**2.1. Impulse Radio Ultra Wideband (IR-UWB)**

IR-UWB is a form of UWB transmission in which data is transmitted using sequences of extremely short pulses with a duration of less than 1ns and a large pulse repetition period (PRP). Due to the extreme short duration of the pulses, IR-UWB is capable of delivering high data rates in the order of several hundred Mbps, but at the expense of reduced transmission range due to the power restrictions.

Inherent to IR-UWB signaling is a high temporal resolution that enables accurate multipath resolution and ranging capabilities. Other interesting features related to the pulsed nature of IR-UWB are its robustness against fading, as well as its low power, low complexity and low cost implementation possibilities. In this respect, IR-UWB is a key technology for providing wireless networks with joint communication and ranging capabilities.

<sup>2</sup> Wireless autonomous networks can be considered as a special subclass of wireless ad hoc and sensor networks with reinforced self-organizing character

This chapter assumes a generic Time-Hopping IR-UWB (TH-UWB) physical layer as described in [21]. Time is divided into frames of length *Tf* and each user transmits one pulse of length *Tp* per frame. Furthermore, by dividing the frames into non-overlapping chips of length *Tc*, multi-access capability is provided. Each user transmits its pulse in a randomly chosen chip, according to a pseudo-random TH sequence (THS). Data modulation follows a pulse position modulation (PPM) scheme. Thus, the signal emitted by the *k*-th TH-PPM transmitter consists of a sequence of pulse waveforms shifted to different times.

$$s^{(k)}(t) = \sum\_{j=-\infty}^{\infty} w\_{lr}(t - jT\_f^{(k)} - c^{(k)}[j]T\_c - \eta b^{(k)}\_{[j]N\_l} - \tau^{(k)}),\tag{1}$$

A typical expression is given in 1, where *wtr*(*t*) represents the transmitted pulse waveform and *Tf* is the average frame time, which is also denoted as the mean pulse repetition period. The inverse of the mean pulse repetition period is referred to as the mean pulse repetition frequency, *Tf* = <sup>1</sup> *pr f* . The expression *b* (*k*) �*j*|*Ns*� represents that each data symbol *<sup>b</sup>*(*k*) can be transmitted by *Ns* identical pulses to enhance the quality of reception. The symbol duration equals then *Ts* = *NsTf* . The TH code value for pulse *j* is given by *c*(*k*)[*j*]. The constant term *η* represents the time shift step introduced by the PPM modulator. Usually, this shift is much smaller than the one due to the TH code (*Tc*). The time shift *τ*(*k*) represents the relative delay time between the instants at which user *k* and a reference user *i* start their transmission; it can be considered as a realization of a random process determined by the actions of the users.

Figure 1 illustrates some of the mentioned parameters; in the example: *Ns* = 1, *c*(*k*) = (2, 3, 4), *b*(*k*) = (1, 1, 0).

**Figure 1.** TH-PPM signal structure.

2 Will-be-set-by-IN-TECH

benefit of IR-UWB over narrowband radio technologies is the possibility to allow concurrent transmissions by using different pseudo-random, time hopping codes (THCs) as a multiple access (MA) method. However, TH codes are not perfectly orthogonal, and even if, Multi User Interference (MUI) is still a challenge due to the presence of multipath fading and the asynchronicity between sources. Beyond it, non-coherent receivers are less robust to MUI than coherent receivers; particularly, interference coming from close-by interferers can be very harmful. Thus, and specially if non-coherent receivers are used, additional interference

This work is motivated by the fact that interference management at the MAC layer has not been extensively explored in the context of IR-UWB autonomous networks yet. The chapter is organized as follows. A general introduction into the field of IR-UWB radio technology and its relevant technical fundamentals is given in section 2. Additionally, a short overview into current research activities and basic principles of MAC protocol design for low to medium data rate IR-UWB networks is given. It follows a discussion about the use of game theory as a tool to model and analyse distributed MAC algorithms in wireless networks. The section

Section 3 introduces distributed Pulse Rate Control (PRC) as a novel approach for interference mitigation in autonomous IR-UWB networks. PRC enables concurrent transmissions at full power, allowing each source to independently adapt its pulse rate - measured in pulses per second (Pps)- to control the impact of pulse collisions at nearby receivers. This section shows that it is possible to incite autonomous users to decrease their impulsive emissions and thus, prevent network resource break-down. Finally, section 4 summarizes the achievements of the

