Digital pulse interval modulation for IR communication systems*a review

Transcription

1 INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS Int. J. Commun. Syst. 2000; 13:519}536 Digital pulse interval modulation for IR communication systems*a review Z. Ghassemlooy* and A. R. Hayes Optical Communications Research Group, School of Engineering, Shezeld Hallam University, City Campus, Pond Street, Shezeld S1 1WB, U.K. SUMMARY This paper presents a brief review of infrared communications systems, modulation techniques and in particular, a digital pulse modulation scheme known as digital pulse interval modulation (DPIM) for infrared (IR) communication systems employing intensity modulation with direct detection (IM/DD). DPIM code characteristics, power spectral density and error probability in terms of the packet error rate are discussed. Performance comparison is made with that of on}o! keying (OOK) and pulse position modulation (PPM). For comparison, relevant expressions for both OOK and PPM are also presented. Using a threshold-detector-based receiver, we show that DPIM outperforms both OOK and PPM in terms of power e$ciency and PPM in terms of bandwidth e$ciency, by taking advantage of its inherent variable symbol duration. However, using a maximum-a posteriori (MAP) detector it provides marginally inferior error rate performance compared with PPM. Copyright 2000 John Wiley & Sons, Ltd. KEY WORDS: optical communications; digital modulation; pulse modulation; infrared communications; optical wireless 1. INTRODUCTION Constraints associated with radio wireless network such as: congested and regulated frequency spectrum, limited bandwidth, and interference with other products, etc. have provided the motivation to look at other means of achieving high-speed wireless connectivity for indoor LAN applications. Infrared (IR) is one such alternative, which was "rst proposed for indoors optical wireless communications in 1979 [1]. Compared with radio frequency, the optical signal carrier considered for wireless communication does not fall under the FCC regulation (FCC regulations apply for radio frequencies within the range of 10 khz}300 GHz) and there is no interference with the electromagnetic spectrum. Since the optical power is con"ned to the room where it is generated, then there is no interference with similar systems operating next door. It o!ers a potentially huge bandwidth, which is unregulated worldwide, and is capable of supporting the high data rates demanded by future multi-media applications. The comparison between radio and infrared for indoors wireless communications is shown in Table I [2]. * Correspondence to: Z. Ghassemlooy, Optical Communications Research Group, School of Engineering, She$eld Hallam University, City Campus, Pond Street, She$eld S1 1WB, U.K. z.f.ghassemlooy@shu.ac.uk Copyright 2000 John Wiley & Sons, Ltd.

2 520 Z. GHASSEMLOOY AND A. R. HAYES Table I. Comparison between radio and intensity modulated/direct detection infrared for indoor wireless communications. Property Radio Infrared Implication for infrared Bandwidth regulated? Yes No Approval not required World-wide compatibility Passes through walls? Yes No Inherently secure Carrier reuse in adjacent rooms Multipath fading? Yes No Simple link design Multipath dispersion Yes Yes Problematic at high data rates Path loss High High Dominant noise Other users Background light Short range Average power proportional to f (t) dt f (t)dt f(t) is the input signal with high peak-average ratio The unregulated optical spectrum allows manufacturers to design a truly global product without the worries of facing regulations, which di!er from country to country. Infrared has a similar behaviour to that of visible light. It is absorbed by dark objects, di!usely re#ected by light-coloured objects and directionally re#ected from shiny surfaces. It can penetrate through glass but not through walls, which means that the same optical carrier can be reused in an adjacent room without interference. For both radio and IR, multipath propagation causes the received electric "eld to undergo severe amplitude fades on the scale of a wavelength. In the former this is the case since the detector used at the receiver is small compared with the transmission wavelength [3]. However, most single-element detectors used for IR applications have an area of &1cm and operate at 850 nm wavelength. Therefore, the relative size of the detector is huge compared to the wavelength, thus preventing multipath fading. Although multipath fading is mitigated in infrared systems, multipath propagation does lead to dispersion, which gives rise to inter-symbol interference in high-speed systems. For a particular IR system, the degree of multipath is complex to predict, and depends on many parameters such as room geometry, materials, the position of the transmitter, receiver and objects within the room, and system design. IR transceivers usually operate in the presence of ambient light, which has signi"cant power at IR wavelengths. Even when optical "ltering is used in the receiver to reject some of the out of band ambient light, the resulting DC photocurrent gives rise to shot noise which is the dominant noise source in a well-designed receiver [2]. As for radio-frequency systems, interference caused by other users is the dominant noise source. The shot noise, path loss and dispersion associated with di!use infrared systems drive the requirement for transceivers to have relatively high optical transmit powers. However, the average optical power emitted by an infrared transceiver is limited by eye safety regulations. Furthermore, electrical power consumption must be kept to a minimum in battery-powered portable devices, which is another constraining factor. Therefore, it follows that the use of a power e$cient modulation scheme would be most desirable, in order to maximize the peak to average power level. Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

