An intelligent hybrid spread spectrum MAC for interference management in mobile ad hoc networks

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An intelligent hybrid spread spectrum MAC for interference management in mobile ad hoc networks Sana Ajmal a,∗, Samra Jabeen a, Asim Rasheed b, Aamir Hasan c a

Electrical and Computer Engineering Department, Centre for Advanced Studies in Engineering, 19 Attaturk Avenue, Sector G-5/1, 44000, Islamabad, Pakistan Electronics Engineering Department, Muhammad Ali Jinnah University, Islamabad, Pakistan c IAA, Air University, Islamabad, Pakistan b

a r t i c l e

i n f o

Article history: Received 8 August 2014 Revised 26 December 2014 Accepted 27 April 2015 Available online xxx Keywords: Medium access control Ad hoc networks Transmission capacity Frequency hopping Direct sequence spread spectrum

a b s t r a c t This paper presents and analyses a fully distributive intelligent hybrid spread spectrum MAC for ad hoc networks. The IHSS MAC scheme has been developed with the aim to mitigate far field interference with the use of a robust DSSS physical layer, while managing near field interference with the use of intelligent slow frequency hopping. The IHSS design ensures a minimum required SINR threshold at active receivers, under low outage probability constraints. IHSS does not inhibit any nodes in space neither thins them out in time. A lower bound on transmission capacity for the case where the size of the frequency hopping zone is variable is derived in this paper. The mathematical model is validated through simulation. The simulation is based on a hopping sequence selection methodology that randomizes the available hopping sequences within a frequency hopping zone around each active receiver. The implementation utilises the RTS/CTS concept of the CSMA MAC, with a slight modification. The performance criterion used for analysis is transmission capacity normalized by the required bandwidth. It is observed that implementation of a suitable sized frequency hopping zone using the proposed IHSS MAC, shows superior performance over ALOHA and guard zone based MACs. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Absence of a central controlling authority and infrastructure is a characteristic feature of ad hoc networks. Consequently, control and management functions are distributed amongst nodes throughout the network. The research on wireless ad hoc networks is fuelled by the fact that these networks represent the most general type of wireless networks. Almost all other types of networks, including cellular, sensor, vehicular, relay, etc. can be treated as sub types of MANETs. While the idea of forming networks ‘on the fly’ is attractive, it also poses some formidable challenges to design optimization and analysis. Requirements of data rate and round the clock connectivity are increasing every day. Complex and dynamic networks, such as vehicular ad hoc networks (VANETs), require increased data rates, improved connectivity and efficient interference mitigation under dense node conditions.

∗

Corresponding author. Tel.: +923315000101. E-mail addresses: [email protected], [email protected] (S. Ajmal), [email protected] (S. Jabeen), [email protected] (A. Rasheed), ahasan-cae@ nust.edu.pk (A. Hasan).

Addressing the challenges of connectivity and resource availability requires efficient routing and medium access control (MAC) [1,2]. Efficient MAC mitigates interference and improves resource availability. Compared to cellular networks, interference in a complex and dynamic ad hoc network cannot be managed in a centralized manner. If interference management is not performed efficiently in a distributed network, the signal to interference plus noise (SINR) falls below the required threshold. This results in an increase in outages. Medium access control (MAC) design is an important factor for managing interference efficiently. An efficient MAC must be designed in a way such that: 1. Its implementation is simple in a distributed network. 2. Probability of outages is upper bounded by a small number through effective interference management. 3. The scarce resources (time, space and spectrum) are utilised efficiently. Most MAC schemes achieve the first two design considerations through inhibiting or suppressing some of the active nodes in time, space, frequency or codes. A few surveys [3,4] provide insights into the MAC schemes for ad hoc networks. Examples include ALOHA [5,6] spread spectrum CDMA [7], TDMA/FDMA [8], directional MAC [9], etc.

http://dx.doi.org/10.1016/j.comcom.2015.04.006 0140-3664/© 2015 Elsevier B.V. All rights reserved.

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Spatial reuse of frequency channels is one methodology for addressing the third MAC design consideration. In narrowband systems, reused frequency channels must be assigned to spatially separated locations to mitigate the interference caused by co-located (in both space and spectrum) frequency channels. However wideband spread spectrum physical layers provide interference averaging. This inherently increases the spatial reuse. Though the reused frequency channels cannot be exactly co-located (for reasonable spreading gains of the spread spectrum physical layer), the spatial separation between them can be much lesser. Achieving a high spatial reuse while ensuring that interference is managed efficiently is a challenging goal. Transmission capacity is a concept that determines utilisation of space at a certain time while upper bounding the outage probability. Spatial or temporal thinning might be required which limits the transmission capacity of the network [10]. Transmission capacity is defined as the intensity of simultaneous and successful transmissions [11–13]. The usefulness of the concept of transmission capacity lies in its tractability, easy computation and relationship with throughput [11]. In an average sense, if all nodes transmit at the same data rate, transmission capacity can be used directly to compute the network throughput. It is well known that medium access control (MAC) plays a key role in optimizing the transmission capacity of ad hoc networks [11,12]. If we look at the existing MAC approaches, the simplest one, ALOHA, and slotted ALOHA, do not guarantee a low outage probability. On the other hand, direct sequence spread spectrum (DSSS)shows suboptimal performance as spreading gain increases, in terms of normalized transmission capacity [14]. Approaches like CSMA and other guard zones based schemes are inhibitive in nature. They limit the transmissions in the near vicinity of active nodes for safeguarding the nodes’ transmissions, and thus limiting the number of simultaneous transmissions. [15–17]. This will be discussed in detail in Section 2. A novel medium access control (MAC) approach utilising a cross layer hybrid spread spectrum system, called intelligent hybrid spread spectrum (IHSS) was presented in [18]. The proposed IHSS approach for medium access control aims at improving the transmission capacity of ad hoc networks above the existing schemes. The strength of the proposed scheme lies in the fact that no node has to abstain from transmission at any given instance of time, while also fulfilling an outage probability constraint. By using a hybrid of DSSS and slow frequency hopping (SFH), the requirements of improved transmission capacity, outage probability and simplicity of implementation can be met simultaneously by the proposed IHSS MAC. This scheme is a cross-layer design. As opposed to the proposed MAC design that utilises a DSSS PHY layer and a FH-CDMA MAC layer, all the existing hybrid spread spectrum schemes are physical layer modulation techniques aimed at improving the bite error rate (BER) performance of the network [19,20]. The rest of the paper is structured as follows: Section 2 presents a review of commonly used MAC schemes. Section 3 outlines the proposed IHSS MAC scheme. Section 4 provides a theoretical analysis of the proposed IHSS MAC and compares its performance with existing MAC approaches. Section 5 presents insights into implementation. Section 6 shows simulation results and proves the validity of the theoretical model. It also explains the effect of mobility on the performance of the IHSS MAC. Section 7 concludes the paper and points out the future research goals. 2. Existing MAC approaches An efficient MAC scheme ensures that every node could transmit whenever it requires sending some data. At the same time, a large proportion of transmission efforts should be successful, especially for delay sensitive and energy efficient networks. A failed effort, also known as an outage, causes an increase in contention rate, and