For the understanding of this chapter it is essential to have a good foundation in IR-UWB technology, as well as a general background knowledge of wireless autonomous networks<sup>2</sup> (AN) and game theory. The purpose of this section is to provide a short overview on these three topics. Furthermore, this section describes the scenario and the simulation model used

IR-UWB is a form of UWB transmission in which data is transmitted using sequences of extremely short pulses with a duration of less than 1ns and a large pulse repetition period (PRP). Due to the extreme short duration of the pulses, IR-UWB is capable of delivering high data rates in the order of several hundred Mbps, but at the expense of reduced transmission

Inherent to IR-UWB signaling is a high temporal resolution that enables accurate multipath resolution and ranging capabilities. Other interesting features related to the pulsed nature of IR-UWB are its robustness against fading, as well as its low power, low complexity and low cost implementation possibilities. In this respect, IR-UWB is a key technology for providing

<sup>2</sup> Wireless autonomous networks can be considered as a special subclass of wireless ad hoc and sensor networks with

wireless networks with joint communication and ranging capabilities.

ends with the description of the investigated scenario and the simulation model.

mitigation features at the MAC layer are required.

work presented and gives directions for future research.

**2.1. Impulse Radio Ultra Wideband (IR-UWB)**

**2. Theoretical background**

range due to the power restrictions.

reinforced self-organizing character

in the investigations.

For more detailed information about UWB technology, the author recommends the book [3], which offers an easy-to-read, but complete introduction to the field. Concerning IR-UWB, see [21].

### **2.2. MAC layer design for low power low data rate IR-UWB networks**

The design space for the MAC layer is large; it embraces several dimensions such as multiple access (MA), interference management, resource allocation and power saving. This section summarises the most relevant research findings concerning the design of the MAC layer for low power, low data rate (LDR) IR-UWB networks.

#### 4 Will-be-set-by-IN-TECH 54 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Pulse Rate Control for Low Power and Low Data Rate Ultra Wideband Networks <sup>5</sup>

The unique characteristics of the IR-UWB physical layer provide both challenges and opportunities for the MAC layer design. A concrete challenge is the impossibility of carrier sensing, as practised in narrowband systems, since an IR-UWB signal has no carrier. Great opportunities such as robustness against MUI and multipath fading derive from IR-UWB's high temporal resolution. This makes uncoordinated access to the spectrum possible, provided that the local offered load is low compared with the available system bandwidth. For instance, at moderate pulse rates, the "dead time" between pulses allows several uncoordinated, concurrent transmissions to be time interleaved. As a result, ALOHA emerges as the most straightforward MA approach for low data rate IR-UWB networks [3, 9]. The inherent resilience of IR-UWB to MUI can be further increased if different links employ different pseudo-random THC in order to determine the temporal position of the transmitted pulses. The combination of ALOHA with TH coding leads to Time-Hopping Multiple-Access (THMA) [21], which is the most representative MA scheme for low data rate IR-UWB networks.

**2.3. Basics of game theory**

Game theory has been applied in the recent past to model complex interactions among radio devices that have possibly conflicting interests. For the designer of wireless communication systems game theory is a powerful tool to analyse and predict the behaviour of distributed algorithms and protocols. Respected reference books are [7]. A short overview focusing on the application of game theory in the field of wireless communications can be found in [5]. A resource allocation problem can be naturally modeled as a game, in which the players are the radio devices willing to transmit or receive data. In general, there is an interest conflict since the players have to cope with a limited transmission resource such as power, bandwitdh or pulse load. In order to resolve this conflict they can make certain decisions (or take certain actions) such as changing their transmission parameters. The most familiar game form is the *strategic* form, which models a single-shot, simultaneous interaction among players. It is worth to mention that "simultaneous" is not used here in its strict temporal meaning. It does not imply that players have to choose their actions at the same point of time, but much more that no player is aware of the choice of any other player prior to making his own decision.