3 DIGITAL PULSE INTERVAL MODULATION 521 This paper is organized as follows: classi"cation of IR links is presented in Section 2, followed by standards and eye safety in Section 3. Section 4 is devoted to the optical wireless channel, whereas modulation schemes is introduced in Section 5. DPIM, its properties and performance are presented in Section 6. Finally, concluding remarks are given in Section CLASSIFICATION OF INFRARED LINKS Figure 1 illustrates classi"cation of IR links [2]. Directed links maximizes power e$ciency by using directional transmitters and receivers, but must be aimed in order to establish a link. Non-directed links employ wide-angle transmitters and receivers, removing the need for pointing and, thus, making them more convenient. Line-of-sight (LOS) systems rely on an uninterrupted line of sight path between the transmitter and the receiver, whereas non-los systems rely on the re#ection of light from the ceiling and walls of the room. The former is capable of delivering capacities up to 1 GB/s, provided the cell diameters are small ((1 m) [1]. Non-LOS link design increases link robustness and ease of use, allowing the link to operate even if there is an obstacle standing between the transmitter and receiver. However, the greatest robustness and ease of use are achieved by the non-directed-non- LOS design, referred to as a di!use system (DS), originally proposed by Gfeller and Bapst [1]. In DS scheme reception is non-directional since the photodiode has a wide "eld of view (FOV). Hence, there is no direct line of sight required between transmitter and receiver, and the optical transmission is very insensitive to interruption. A DS manufactured by Spectrix [4] composed of a single base station, employing LEDs, is capable of delivering 4 MB/s to a number of users within a m size room. A 50 MB/s experimental system has also been reported [4]. Directivity of the light source and the photodetector is a very important parameter in nondirective optical communication. Wide FOV is highly desirable for a robust system. The FOV can be enlarged either by using a di!usion lens or by using an array of LEDs together with an array of photodetectors. Figure 1. Classi"cation of infrared links. Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

4 522 Z. GHASSEMLOOY AND A. R. HAYES 3. STANDARDS AND EYE SAFETY There are several &Infrared Data Association' (IrDA) [5] standards in existence today, covering a wide range of bit rates from 9.6 kb/s to 4MB/s. However, all links require a LOS and are only speci"ed to work over a 1 m range. All IR serial ports found on laptop and palmtop computers are IrDA compliant. IR serial ports are now also found on some digital cameras, personal digital assistants and mobile phones. For IR LANs there exists the IEEE standard, which speci"es three physical layers, two using radio with spread spectrum modulation and one using IR. The IR physical layer speci"es optical signals in the 780}950 nm wavelength range, and bit rates of 1 or 2 MB/s using di!use propagation [6]. However, radiation in this wavelength can be focussed onto the retina, causing thermal damage. Therefore, IR transceivers must conform to inherently safe class 1 of the IEC 825 standard. The eye safety limit is a function of the viewing time, wavelength and apparent size of the optical source. The standard makes a distinction between point sources (which the eye can focus) and large area sources, which form an extended image on the retina. The standard treats laser and LED sources equally. For modulated optical sources, generally, the average power level limits the transmitted optical power. In general, the average power for a pulse train of duration 100 s must not exceed the power of a single pulse of duration 100 s [7]. Table II shows the Class 1 power limits for both point and extended sources for a number of important wavelengths [8]. 4. THE OPTICAL WIRELESS CHANNEL In non-line-of-sight applications, coherent optical communication, in which the frequency or phase of the optical carrier is mixed with light from a laser local to the receiver, is not possible since the received signal will be spatially incoherent. For IR wireless links, the most viable method is to employ intensity modulation (IM), in which the instantaneous power of the optical carrier is modulated by the signal. The receiver makes use of direct detection (DD), where a photodetector generates a current, which is proportional to the instantaneous received optical power. The IR channel using IM/DD may be modelled as a baseband linear system as illustrated in Figure 2, with instantaneous input optical power x(t), output current y(t), an impulse response of the channel h(t), and photodiode responsivity R [2]. IR links usually operate in environments containing an intense amount of ambient light, emanating from both natural and arti"cial sources. The average combined power of all the background light sources results in shot noise, Table II. Class 1 source maximum permissible exposure (MPE) power limits [8]. Wavelength Point source MPE Extended source MPE (α(α "0.011 rad, (α'α "0.1 rad, exposure time '1 s) exposure time '1 s) 850 nm 0.44 mw 0.8(α /α )mw 980 nm 0.8 mw 0.8(α /α )mw Notes: α is the angle subtended by the source at measurement point [8]. MPE is equal to power captured by 50 mm diameter aperture 100 mm from the optical detector. Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