leads to drop in overall network throughput. It also causes wastage of power and time used for transmission. A successful transmission is ensured by eliminating all interferers falling inside the contention domain of the receiver. This elimination guarantees that the signal to interference plus noise ratio (SINR) at the receiver is above a minimum required threshold. The elimination of interferers creates empty spheres (exclusion zones), that do not contain any interferers, around each receiver. The size of the spheres is inversely proportional to the number of simultaneous transmissions in any given area (also known as transmission capacity). An efficient MAC scheme tries to improve the transmission capacity by reducing the size of the spheres and packing them closely and tightly [21]. With the inception of ad hoc network concept, ALOHA and its variants were considered attractive options, due to their ease of implementation in a distributed network. Nelson conducted the first study of ALOHA’s performance in a multi-hop network by considering a finite number of nodes within two hops [22]. By using the concept of spatial reuse, Ghez et al. defined the ALOHA based model for an infinite network [23]. In simple ALOHA, any node which has data to send, can transmit without any restriction. If a collision occurs, the colliding nodes wait a random amount of time and retransmit the destroyed packets. The work of Baccelli et al. [5] investigates the ALOHA MAC design for ad hoc networks with randomly distributed nodes. Their work captures the spatial distribution that is enforced through the use of ppersistent ALOHA MAC. In p-persistent schemes, when a node has a data to send, it accesses the channel with a certain medium access probability (MAP) p. Such an approach is ideal from an implementation perspective in ad hoc networks. It does not require any coordination in a distributed topology. Baccelli et al. also proved that the medium access probability p determines the size of a random exclusion zone around each node. The mean radius of the exclusion zone is proportional to √1p . They showed that by fine tuning the MAP for maximizing the intensity of successful transmissions, the outage probability goes as high as 0.63. Weber et al. found the transmission capacity of uniformly distributed random nodes for an ALOHA-like MAC [12] using the probability distribution function of aggregate interference at a typical receiver [24]. They also showed that the capacity is primarily limited by the nearest interfering node. The idea to use spread spectrum techniques for ad hoc networks has also been proposed by the researchers. In [10], the authors have pointed out the desirability of using spread spectrum techniques at the physical layer of ad hoc networks. Spread spectrum techniques inherently provide better security and protection against interference. The two spread spectrum techniques commonly considered suitable for ad hoc networks are frequency hopped spread spectrum (FHSS) and direct sequence spread spectrum (DSSS). By dividing the bandwidth into M sub-channels, FHSS results into thinning of interferers on a certain band. On the other hand, in DSSS, the spreading and despreading of the signal reduces the SINR requirement by M [10]. In [14] the authors find the achievable transmission capacity using ALOHA in networks with spread spectrum physical layer. Carrier sense multiple access (CSMA) [23] is a very popular MAC protocol for wireless ad hoc networks. Concept of medium sensing and random back-off minimizes the probability of simultaneous transmission of any two nodes within each other’s contention domain. To avoid the hidden node problem in CSMA [25], the IEEE 802.11 [26] standard uses RTS/CTS (request to send) packet exchange in CSMA/collision avoidance (CA). This has the effect of creating guard zones around both transmitters and receivers in the same time slot. Guard zone is defined as an area around an active node, where all interfering transmissions are inhibited [15–17]. Contrary to the approach used in CSMA, only the receiver is required to be protected

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from interference. Thus guard zones may be employed around active receivers only. Hasan et al. analysed guard zones around active receivers only, using a slight modification of the CSMA/CA approach [15–17]. Hasan et al. also determined the optimum size of the guard zone that maximizes the node packing in the network [15]. They analysed a direct sequence spread spectrum network with spreading gain M ≥ 1. The spreading gain of unity was used to represent a narrowband system. They showed that creating optimal sized guard zones around active receivers improves the transmission capacity over ALOHA based networks, using the same spread spectrum physical layer. Their analysis also promises improvement for transmission capacity over classical RTS/CTS based guard zones created using CSMA/CA approach of IEEE 802.11. Directional antennas based MAC is another notable MAC scheme [27]. Researchers [27,28] have focused on finding the transmission capacity improvement for networks with nodes using directional antennas. The results show that capacity improvement is a factor of (logn2 ) with complex signal processing. In [9], the authors proposed a MAC protocol with multiple directional antennas at each node. The MAC shows an improvement of 2–3 times over omnidirectional antennas. A slightly different interference mitigation approach involves the use of interference cancellation techniques. However, a small percentage of error in signal estimation may significantly reduce its advantages. After analysing the current MAC approaches, we can conclude that none of the approaches allows simultaneous concurrent transmissions by all nodes and has one or more following limitations: • Some approaches do not guarantee a low outage probability. • Some approaches remain suboptimal in terms of normalized transmission capacity with large spreading gains. • Some approaches limit the number of concurrent transmissions around active receiver. 3. Intelligent hybrid spread spectrum (IHSS) MAC All the existing MAC approaches work on the principle of elimination of interferers. Elimination is done by either orthogonalising them in time (TDMA), frequency (FDMA), code (CDMA), or enforcing spatial separation (guard zones, ALOHA, CSMA). All of these approaches result in inhibiting some of the active transmitters in any of the four domains, i.e. time, frequency, code or space. We hereby propose an intelligent hybrid spread spectrum (IHSS) MAC scheme, which ensures that no active node has to be inhibited from transmitting in any of the above mentioned domains. Intuitively, this will greatly increase the transmission capacity of the network. It uses a hybrid of frequency hopping spread spectrum (FHSS) and direct sequence spread spectrum (DSSS) physical layers to achieve a higher intensity of successful transmissions per unit area. While designing the IHSS MAC scheme, we ensured that the following two design considerations are met: • Scheduling can be implemented in a distributed manner in the ad hoc network. • An acceptably low outage constraint  can be met at each node, by mitigating node-to-node interference. This paper aims at providing a mathematical analysis and the transmission capacity improvement by using the IHSS MAC scheme. It does not include implementation details of IHSS. However for the interest of the readers, IHSS can be implemented by modifying the popular CSMA/CA approach. Using the RTS/CTS packets, specific information about the available pool of frequency hopping sequences can be communicated to the interferers in the range of the active receiver.

