/N0 = 0 dB and a maximum of 4 simultaneous packets.

996 M. Rice et al. / Digital Signal Processing 19 (2009) 990–997

Fig. 4. System capacity versus E/N0 at beam edge and a maximum of 4 simultaneous packets.

Fig. 5. System capacity versus maximum number of simultaneous packets with E/N0 = 0 dB.

Figure 4 shows how the capacity changes with the power available. The optimum individual user rate is chosen foreach point in Figs. 4 and 5. The capacity increases as the variation between received user powers increases. This isexpected because the MUD is able to take advantage of received packets with more power and the distributions withgreater variation also have a greater average power.

Figure 5 shows that increasing the capability of the MUD improves capacity but as mentioned earlier it is not agood design to increase the maximum number of simultaneous packets indefinitely.

M. Rice et al. / Digital Signal Processing 19 (2009) 990–997 997

3. Conclusion

The capacity of an Aloha system using multi-user detection has been analysed. It was assumed that a strong errorcontrol coding is used and a fairly sophisticated multi-user detector so that the performance tracks the Shannon limits.The capacity is doubled over Aloha using a single user detector for the typical conditions of E/N0 = 6 dB and amulti-user detector capable of receiving four packets simultaneously. The target application is situation awarenessmessaging over satellite. Over the satellite channel it is usual to experience variation in the received packet powers asa consequence of the various positions of users within the antenna’s spot beam. It was shown that the capacity of themulti-user detection system was increased as a result of the packet power distribution.

References

[1] G. Cahlink, Better blue force tracking, Air Force Mag. 87 (6) (2004) 66–69.[2] N. Abramson, The throughput of packet broadcasting channels, IEEE Trans. Commun. COM-25 (1) (1977) 117.[3] L. Ahlin, J. Zander, Principles of Wireless Communications, second ed., Studentlitteratur, Lund, 1998, pp. 403–406.[4] S. Roy, H.Y. Wang, Performance of CDMA slotted ALOHA multiple access with multiuser detection, in: Proceedings of the IEEE Wireless

Communications and Networking Conference, WCNC 99, vol. 2, 21–24 September 1999, pp. 839–843.[5] D. Divsalar, M. Simon, D. Raphaeli, A new approach to parallel interference cancellation for CDMA, in: Proceedings of the Global Telecom-

munications Conference, GLOBECOM’96, vol. 3, 18–22 November 1996, pp. 1452–1457.[6] T.M. Cover, J.A. Thomas, Elements of Information Theory, Wiley, New York, 1991, pp. 388–399.[7] B.E. Shrader, Multiuser detectors for S-TDMA multihop radio networks, Masters thesis, Royal Institute of Technology, Stockholm, Sweden,

September 2001.[8] S.A. Hovanessian, Radar System Design and Analysis, Artech House, Norwood, MA, 1984, p. 31.

Dr. Mark Rice is Founder and Chief Technology Officer of DSpace, now a subsidiary of EMS Satcom. Mark is responsiblefor overall direction of DSpace’s satellite communications product development and shaping of the product strategy. Mark is aspecialist in the global satellite industry, and has regularly published in technical literature and is co-author of five patents. Markgraduated from the University of Manchester with B.Sc. in 1984 and Ph.D. in 1989 in electrical and electronic engineering, is aMember of the Institution of Engineering and Technology, a Chartered Engineer and holds an adjunct position within the Institutefor Telecommunications Research at the University of South Australia.

Dr. Tim Giles is DSpace’s research leader in the area of modem and radio communication systems and has 17 year workingexperience in satellite and high frequency (HF) systems. He has published 4 patents and over 40 technical papers entirely withinthe field of radio communications. He began his career in applied HF radio research with the Defence Science and TechnologyOrganisation (DSTO). Tim joined the Institute of Telecommunications Research (ITR) at the University of South Australia in 1997,where he concentrated on commercial satellite communications research and development. His next position was with the RoyalInstitute of Technology (KTH), Stockholm, Sweden. His main roles were teaching under graduates and post graduates, advisingpost graduates and research in the field of ad–hoc radio networks. Tim now leads research within DSpace creating and improvingproducts and services. Tim has a Bachelor and a Ph.D. degree from the Electrical and Electronic Engineering Department of theUniversity of Adelaide and is multilingual (English, Swedish, and German).

Dr. Michael Peake has been a researcher for seven years with DSpace. He has published 3 patents and a number of papersand commercial reports in the fields of fluid mechanics, sonar, radar, and satellite communications. During his 14 year career,Michael has taught undergraduates at Adelaide University and the University of South Australia as well as performing researchfor the Cooperative Research Centre in Robust and Adaptive Systems. Prior to joining DSpace Michael developed sonar and targetidentification algorithms for Cooperative Research Centre for Sensor Signal and Information Processing (CSSIP). His Bachelor ofMath Science degree with first class honours was awarded by the University of Adelaide in 1988 while his D.Phil. was awardedby Oxford University in 1994. Furthermore, Michael is an active member of the Australian Mathematical Olympiad Committee,training the next generation of mathematicians.