5 DIGITAL PULSE INTERVAL MODULATION 523 Figure 2. IR channel model. which is the dominant noise source in typical infrared receivers. The shot noise, n(t), is accurately modelled as white, Gaussian and independent of the received signal. The IR channel di!ers from the conventional Gaussian-noise channel, since x(t) represents power rather than amplitude. This leads to two constraints on the transmitted signal: (i) x(t) must be non-negative and (ii) the average value of x(t) must not exceed a speci"ed value P *lim ¹PR 1/2¹ x(t)dt. In contrast to the conventional channels, where signal-to-noise ratio (SNR) is proportional to the power, in IR systems the received power and the variance of the shot noise are is proportional to the detector area A and A, respectively. Thus, the SNR is proportional to A which implies that system may be operated at a low-power level but using large area detectors. However, as A increases so does its capacitance, which has a limiting e!ect on the receiver bandwidth. There are three main sources of ambient light: sunlight, incandescent and #uorescent lamps, all of which emit relatively high-power levels at the desired IR wavelength, as shown in Figure 3 [3]. Optical "ltering may be employed to reject out of band light sources, but the level of ambient light is still much higher than the received signal power (typically 25 db). Sunlight represents an un-modulated light source with a broad spectral width and a maximum power spectral density (PSD) located at&0.5 μm, producing a DC photocurrent. Incandescent lamps are modulated at 100 Hz from the main supply, with a maximum PSD &1 μm, but their slow response time means that few higher harmonics are present. Fluorescent lamps (FLs) come in two varieties: (i) those driven by the mains frequency with spectral signature containing harmonics into the tens of khz and (ii) energy e$cient high-frequency electronic ballasts with switching frequencies in the 20}40 khz range and an spectral signature containing harmonics into the MHz range. FLs sources not only contribute to shot noise, but also produce a periodic interference signal at the receiver. Therefore, to minimize the e!ect of noise and interference optical or electrical "ltering, modulation techniques, or a combination of these can be used. 5. MODULATION SCHEMES At low frequencies, generally below 100 khz, noise and interference from ambient light dominates receiver performance. For this reason, base-band data transmission is not considered adequate to ensure stable signal transmission. Therefore, modulation of some kind needs to be employed in order to shift the spectrum beyond a few hundred Hertz. There are many di!erent types of modulation schemes, which are suitable for IR communication systems each with its own advantages and disadvantages. Since the average optical power emitted by an IR transceiver is limited, the performance of modulation techniques is compared in terms of the average received optical power required to achieve a desired bit error rate at a given data rate. As mentioned Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