3

It is imperative to mention here the difference between some existing hybrid spread spectrum systems and the proposed intelligent hybrid spread spectrum MAC. A variety of hybrid systems have been proposed and compared in the past [19,20,29]. All of these are modulation schemes based on a combination of DSSS and fast or slow frequency hopping (FFH or SFH). The proposed IHSS is a novel scheme for medium access control designed using a hybrid of the two spread spectrum techniques. The previous hybrid modulation schemes and the proposed MAC scheme have a different perspective and very different performance parameters based on their implementation on two different layers of the network model. The hybrid modulation schemes are implemented purely on the PHY layer. IHSS used a DSSS PHY layer and a FH-CDMA MAC layer. In [30] researchers have devised a neat methodology to implement spread spectrum modulation techniques (including hybrid techniques) without the requirement of a priori coordination. The research on hybrid modulation techniques takes BER and Eb /No as the performance parameters. We, by the use of IHSS, are trying to maximize the transmission capacity of the ad hoc network through intelligent interference management. Consequently, these two are separate and unequal domain and should be analysed in the same light. 3.1. MAC design Fig. 1 shows the model for the proposed IHSS MAC scheme. The node in the centre is any typical receiver in the network. All the other nodes are interferers. The transmitter from which the typical receiver is receiving lies at a distance d from the receiver. Note here that from the perspective of any other receiver in the network, the concept of the proposed MAC scheme remains the same as shown in this figure. The success of a transmission is usually measured by the signal to interference plus noise ratio (SINR). Instead of just SNR (signal to noise ratio), SINR determines the performance of an ad hoc network, because of the wireless nature and random node deployment. If the received SINR is above a minimum required threshold, denoted as β , the transmission is considered successful. Otherwise, the receiver is unable to decode the received signal correctly, resulting in a failure of transmission, or outage. To better understand SINR in an ad hoc network, one can start with a simple illustration. Moreover, we considered line of sight communication between two nodes, by ignoring all multipath reflections. Hence, the transmitted signal from a transmitter travels a Euclidean distance x to the receiver. Even in this basic free space path loss model, the signal is attenuated by the square of the distance travelled to the receiver. Now consider the scenario where there are a number of transmitters simultaneously transmitting to their intended receivers, in the same frequency band. All these transmissions collectively contribute to interference at the reference receiver. The interfering signals are attenuated by the square of distances from the interfering transmitters to the reference receiver. If the signal has obstacles and reflectors/scatterers in its pathway to the receiver, the power decay is proportional to distance raised to the power of path loss exponent α . The path loss exponent generally varies between 2.5 and 4. The received SINR at any typical receiver is thus a function of the distance between the receiver and its transmitter; and the distances between the receiver and the interferers. Hence, SINR is heavily dependent on inter-node distances. It has been studied in [31] that interfering nodes can be divided into near field interferers and far field interferers. The distinction between the two sets of nodes is made depending on the amount of interference they contribute at the reference receiver. If all transmitters transmit with same power, then near field interferers affect the intended receiver more than the far field interferers due to lesser distance.

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Fig. 1. Hybrid intelligent frequency hopping/direct sequence spread spectrum in an ad-hoc network.

Using the same concepts, we propose a scheme in which all nodes employ DSSS physical layer as the baseline. The DSSS physical layer mitigates the interference by a factor of the spreading gain. To mitigate the near field interferers FHSS physical layer is used. Thus the interfering transmitters within a certain distance č of the receiver are made to hop, intelligently, on a different frequency hopping sequence. This mitigates the interference from nearby interferers within the disc b(0, č ). The different nodes in Fig. 1 signify the different frequency hopping sequences being used. To sum it up, we mitigate the interference from the far away nodes by the use of DSSS only. The more detrimental interference from the nearby nodes is mitigated by frequency hopping on top of direct sequence spreading. An interesting comparison can be made with the use of hybrid spread spectrum modulation techniques such as [19,20]. However, please note that these techniques are modulation techniques and have different performance parameters as compared to the cross layer design of the proposed IHSS MAC. 3.2. System model We modelled our network as a large ad hoc network, with randomly deployed nodes. Static or randomly moving nodes are deployed uniformly over the network area. Hence, the system can be modelled using a homogeneous Poisson Point Process (PPP). This is not a compromising assumption as the homogeneous PPP represents the worst case scenario [32]. However, marks can be added to the points of the baseline ground process to provide additional information about the points [33]. We thus model the system with a marked homogeneous PPP in a 2D plane, denoted as:

(λ ) = {(Xi , di )}

(1)

The average node density per unit area of the network is denoted as λ. The points Xi represent the transmitters contending for channel access at any given time. Each transmitter has a mark that represents its intended receiver. The ith mark is the intended receiver of the ith transmitter. Therefore, di represents the distance between the ith Tx–Rx pair. The maximum transmission range of any transmitter is r. All nodes employ a spread spectrum physical layer for transmission, using a DSSS spreading factor of MDS . By using DSSS the interference is mitigated by a factor of MDS , resultantly increasing the supportable node intensity under the outage probability constraints. An FH zone radius č is defined around each active receiver. Specifically, the interfering nodes falling within the disc b(0, č ) around each active receiver are made to choose different frequency hopping sequences. The pool of MFH frequency hopping sequences is predetermined prior to its allotment. Thus the FHSS spreading factor is MFH .