Pulse Rate Control for Low Power and Low Data Rate Ultra Wideband Networks 55

• The possible actions that the players can choose. Assume that player *i* can choose among |*Ai*| possible actions (strategies). Then, the set of possible actions of player *i* is **Ai** <sup>=</sup> {*ai*,1, *ai*,2, ..., *ai*,|*Ai*|}, and the game's global action space **<sup>A</sup>** is given by the cartesian product of the action set of each player **<sup>A</sup>** <sup>=</sup> *<sup>A</sup>*<sup>1</sup> <sup>×</sup> *<sup>A</sup>*<sup>2</sup> <sup>×</sup> ... <sup>×</sup> *<sup>A</sup>*|*N*|. If player *<sup>i</sup>* chooses strategy *ai* ∈ **Ai** in a game move, the action profile chosen by all players is denoted as the vector **<sup>a</sup>** = (*a*1, *<sup>a</sup>*2, ..., *<sup>a</sup>*|*N*|)=(*ai*, *<sup>a</sup>*−*i*), with **<sup>a</sup>**−**<sup>i</sup>** = (*a*1, *<sup>a</sup>*2, ..., *ai*−1, *ai*+1, *<sup>a</sup>*|*N*|) representing

• The utility function, which describes the satisfaction level or payoff of player *i* given a certain action profile **a**. The vector of utilities is denoted as **u**(**a**) =

To model asynchronous, continuous interactions as those which characterise resource allocation problems in AN the *strategic* form game model is however insufficient. The author agrees with the opinion advanced in [14] and considers *asynchronous, myopic, repeated* games as the most appropriate game model to analyse those problems. At this point it has to be stressed that the work in [14] provides a key result for the application of game theory in the analysis and modeling of AN, since it formalises the relation between the AN's *steady states* and the game behaviour characterised by the Nash equilibria (NE). Theorem 4.1 in [14] proofs that the *steady states* of an AN modeled by an *asynchronous, myopic, repeated* game with stage game Γ �**N**, **A**, **u**�, where all players are rational and act autonomously, coincide with the Nash

Notice that an NE is a strategy combination **a**∗, where no player can improve his utility by individually deviating from its strategy. The existence of an NE for a game significantly

<sup>6</sup> We use bold capital letters to denote sets and bold small letters for vectors; for the sake of simplicity we have omitted

<sup>A</sup> *strategic* form game <sup>Γ</sup> �**N**, **<sup>A</sup>**, **<sup>u</sup>**� is defined by the following elements6:

• A set of players, **N** = {1, 2, ..., |*N*|} with cardinality |*N*|.

the strategies of all players except of player *i*.

{*u*1(**a**), *<sup>u</sup>*2(**a**), ..., *<sup>u</sup>*|*N*|(**a**)}.

equilibria of the stage game Γ �**N**, **A**, **u**�.

the superscript T for transposed vectors

However TH codes are not perfectly orthogonal, and even if, due to asynchronicity between sources and multipath fading, THMA is still sensitive to impulsive interference. As for CDMA systems, interference coming from a near-by interferer, the so called *near-far* effect, can be very harmful and must be managed in order to avoid performance degradation. For instance, at the physical (PHY) layer multi-user receivers3 can efficiently address the *near-far* effect at the cost of moderate to high additional hardware [19]. At the link layer, based on the estimation of the wireless link quality, it is possible to adapt the transmission rate to the level of interference experienced at the receiver; the goal can be the improvement of the data rate while satisfying a minimum BER requirement [12].

Within the MAC layer the adaptation of transmission parameters corresponds to a resource allocation task. In the technical literature some approaches on THMA resource allocation can be found, for instance in [18]. A broadly accepted result concerns the optimal power allocation in terms of *proportional fairness*4. Note that in autonomous networks with random topology, *proportional fairness* satisfyingly combines fairness and efficiency and outperforms other known performance metrics such as *max-min fairness* or *max total capacity*. This result indicates that the only necessary power control in a IR-UWB network, whose physical layer is in the linear regime5, is the scheduling function 0 <sup>−</sup> *Pmax*. In other words, each node should either transmit with full power or not transmit at all [18]. Another common finding is the existence of an *exclusion region* around every destination such that the reference source and nodes within this area cannot transmit simultaneously. This is similar to the IEEE 802.11 CSMA/CA strategy. Certainly, the *exclusion region* vanishes granted that the system has infinite bandwidth (*W* → ∞). However, in a practical IR-UWB network the bandwidth is always finite and the size of the *exclusion region* may become a critical issue forcing the MAC designer to concentrate on the scheduling task.

It can be concluded that for IR-UWB networks, and when maximizing rates is the design objective, near-far effects should be tackled by combining scheduling and rate adaptation. Particularly, for low power networks the optimal MAC layer design follows an "all at once" scheduling while it adapts the transmission rates to interference [18].

<sup>3</sup> Those which can receive on *M* channels concurrently.

<sup>4</sup> The power allocation that maximises the sum of the log of source rates, which is a concave objective function.

<sup>5</sup> When the rate of a link can be approximated by a linear function of the signal-to-interference-and-noise ratio.