6 524 Z. GHASSEMLOOY AND A. R. HAYES Figure 3. Optical power spectrum of common ambient infrared sources. earlier, coherent-based systems are not a viable option, therefore, this leaves only one other alternative, which is based on some form of intensity modulation scheme with direct detection (IM/DD) [2] OOK Of all the various modulation schemes for IM/DD, OOK is the simplest, in which a zero and one are represented by zero intensity and some positive intensity, respectively. OOK can use either non-return-to-zero (NRZ) or return-to-zero (RZ) pulses. With OOK-RZ, the pulse duration is lower than the bit duration, giving an improvement in power e$ciency over OOK-NRZ at the expense of an increased bandwidth requirement. The detailed performance analysis of OOK on AWGN channel can be found in References [2,3,9,10]. OOK has found use in commercial IR systems such as IrDA links operating below 4 MB/s. In these links, return-to-zero-inverted (RZI) signalling is used, in which a pulse represents a zero rather than a one. At bit rates)115.2 kb/s, the pulse duration is nominally 3/16 of the bit duration, whereas, for data rate of 576 kb/s and MB/s the pulse duration is nominally of the bit duration [11] PPM OOK keying is unable to provide the power e$ciency required by many optical wireless applications. But there are alternative modulation schemes, better known as pulse modulation techniques, see Figure 4, which o!er an improvement in power e$ciency at the cost of relatively poor bandwidth e$ciency. One such a technique is known as pulse position modulation (PPM), in which M data bits are mapped to one of possible symbols, where "2 (see Figure 5). Each symbol consists of a pulse occupying one slot and!1 empty slots. The information is encoded by the position of the pulse within the symbol. By increasing the number of bits per symbol the power e$ciency of the code is improved at the expense of bandwidth e$ciency. PPM has been used widely in IR communication systems and is adopted for the IEEE infrared physical layer standard [6]. It is also used in IrDA serial data links operating at 4 MB/s [11]. There are Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

7 DIGITAL PULSE INTERVAL MODULATION 525 Figure 4. Modulation tree. Figure 5. OOK, PPM and DPIM coding schemes. several types of PPM, such as di!erential PPM, multiple PPM and overlapping PPM. In addition to these, coded schemes such as convolutional-coded PPM and trellis-coded overlapping PPM also exists each with their own advantages and disadvantages as outlined in References [12,13]. Compared with OOK, PPM does increase system complexity since both slot and symbol synchronization are required in the receiver. There exists an alternative modulation scheme known as DPIM, which o!ers an improvement in terms of bandwidth e$ciency compared with PPM, and power e$ciency compared with both PPM and OOK. Furthermore, it also o!ers simpli"ed receiver design since DPIM does not require symbol synchronization. The following section outlines the code properties, spectral characteristics and error probability performance of DPIM and the results obtained are compared with those of PPM and OOK. Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

8 526 Z. GHASSEMLOOY AND A. R. HAYES 6. DPIM In each PPM symbol, the empty slots following a pulse are essentially redundant, and it is this redundancy which is removed when adopting digital pulse interval modulation (DPIM). In DPIM, information is encoded by varying the number of empty slots between adjacent pulses [14]. As with -PPM, -DPIM maps each block of M"log input bits to one of possible symbols (see Figure 5). Unlike -PPM however, symbol durations are variable and determined by the information content of each particular symbol. In order to avoid symbols, which have no slots between adjacent pulses, a guard slot may be added to each symbol immediately following the pulse. Thus, each symbol consists of a pulse of constant power with duration)one slot, followed by k slots of zero power, where 1)k). This may be expressed as S (t)" n¹ P, )t((n#1)¹ (1) 0, (n#1)¹ )t((n#k#1)¹ where ¹ is the slot duration. The minimum and maximum symbol duration are 2¹ and ( #1) ¹, respectively. In -PPM each symbol has a "xed duty cycle of 1/, whereas in -DPIM symbols have a variable duty cycle, the average of which is higher than 1/. Consequently, for a "xed value of, DPIM has a higher average power requirement compared with PPM. In -PPM, the slot rate is given as R " R /M, where R is the OOK bit rate. In -DPIM, there are two options for the slot rate, as discussed in the following sections L-DPIM A The slot rate may be chosen such that the average symbol duration is equal to the time taken to transmit the same number of bits using OOK/ -PPM. This is denoted as -DPIM. Thus, the slot rate is given as R R /M, where "( #3)/2 which includes a guard slot. This " achieves the same average data rate as OOK/ -PPM, but requires only approximately half the bandwidth (see Figure 6). As an example, if the bandwidth, =, required to support a data rate of R using OOK-NRZ is R, then for 16-PPM, ="4R whereas for the same average data rate, 16-DPIM has a bandwidth requirement of =+2.4R L-DPIM M Alternatively, the slot rate may be chosen such that the maximum symbol duration is equal to the time taken to transmit the same number of bits using OOK/ -PPM. This is denoted as -DPIM. In this case the slot rate and average data rate are given as R "( #1)R /M and R "( #1)R, respectively [15]. The average data rate and bandwidth requirement of / -DPIM relative to OOK/ -PPM are shown in Figure 6. As increases, the average data rate approaches twice that of OOK/ -PPM. Intuitively, this must be the case since the average symbol length of -DPIM is approximately half that of OOK/ -PPM. This can be used to improve the power e$ciency of DPIM since an extra bit per symbol can be encoded without increasing the slot rate or reducing the average data rate. Note that, compared with -PPM, -DPIM requires a slight increase in bandwidth by a factor of ( #1)/ in order to Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