For the scope of this paper, we considered slow hopping in which there is a single frequency hop during a single channel access interval. The following additional assumptions have been made for simplification purpose: • Distance dependent path loss is the most dominating degradation of the signal in ad hoc environment [12]. Thus all channel effects, except path loss are ignored for the scope of this work. • Each node chooses a transmit power Pt to ensure that Pr is a constant throughout the network. This is known as pairwise power control. Thus, for the path loss exponent α > 2, Pt = Pr diα [34]. • A minimum SINR of β must be met at the receiver, for the outage probability constraint. A small outage probability  , i.e. 0 <   1 is ensured in the system. If the transmitter–receiver separation is fixed at d, this has the same mathematical connotations as employing pairwise power control. The marked homogeneous PPP thus becomes (λ ) = {(Xi , d )}. These might seem compromising assumptions. However, these allow for capturing of the baseline trends with the use of the proposed MAC scheme. These also allow the mathematical analysis to be tractable and the subsequent inferences to be cleanly developed from a network capacity theory perspective. Subsequent concerns, like realistic channel fading, variable transmitter receiver separation, etc. can be taken up as a future research goal. However, these concerns will be built on the baseline model defined above. For the proposed model, conditioning is done based on Slivnyak’s theorem resulting in Palm distribution for transmitters [35]. The Slivnyak’s theorem states that placing a node at the origin does not alter any of the properties of the PPP. Thus, the mathematical analysis can be done taking the receiver at origin as typical and capturing the behaviour throughout the network. 4. Theoretical analysis Using the system model described in the previous section, we hereby derive the transmission capacity of an ad hoc network employing the proposed intelligent hybrid spread spectrum (IHSS) MAC scheme. If a typical receiver is placed at the origin, it faces interference from two sets of transmitter nodes: (1) set of nodes within the frequency hopping zone of the receiver, hereby called the near field nodes; and (2) the set of nodes outside the frequency hopping zone, hereby called the far-field nodes. Fig. 2 represents the two sets of interferes around an active receiver which contribute to interference. Both sets of nodes may cause outages at the receiver under consideration. We denote the outage probability due to interference from

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5

where

δ=

r −α

−

β

η

(5)

Pt

Using Chebychev’s inequality [35], the aggregate interference Y, arising from interfering nodes of the Poisson Point Process m , and its statistical measures can be used to find the solution to the above equation.

Y =



| Xi |−α

(6)

i∈m

P0 (Y ≥ δ MDS ) ≤

σY2 (δ MDS − μY )2

(7)

Here, σY2 represent the variance of aggregate interference while μY represents its mean. Using Campbell’s theorem [35] and the statistical measures of Y, we can solve for maximum supportable node intensity outside the frequency hopping zone with radius č, under outage probability constraints of  f [14]:



Fig. 2. The areas in which the interfering nodes, around the receiver, can be divided. The darker grey shaded regions represent the near field interferers, while the light grey region represents the far field interferers.

inside the FH zone is n . At the same time, the probability of outage due to interference from outside FH zone as  f . The reader may argue that interference from within the FH zone is orthogonalised by orthogonal slow frequency hopping sequences. Hence, the probability of outage from inside the FH zone is zero i.e. n = 0. However, it is known that there is a non-zero probability that the number of points inside any disc in a PPP, can exceed a fixed number [33] MFH (or the number of frequency bands/hopping sequences available). Thus the probability of outage from within the FH zone cannot be zero for any non-zero size of the FH zone. Therefore, a node may face interference from within the FH zone b(0, č ) or from outside it. Outages due to interference from within the FH zone or from outside it are independent, but not mutually exclusive, events. Thus the overall outage probability can be expressed as:

 = n +  f − n  f

(2)

Let us first consider the interference from outside the frequency hopping zone and the associated outage probability. We assume that the code cross co-relation of the pseudo-noise (PN) sequences used for DSSS is M1 [36]. The SINR requirement, that can lead to an analDS

ysis of the supportable node intensity outside the frequency hopping zone, denoted as λf can be evaluated from the constraint below:



DS : P0

hPt r−α  MDS η + ι m hPt

β

≤ | Xi |−α MDS



≤ f

λf =

(δ MDS )2 č2(1−α )



 f (α − 1 ) π

(8)

This corresponds to the supportable intensity when there is only one band available for DSSS spreading, (i.e. MFH = 1). However, when the frequency hopping spreading factor MFH > 1, the supportable intensity becomes:

λ = MFH λ f

(9)

Here, λ is the overall intensity of the network and must be supported both inside and outside the FH zone. If the number of interferers within the frequency hopping zone to meet the outage probability constraint for near-field interferers by n , we must put an upper bound on the probability of the event that the number of interferers in the FH zone exceeds the number of available hopping sequences.

P[φ (Ač ) ≥ MFH ] ≤ n

(10)

Here, Ač is the area of the frequency hopping zone.

Ač = λπ č2

(11)

Using Eq. (8) and (9),

Ač = MFH (δ MDS )2  f (α − 1 )č2α

(12)

Within the frequency hopping zone, one frequency hopping sequence will be used by the receiver. For a PPP, the probability of having at most MFH points (including the active receiver under consideration) in a bounded area Ač is [35]:

(3)

Here, the P0 represent the Palm probability of outage at the reference receiver, placed at the origin. The DSSS physical layer has a spreading gain of MDS , noise power is η, and the channel response is represented by h. The other parameters used are as described in the system model. Eq. (3) gives the Palm outage probability such that the SINR at the reference receiver falls below the threshold Mβ . This



P[φ (Ač ) ≤ MFH − 1] = e−λAč

M FH −1 n=0

(λAč )n n!

(13)

Following from Eqs. (10) and (13), this reduces to



1 − n ≤

(MFH , λAč ) (MFH )



(14)

DS

is based on the interfering nodes on a single frequency hopping sequence, represented by the point process m . For the case of the system model in consideration, and using all simplifying assumptions, this can be further reduced to the Palm probability as follows:



P

0

 i∈m



−α

| Xi | ≥ δ MDS

(4)

where  (., .) and  (.) are the incomplete and complete gamma functions respectively. This can be used to find the minimum number of frequency hopping sequences required for a certain FH zone radius č and under the outage probability constraint n . We will now endeavour to find the number of frequency hopping bands required under the FH zone radius and the outage probability constraints.

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Fig. 3. The requirement of MFH versus the outage probability from within the FH zone (n ) and from outside it ( f ).

Table 1 List of parametric values used for analysis and simulation.

4.1. Minimum size of FH zone Since bandwidth is a scarce resource, we intend to keep the FH zone radius at its minimum. At the same time, FH zone must orthogonalise near field interferers and ensure outage probability constraint is met. Hence, the smallest sized FH zone can ensure the least spreading gain while meeting the outage probability requirement. In [37], the authors found that a single interfering node within the critical interference range (critical radius, s) may cause an outage at the receiver. Thus the interference from within the critical radius must be orthogonalised. They also defined the critical radius around an active receiver. If a minimum FH zone size requirement is to be placed with the condition that č ≥ 0, then the critical radius serves as the minimum required FH zone radius. Therefore, čmin = s

Value

α (path loss exponent) β (minimum SINR threshold at receiver)

4 5 dB 100 m 5 2

d (transmitter–receiver separation) M2 (DSSS spreading gain) (where unspecified) M1 (FHSS spreading gain) (optimum, where unspecified)

using ALOHA like MAC, were derived in [12]. The tighter lower bounds for the same were derived in [15]. The bounds for both spread spectrum techniques are reproduced below.

 α − 1 M α

π

α

π

α − 1 

where

s = (δ MDS )

Parameter

− α1

The requirement of DSSS arises from the fact that if the interference is not mitigated using DSSS (i.e. MDS = 1), the critical radius s (and thus the minimum required FH zone radius) is greater than the max transmission range r. For simple implementation of the scheme, the radius of the FH zone should be less than or equal to the maximum transmission range. An FH zone size larger than the transmission range makes it difficult to coordinate with the surrounding interferers, rendering the implementation of intelligent frequency hopping infeasible. Due to this reason, DSSS spreading factor should not be less than minimum SINR threshold, i.e. MDS ≥ β [13]. Fig. 3 shows the results for requirement of FH bands versus various outage probability constraints. It can be seen that for any appropriate network wide outage probability constraints, i.e. n =  f ≈ 2 , the minimum required number of hop bands is 2. 4.2. Comparison with existing MAC approaches Researchers have mathematically analysed most of the existing MAC protocols for the exact transmission capacity or bounds on it. The upper bounds on transmission capacity for both FHSS and DSSS

(δ ) α ≤ λFH ≤ 2

(Mδ ) α ≤ λDS ≤ 2

 M α2 (δ ) π

(15)

 2 (M δ ) α π

(16)

In this section, we aim to compare the transmission capacity achieved through the use of the proposed IHSS MAC scheme, with that achieved through ALOHA based FH-CDMA and DS-CDMA. For the comparison purpose, we used the same mathematical model as in the previous section. Table 1 gives the parameters used for analysis. Fig. 4 compares the normalized transmission capacity for ALOHA based DSSS and FHSS with the results obtained for the IHSS MAC scheme. It can be seen that the normalized transmission capacity for frequency hopping in a pure ALOHA network is approximately linear. That is to say that the transmission capacity scales linearly with the spreading gain M, for a bounded outage probability. For DSSS in a pure ALOHA network, the rate of growth in transmission capacity decreases with an increase in spreading gain. This implies that the increase in the number of supportable users with increasing spectrum is not linear in the case of DSSS. The reason for this is the near-far effect. It is obviously preferable to use frequency hopping and avoid interference than use direct sequence spread spectrum to suppress it [12], if there is no other type of scheduling being performed. It can be seen from Fig. 4 that the proposed hybrid MAC scheme shows clear advantage over ALOHA with DSSS physical layer. For low values of the overall spreading gain M, it also outperforms ALOHA

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7

Fig. 4. Normalized transmission capacity vs. the overall spreading gain (M = MFH ∗ MDS ), with the minimum sized frequency hopping zone. MFH (minimum) = 2.

with FH, but is suboptimal for higher values of M. The reason for this is similar to the reason for suboptimal performance of DSSS as M increases. As the spreading gain is increased, the supportable node intensity in the network increases. The increasing number of active interferers just outside the frequency hopping zone, which have not been orthogonalized by intelligent frequency hopping, causes a great amount of interference. The increasing node intensity with increasing MDS and the decreasing FH zone size (minimum requirement), increases the aggregate interference from the interfering nodes outside the FH zone. If somehow, the intelligent frequency hopping could be performed over the whole network (i.e. FH zone size → ∞), there would be zero interference as all nodes will be transmitting on orthogonalised channels. This would be ideal from transmission capacity perspective. However, coordination for intelligent hopping over a huge area is infeasible from an implementation perspective. Moreover, it also requires a huge spreading gain. Thus a trade-off must be reached between transmission capacity and complexity of implementation. Though the use of DSSS is suboptimal for normalized transmission capacity at larger spreading gains, it decreases the size of the interference domain around the active receivers. Therefore, having a DSSS physical layer is essential for decreasing the minimum required FH zone size up to the maximum transmission range r. Fig. 4 also compares the transmission capacity achieved with the use of optimum sized guard zones and that achieved with the proposed hybrid scheme using a minimum sized frequency hopping zone. The curves show that the performance of the proposed scheme falls below that of optimum sized guard zones based MAC. Though it is counter intuitive, the reason for this is simple. The guard zones based MAC uses guard zones of optimal size that maximizes the transmission capacity in the network. The optimum guard zone size is slightly larger in size than the critical radius. This suggests that the interfering nodes farther away from the critical radius also contribute to the aggregate interference and thus outages. In the next section, we will find the optimum size of the FH zone radius that maximizes the transmission capacity under the constraints of coordination range and outage probability.