9 DIGITAL PULSE INTERVAL MODULATION 527 Figure 6. Normalized average data rate and normalized bandwidth requirement versus number of bits per symbol. accommodate the additional guard slot. For the remainder of this paper, unless otherwise stated, the DPIM option used is assumed to be DPIM Spectral properties A DPIM pulse train may be expressed as [14] x(t)" a p(t!n¹ ) (2) where p(t) is the rectangular pulse shape, ¹ is the slot duration and a is a set of random variables that represent the presence or absence of a pulse in the nth time slot. It can be shown that the sequence x(t) is a cyclostationary process [16] and following the method outlined in Reference [17], its PSD may be calculated using S( f )" 1 ¹ P ( f ) S ( f ) (3) where P( f )"¹ sin (π f ¹ )/π f ¹ is the Fourier transform of the pulse shape, and S ( f ) is the PSD of the slot sequence. Assuming that the slot sequence is uncorrelated, the slot autocorrelation function was expressed as [14]: R(k)" σ #m, k"0 m, ko0 (4) where m and σ are the mean and variance of the slot sequence, respectively. However, this assumption does not give accurate results for the PSD close to DC. Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

10 528 Z. GHASSEMLOOY AND A. R. HAYES Instead R(k) was derived theoretically and is given as [18] R ", k"0 0, k"1 1#4 1#1#4 2! 1!1#4 2, 2)k) #1 1 R, k' #1 (5) As one may expect, R approaches as k increases. It is found that for k'5, R can be approximated as with a good degree of accuracy. Since the mean value of the slot sequence is non-zero, the spectrum may also contain delta functions. However, as we are considering rectangular pulses, which occupy the whole slot, the nulls of P ( f ) cancel out the delta functions, except at DC. The continuous component of S ( f ), S ( f ), is given as [17] S ( f ): (R! )e (6) Figure 7 shows the PSD for 8-DPIM, assuming a rectangular pulse shape is used. Also shown for comparison is the PSD for OOK and -PPM (the expressions for PSD for -PPM and OOK are Figure 7. PSD for OOK-NRZ, 8-DPIM and 8-PPM (all curves represent the same average transmitted optical power and assume a rectangular pulse shape is used). Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