4.3. Effect of FH zone size If the frequency hopping zone size is increased, the transmission capacity will increase. However, it should not exceed the maximum transmission range. It is known that if MDS ≥ β , then s ≤ r [38].

If the FH zone size is increased beyond the critical radius s, then, the events that can cause outage are as follows: 1. If number of nodes within the critical radius is greater than the FH bands. 2. If the aggregate interference from the disk outside the critical radius but within the FH zone is greater than a threshold δ MDS . 3. If the aggregate interference from outside the FH zone is greater than a threshold δ MDS . 4. A combination of two or more of the above. Considering the conditions for outage described above, the three outage events can be described as follows:

E1 = ψ

| (ψ ) ∩ b(O, s ) ≥ MFH

E2 = ψ

|



Pt

m (ψ )∩a(O,s,č )

E3 = ψ



|

Pt

| Xi (ψ )−α |≥ δ MDS

| Xi (ψ )−α |≥ δ MDS

(17) (18) (19)

m (ψ )∩b¯ (O,č )

E1 pertains to the nodes within the critical interference range. If even one node within this range is not orthogonalised, an outage is sure to occur. Note that the PPP without thinning on the MFH frequencies is used here for analysis. On the other hand, E2 pertains to nodes within the FH zone, but outside the critical interference range. Note that in the disc a(O, s, č ), the nodes on a single frequency channel might be more than one, but may not cause an outage. An outage occurs if the nodes on a single frequency channel generate enough interference that exceeds the acceptable threshold. Similar description exists for E3 . To proceed further, we need to find out the number of frequency channels MFH for frequency hopping. If we limit MFH by the number of nodes within the FH zone, it will provide us an upper bound on the outage probability. However, the actual outage probability might be lower than this as more number of nodes can be accommodated in the annulus a(O, s, č ) depending on their geometry. The upper bound on outage probability will provide the lower bound on transmission capacity. Thus we define a combined event E12 that can provide an upper bound on outage probability from within FH zone. E12 is an outage event such that the number of nodes within the FH zone exceed the number of frequency hopping bands.

E12 = ψ

| (ψ ) ∩ b(O, č ) ≥ MFH

(20)

The outage probability, from within the FH zone is defined by Eqs. (11)–(14). Following the analysis for the case of č = čmin , the

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Fig. 5. Required FHSS spreading gain and the resulting normalized transmission capacity, if the frequency hopping zone size is varied from čmin to č > r. The maximum transmitter receiver separation r = 100 m and DSSS spreading gain = 16.

Fig. 6. Normalized transmission capacity for fixed M1 .

supportable active node intensity is: 2α

λ = MFH λAč = MFH (δ MDS )  f (α − 1 )č 2

(21)

It is to be noted that unlike the case of minimum sized FH zone, the supportable node intensity is not independent of MDS . Fig. 5 a shows the required FH spreading factor MFH as the FH zone size č is increased for a fixed MDS and a fixed outage probability threshold. For any č greater than the minimum required FH zone size,

the number of required hop bands increases, as was evident from Eq. (11). Fig. 5b shows that the transmission capacity increases as č is increased. If the frequency hopping radius is fixed at r and the interference domain is reduced by increasing the value of DSSS spreading gain MDS , the transmission capacity is maximized at a certain value of MDS . Fig. 6 shows the behaviour of normalized transmission capacity with varying MDS , for the minimum required value of MFH = 2 and

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9

Fig. 7. Effect of frequency hopping zone size.

MFH = 3. Frequency hopping is performed over the maximum transmission range r. DSSS spreading gain is varied to capture the transmission capacity maximization point. It can easily be observed that for smaller values of MDS , the transmission capacity gets a hit if the value of MFH is increased above the minimum required value of 2. For larger values of MDS , it can be verified from Fig. 5 that the minimum required MFH is 3. The value of MFH increases for larger values of MDS . Thus for larger values of MDS , a higher value of MFH = 3 results in a higher transmission capacity. It can be concluded that the minimum required frequency hopping gain is also the optimum value for MFH . Using the inferences above, the effect of increasing the size of the frequency hopping zone was analysed. Fig 7 shows that the normalized transmission capacity increases significantly with a very small increase in the frequency hopping zone size. It exceeds the transmission capacity achieved with the guard zone based MAC for FH zone slightly larger than čmin . Specifically, when the size of the FH zone is increased from čmin to 1.2čmin , the transmission capacity normalized by bandwidth used, exceeds that achieved through guard zones. This provides an important result as opposed to the analysis presented in [12] for random access networks. The capacity in an IHSS network is not primarily limited by the nearest interferer only. Interferers farther away, but near the active receiver, also limit the capacity of the network. To find the optimum size of the FH zone, we need to search for an optimum solution over all possible values of MDS and č, such that MDS ≥ β and č = r. The optimum solution will provide the point where transmission capacity is maximized. The proposed scheme provides an additional advantage over the guard zone based MAC that under the bounds of active node intensity, as dictated by the achievable transmission capacity, no node will ever abstain from transmission.

exchange. The information regarding available frequency hopping sequences is communicated with the RTS message by the transmitter. The CTS message contains information about the frequency hopping sequence, randomly chosen from the common set of available hopping sequences for both the transmitter and receiver. The chosen hopping sequence is confirmed by the transmitter through a Hopping Sequence Confirmation (HSC) broadcast message. The robust underlying DSSS physical layer eliminates the need for carrier sensing. All the information required by the IHSS MAC is available through one hop broadcast messages. Thus the hidden and exposed node problems are solved. The nodes that cannot receive the information regarding the chosen hopping sequence, because they are hidden from the receiver, are provided this information by a broadcast frame sent by the transmitter, after receiving the CTS. In this way, all nodes maintain two pools of hopping sequences:

5. Distributed implementation design

The analysis of the previous section shows promising results with the use of the proposed hybrid MAC scheme in ad hoc networks. It is interesting to note that the system model based on the marked homogeneous Poisson Point Process (PPP) is rarely practical. Our aim is to cleanly develop a baseline model for the mathematical analysis of the proposed IHSS MAC. The only point process, with analytically tractable mathematical properties is the PPP. However, it must again be emphasized that the PPP represents the worst possible randomness of the nodes. Also, for large networks like nodes in playgrounds, or for networks with some geographic restrictions, like university hallways, etc. the Poisson Point Process is a neat model for node layout within that geographically bounded area. Since the mathematical results need to be verified, the simulation model used is also based on random Poisson Point node distribution. More

Feasibility of distributed implementation of the proposed scheme, in an ad hoc network, is an important aspect for analysis. The proposed IHSS scheme must be implemented in a distributed manner, such that little coordination is required around each receiver for intelligently choosing hopping sequences. IHSS design inherently caters for the dense network situation where each transmitter may fall within the frequency hopping zone of an active receiver. Though the detailed implementation of IHSS MAC is out of the scope of this paper, and can be found in [39], the interested reader may note that IHSS can be implemented with a very simple modification of the CSMA with RTS/CTS MAC. Each node maintains a pool of available frequency hopping sequences by monitoring the RTS/CTS

• Receiver pool: Pool of available hopping sequences that are not being used by transmitters in the vicinity of the node. The node may use these hopping sequences for reception. • Transmitter pool: Pool of available hopping sequences that are not being used by any receivers in the vicinity of the node. The node may use these hopping sequences for transmission. Fig. 8 provides an idea into what the exact implementation will look like. As a result, in dense networks, each node intelligently hops on a sequence orthogonal to the sequences being used within its vicinity. This orthogonalizes any near field interference. At the same time, each node also uses DS-CDMA to mitigate far field interference and to reduce the critical radius, and thus the minimum required FH zone size, to less than the transmission range of the node. 6. Simulation results

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Fig. 8. IHSS basic implementation based on slight modification of RTS/CTS broadcast messages.

Algorithm 1: Pseudo code for IHSS scheduling. 1

2

3 4 5 6 7

8

9 10 11

12 13 14 15 16 17 18 19 20 21 22

Generate active transmitters at a certain time instant t, with intensity λ; For each active transmitter, place a receiver independent and identically distributed in 0 ≤ θ < 360 deg and at a fixed distance r; Define the size of frequency hopping zone as č = r; if There is a node left, then Select the next node Xi ; if There is a frequency in the pool, then Assign a random frequency, from the pool of available frequencies, to Xi ; if Xi falls inside the frequency hopping zone of any receiver in the network then Modify the available pool of frequencies of Xi ; Go to step no. 6; else if Any previously generated / selected transmitters inside the frequency hopping zone of the receiver of Xi then Modify the available pool of frequencies of Xi ; Go to step no. 6; else Mark the node as active on the assigned frequency; Go to step no. 4; end else Do not accept the node for scheduling; Go to step no. 4 end end

For the simulation using SFH, the nodes within the minimum required frequency hopping radius čmin of an active receiver are made to choose a frequency band from the available pool of frequencies. The choice is made such that no other node is using that frequency band within the frequency hopping sequence around an active receiver. This information is implicitly inferred from the RTS and CTS broadcast messages, and each node maintains a frequency pool state based on this information. From the receiver frequency pool, first the frequencies common to both the transmitter and receiver are segregated. Then the selection of a common hopping sequence is made such that each available sequence has a uniform probability of being selected. For the case of Fast Frequency Hopping, a similar methodology can be employed by assigning numbers to hopping sequences instead of frequency bands. The simulation was carried out using MFH = 3 and MDS = β . This presents the unique case where FH zone size is the maximum possible (equals transmission range). At the same time the critical radius was also equal to the FH zone size, which is the minimum required FH zone size. To add a degree of freedom to the implementation of the proposed technique, MFH was chosen to be 3 instead of the minimum requirement of 2. A set of active transmitters was generated and deployed in an XY plane according to Poisson Point Process distribution. Transmitters and receivers were placed 100 m apart, i.e. r = 100. The intensity of nodes was kept at the maximum transmission capacity achievable (analytical result) with the use of parameters defined in the paragraph above. We assumed that all nodes transmit at network wide constant data rate of 1 Mbps. The simulation was carried out 100,000 times for obtaining the results for aggregate interference received at each receiver, and its statistical parameters. 6.1. Validity of mathematical model

practical models, though not within the scope of this research, will intuitively lead to better performance than what is achieved with the use of PPP node distribution. Accordingly, we designed an algorithm for implementation of the scheme and verified it. Algorithm 1 describes the pseudo code of the proposed scheme. Subsequently, an ad hoc network was simulated that uses the proposed hybrid MAC.

Validity of mathematical model is always an important concern for the researchers. The mathematical model described in the previous section was developed based on Campbell’s theorem [35]. However, it is known that the Campbell’s theorem is not directly applicable to a system that uses frequency hopping within a zone and direct sequence spread spectrum outside it.

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Fig. 9. Variance of Interference against the path loss exponent for simulation and Campbell’s theorem.

Fig. 10. Nodes in an ad hoc network intelligently choosing frequencies to transmit (3 frequencies).