11 DIGITAL PULSE INTERVAL MODULATION 529 given in the appendix). The ripples in the spectral pro"le of DPIM are due to the discrete-time Fourier transform of the slot autocorrelation function. Unlike - PPM, DPIM has a non-zero DC component, but this is small compared with that of OOK. By observing the null positions of the PSD, the increased bandwidth e$ciency of DPIM is evident. The bandwidth requirement of 8-DPIM is only &1.8 times that of OOK, whereas 8-PPM requires &2.7 times as much bandwidth to achieve the same data rate Error performance A typical optical wireless communication system model based on threshold detection is illustrated in Figure 8. Following a similar approach adopted by Moreira et al. [9] the following assumptions are made: (i) distortion-free channel, (ii) no bandwidth limitations imposed by both the transmitter and receiver, (iii) dominant noise source is the background light level, (iv) no interference due to arti"cial light source and (v) an error in any slot of the packet will invalidate the entire packet. In the following sections, the error performance analysis for DPIM is presented and results are compared with OOK and -PPM. However, before this, for the purpose of comparison, the error performance analysis for OOK and -PPM are brie#y discussed OOK. Assuming an average received optical signal power of P, and a photodetector responsivity of R, in the absence of noise, the peak output of a unit energy matched "lter when transmitting &0' and &1' will be 0 and 2RP ¹, respectively. Assuming equally likely ones and zeros, the optimum threshold level, which minimizes the probability of error, lies midway between these two levels. In the presence of additive white Gaussian noise (AWGN) with double-sided power spectral density η /2, for OOK the probability of bit error (BER) is given as P "Q(2RP /N ) (7) where the average energy per bit E "2RP ¹, and noise power N "R η. The BER versus SNR for OOK-NRZ is shown in Figure 9. Also shown for comparison, is the BER for OOK-RZ for di!erent values of duty cycles γ. Note that the electrical SNR is de"ned in terms of average electrical power, i.e. SNR"RP /N, which is half the actual SNR for OOK- NRZ, 1/4 the SNR for OOK-RZ (γ"0.5) and 1/8 the SNR for OOK-RZ (γ"0.25). To achieve the same BER performance as OOK-RZ with 50 and 25 per cent duty cycles, OOK-NRZ requires additional 3 and 6 db SNR, respectively. Although OOK is the simplest scheme, it lacks power e$ciency compared with PPM and DPIM. Figure 8. A typical IR system block diagram employing threshold detector for binary IM/DD schemes (for OOK, -PPM and -DPIM Z OOK "RP, for -PPM, Z - "LRP, Z - " RP, respectively. Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

12 530 Z. GHASSEMLOOY AND A. R. HAYES Figure. 9. Bit-error rate versus electrical SNR for OOK-NRZ and OOK-RZ (γ"0.5 and 0.25) and for 8-PPM using a threshold detector PPM. In the absence of noise, the peak output of the unit energy matched "lter when a pulse is transmitted will be RP M¹, and for empty slots the output will be &0'. Since the probability of receiving a &1' is less than the probability of receiving a &0', then the optimum threshold level α, does not lie midway between one and zero levels. It is a complex function dependent on and the distribution of ones and zeros. In the presence of AWGN with double-sided PSD η /2, the probability of slot error for -ppm is given as P - "(!1) Q α η /2 #1 Q E!α η /2 (8) where E " RP ¹ M is the energy of a pulse. Setting the threshold level midway between one and zero levels, (8) reduces to P - "Q(E /2η ) (9) The average energy per bit E "E /log. As each symbol contains slots, the probability of symbol error P - "1!(1!P - ). If we consider all symbols to be equally likely, then the probability of symbol error may be converted into a corresponding bit-error rate by the following [19] P - "[ /2(!1)]P - (10) Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

13 DIGITAL PULSE INTERVAL MODULATION 531 Figure 9 shows a plot of BER versus electrical SNR for 8-PPM for two threshold level settings, where there is very little di!erence in performance between PPM with optimum and midway threshold levels. For a given BER the 8-PPM requires &8, &4.5 and &2 db lower SNR compared with OOK-NRZ, OOK-RZ (γ"0.5) and OOK-RZ (γ"0.25), respectively. A further 3 db improvement in SNR can be achieved if soft decision decoding is used instead of threshold detection [19] DPIM. In DPIM, the pulses de"ne the symbol boundaries and hence, an error is not con"ned to the symbol in which the error occurs. Consider a packet of data encoded using DPIM. A pulse detected in the wrong slot would a!ect both symbols either side of the pulse, but would have no in#uence on the remaining symbols in the packet. A pulse not detected would combine two symbols into one longer length symbol, and conversely, detecting an additional pulse would split one symbol into two shorter length symbols. Both these errors would result in a shift of the remaining symbols in the packet. Thus, it is clear that the conversion given in (10) is inaccurate for DPIM. In order to compare the performance of DPIM with other modulation schemes, we base our analysis on the packet error rate (PER). A packet is considered to be in error if one or more of the symbols within the packet are in error. This may be expressed as P "1! (1!P SE ) (11) where P is the probability of packet error, > is the number of symbols in the packet and P SE is the probability that the nth symbol is in error. At the receiver (see Figure 8), in the absence of noise, the peak output of a unit energy matched "lter when a pulse is transmitted will be RP ¹ M, and for empty slots the output will be zero. The energy of a pulse is given as E - "(RP ) M/R and the average energy per bit is E - "E - /M. Assuming that the threshold level is set at the mean of the expected &one' and &zero', then the packet error rate for N-slot F-bit packet is PER"1!(1!P - )+NP -. In the presence of AWGN with double-sided power spectral density η /2, the probability of slot-error is given as P - "Q(RP M/2N ), where N "R η. Thus, the error probability is PER +NQ(RP M/2N ) (12) Similarly, the error probability for OOK and -PPM packets are given as PER +NQ(RP 2/N ) (13) PER - +NQ(RP M/2N ) (14) As with -PPM, since the probability of receiving a zero P(0)"(!1)/ is greater than the probability of receiving a one P(1)"1/, then the optimum threshold level α does not lie midway between one and zero levels. Therefore, the P e-slot- -DPIM is given as!1) P "( - Q α η /2 # 1 Q E!α η /2 (15) Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

14 532 Z. GHASSEMLOOY AND A. R. HAYES where E"E. Thus, the packet error rate for DPIM is given as - PER - " N! F M Q α η /2 # F M Q E!α η /2 (16) For a simple threshold-detection-based receiver, the PER was calculated for OOK, -PPM and DPIM based on the following parameters: packet length set to 1024 bits, data rate of 1 MB/s and a background power of!10 dbm/cm. Figure 10(a) shows the calculated PER versus average received irradiance for OOK-NRZ, -PPM and -DPIM, for "8 and DPIM has approximately a 5 db power advantage over OOK-NRZ, but requires about 1 db more power than 16-PPM. Figure 10(b) shows the PER for 16-PPM, 16-DPIM, 16-DPIM and 32-DPIM. 16-DPIM is approximately 1.3 db inferior to 16-DPIM, but does give nearly twice the throughput. 32-DPIM is particularly attractive, since it gives approximately 0.6 db power advantage over 16-PPM and has a lower bandwidth requirement. 32-DPIM has an average symbol length of 17.5 slots compared to 16 slots for 16-PPM, but encodes one more bit and Figure 10. PER versus average received irradiance (a) for OOK-NRZ, -PPM and -DPIM (for "8 and 16), and (b) 16-PPM, 16-DPIM, 16-DPIM and 32-DPIM. Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

15 DIGITAL PULSE INTERVAL MODULATION 533 therefore, the slot rate is lower. However, it should be noted that in the absence of inter-symbol interference, the optimum maximum likelihood receiver for -PPM (in which the largest of samples is designated as the slot containing the &one') has been shown to give an improvement in terms of optical power of 1.5 db over a threshold detector-based receiver [9], and hence, this would out perform 32-DPIM. Optical power requirement versus bandwidth requirement is another important system performance indicator. Following Reference [17], the average optical power requirement for -DPIM is normalized to that required by OOK to send 1kB packets at an average packet error rate of 10. For -DPIM with one guard slot, the average power requirement is P - "8/( #3)M P (17) where P "1/R 0.5N Q (PER/N) is the power requirement for OOK. For -DPIM with no guard slot the power requirement would be the same as (17), except for replacing the denominator with ( #1)M. Similarly the normalized power requirement for -PPM can be found to be P - " 2 M P (18) Figure 11 shows the average optical power requirement versus bandwidth requirement for OOK, -PPM and -DPIM (with and without the guard slot). The bandwidth requirement, de"ned as the span from DC to the "rst null in the PSD of the transmitted waveform, is also normalized to OOK. From the plot it can be observed that OOK-RZ (γ"0.5) has a 0.06 db lower power requirement compared with 4-PPM (using a threshold detector) and the same bandwidth requirement. However, to further reduce power e$ciency, it is more e$cient to switch to another modulation technique rather than reduce γ further. To highlight this point, if we compare OOK-RZ (γ"0.33) with 8-PPM (TH), we see that 8-PPM o!ers a 1.4 db reduction in average optical power and requires less bandwidth. For PPM, the MAP detector consistently outperforms optimum threshold detection by approximately 1.5 db. From the graph it is clear that the curve for both DPIM schemes is below that of PPM-MAP. For a normalized bandwidth requirement of 3, DPIM using 1 guard slot has approximately the same power requirement as PPM-MAP and DPIM without a guard slot has a normalized power requirement which is lower by&0.2 db. When considering only threshold detection based receivers, the power e$ciency of DPIM is evident if the performance of 32-DPIM is compared with 16-PPM. 32-DPIM (using one guard slot) has an average power requirement of!6.7 db compared with!6 db for 16-PPM, and requires a slot rate of just 3.5R compared with 4R for 16-PPM. 7. CONCLUSIONS The basic properties and characteristics of DPIM for IR communications systems have been presented. Unlike -PPM, DPIM requires no symbol synchronisation and it o!ers higher transmission capacity, which may be used to improve, both power and bandwidth e$ciencies. The power spectral density of DPIM has been calculated using a new expression for the slot Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