For validating the mathematical model, we took help from the simulated network. The simulation verifies the closeness between the average and variance of interference calculated through the Campbell theorem, and the statistics obtained through simulation. The correctness of results validates the assumption that even with intelligent hybrid spread spectrum MAC, the network’s spatial statistics closely match the Poisson distribution. Fig. 10 shows the simulated network. The three markers show the three frequencies used for frequency hopping. The nodes depicted with dot markers are the ones facing outages due to lack of availability of a free frequency band. Fig. 11 compares the mean of interference obtained from simulation and that from Campbell’s theorem. It can be observed that the two means match exactly for α ≥ 3. For smaller values of the path loss exponent, the results are optimistic in the sense that simulation shows smaller values for average interference than the mathematical values. The average of interference reduces with increasing values of α . The reason for this is intuitive. As path loss increases, the interfering signal strength reaching the receiver also decreases. Similar results can be observed for variance (see Fig. 9). It can be observed from Figs. 11 and 9 that the simulated results show lesser average interference, as well as lesser variance in inter-

ference, as compared to the mathematical model. Lesser interference obviously leads to better transmission capacity. We also verified the mathematical model by applying the two standard Poisson validity tests [35]. Samples for the two tests were collected over 10,000 realizations. Following from the results shown in Fig. 11 and 9, the value of α was chosen to be 4. The two Poisson tests are as follows: • Uniform, independent and identically distributed active nodes: The probability density function for distance of active transmitters (on a certain frequency) from the origin should be fx (x ) = 2x R . • Spatial distribution of nearby interferers: Pdf of the counting measure of scheduled transmitters (on a certain frequency) in an area, should confirm with the Poisson distribution. Fig. 12 shows the results of two Poisson tests carried out over the simulated network. The analysis verifies that the mathematical model closely matches a Poisson distributed network. It also captures the lower bound on normalized transmission capacity. In practice, the normalized transmission capacity is more than that derived through the system model based on Campbell’s theorem. Also the lower bound is tight for the values of α ≥ 3.

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Fig. 11. Mean of interference vs. the path loss exponent for simulation and Campbell’s theorem.

Fig. 12. The two standard tests for validating the assumption of homogeneous Poisson Point Process. (a) shows the results of the interferers’ distance test while (b) shows the results of the test of counting measure of nearby interferers.

6.2. Effect of mobility Mobility is a determinant of the macroscopic dynamics of the channel environment. Mobility causes variation in distances, which causes a fluctuation in path gains [40]. It also results in an alteration of the spatial distribution of the nodes, which may cause violation of the dictates of the medium access control within the channel access time. Mobility plays an important role in determining the node geometry and performance of any MAC scheme. It is known that with random mobility [41], the distribution and statistical measures of the Poisson Point Process are not altered. This

is because each time interval is another realization of the Poisson Point Process. Other mobility models, like those having temporal or spatial dependencies, or geographic restrictions, [42] may alter the node geometry of the network [41]. Our aim, within the scope of this paper, is to develop a clean baseline model for analysing the transmission capacity of the network, with the use of the proposed IHSS MAC. Therefore, we have selected the basic mobility model which does not alter the node geometry statistics, namely , such the Random Walk Model, for the analysis. In the Ransom Walk Mobility model, each interferer picks a direction of movement randomly and independently, such that  ∈ [0,

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Fig. 13. IHSS with mobility.

2π ]. The interferers move in this this direction for the whole time period during which the reference pair is communicating. All the nodes move at a speed of 72 km/h. This value was selected as a realistic or usual value for vehicular speeds. In practical world, most nodes, except vehicles on a highway, will be moving at much slower speeds, causing much lesser variation in the channel environment. Poisson Point Process and the random mobility model represent the worst case model for node distribution and channel variation. In a more practical node layout and mobility model, the resulting outage probability will be lesser than what is achieved by the use of these impractical models. Consequently, the transmission capacity calculated here is the lower bound on the performance of the IHSS MAC. Since the design of IHSS is based on the baseline IEEE 802.11 specifications, the parameters used for simulation are the same as defined in IEEE 802.11. The maximum channel occupancy time allowed in IEEE 802.11 is 32.767 ms. Larger MAC frames lead to larger probability of collision and outage. The maximum size of the frame, as specified by IEEE 802.11 is 1500 bytes excluding the header and trailer overhead. With a data rate of 1 Mbps, only two frames of this size can be transmitted at a stretch within the maximum allowed channel occupancy time. Up to seven frames of 500 bytes can be transmitted consecutively within the same time. A violation of the MAC dictates can occur if a transmitter node, enters the frequency hopping zone of another active receiver. An outage can occur if the interfering node that enters the frequency hopping zone is using the same hopping sequence that is being used by the active receiver. Fig. 13 shows the performance comparison of IHSS if the nodes in the network are static or mobile. It can be observed that mobility causes negligible deterioration in IHSS’s performance. As MDS increases, the supportable node density also increases. In such a situation, there are more nodes lying on or near the boundary of the frequency hopping zone. This results is greater chances that interferers using the same hopping sequence can come inside the FH zone. However, at the same time, this must be noted that in practice, a larger MDS means a smaller critical radius, and better interference averaging. Therefore, the probability that the interfering nodes entering the FH zone will cause an outage is much lesser.

The reason for negligible effect of mobility on the performance of IHSS is also dependent on a simple game of numbers. In the maximum channel occupancy time, at the average vehicular speed of 72 km/h, the maximum distance that can be moved by an interferer is 0.66 m. This is a very small distance when considered in reference to the node spacings in a network. On top of this, the distance moved is halved for maximum frame size and is only 0.094 m for an average frame size of 500 bytes. 7. Conclusion and future work The proposed IHSS MAC scheme shows clear advantage in terms of transmission capacity, normalized by the required spectrum, over ALOHA and Guard Zone based spread spectrum MAC protocols, especially for small spreading gains. The minimum size of the frequency hopping zone is defined as the range within which the presence of any non-orthogonalised interferer can cause an outage. However, it was observed that this is not the optimum size of the frequency hopping zone. Normalized transmission capacity increases significantly by a small increase in the size of the frequency hopping zone. The constraint of performing the intelligent frequency hopping locally, within a certain frequency hopping zone less than the maximum transmission range, ensures easy coordination and implementation. Finding the most optimum size of the frequency hopping zone requires optimization over all possible spreading gains. This is left out of scope of this paper and a future goal of the research. IHSS is simple to implement and can be used for distributed scheduling in ad hoc networks. In future, we will also endeavour to relax the assumption of fixed transmission distances and fixed transmission power to variable ones. Comparison of the proposed IHSS MAC with the existing hybrid spread spectrum modulation techniques requires extensive problem formulation and analysis. Specifically, the analysis of outage probability through bit error rate needs analysis in specific environments and network parameters needs to be carried out. This can be an interesting area to explore in future research. Such a study will be a step forward in cross layer analysis and impact of the performance of one layer over a higher layer.

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