16 534 Z. GHASSEMLOOY AND A. R. HAYES Figure 11. Normalized optical power requirement versus normalized bandwidth requirement for various modulation schemes. autocorrelation function. Detailed analysis for PER performance for a threshold-based receiver has been presented and the results are compared with OOK and -PPM. For a given bandwidth, it o!ers better PER performance compared with both OOK and -PPM. Packet error rate performance becomes marginally inferior compared with -PPM when employing a MAP detector. APPENDIX: POWER SPECTRAL DENSITY The general expression for the power spectral density of a digital signal is [20] F( f ) R(k)" R(k)e j2π¹ ¹ (A1) Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

17 DIGITAL PULSE INTERVAL MODULATION 535 Where F( f ) is the Fourier transform of the pulse shape f (t), and R(k) is the autocorrelation function of the data. The general expression for the autocorrelation function is given as [20] R(k)"a a " (a a ) P (A2) where a and a are the levels of the pulses at the nth and n#kth bit positions, respectively, and P is the probability of getting the product (a a ), with I being the number of possible values for the product a a. Note that the PSD is dependent on only two parameters: the pulse shape used and the statistical properties of the data. Assuming that a one is represented by a pulse of amplitude A and a zero by &0'. If ones and zeroes are equally likely, the autocorrelation function (ACF) R(k)" A for k"0 and R(k)" A for ko0. For rectangular-shaped pulses of duration ¹, F( f )" ¹ sin(π f ¹ )/π f ¹. OOK-NRZ: For OOK-NRZ the power spectral density is given as But the Poisson sum formula states that P ( f )" A¹ 4 sin π f ¹ π f ¹ 1# e e" 1 ¹ δ f! n ¹ Since F ( f )"0 atf"n/¹, no0, PSD can be simpli"ed to (A3) (A4) P ( f )" A¹ 4 sin π f ¹ π f ¹ 1# 1 ¹ δ ( f ) (A5) PPM: Assuming rectangular-shaped pulses, the detected electrical power spectrum of -PPM is given as [21] S(ω)"P(ω) ¹ 1 1!1 #2 ķ!1 cos kω¹ #2π ¹ δ ω!2πk ¹ (A6) REFERENCES 1. Gfeller FR, Bapst U. Wireless in-house data communications via di!used infrared radiation. Proceedings of the IEEE 1979; 67(11):1474} Barry JR. =ireless Infrared Communications, Kluwer Academic Publishers: Boston, Kahn JM, Barry JR. Wireless infrared communications. Proceedings of the IEEE 1997; 85(2):265} SpectrixLit: 5. IrDA URL: 6. IEEE standard for Local Area Networks. IEEE Press: New York, British Standard BS EN : 1994 (derived from IEC 835-1). 8. Street AM, Stavrinou PN, O'Brien DC, Edwards DJ, Tutorial review*indoor optical wireless systems*a review. Optical and Quantum Electronics 1997; 29:349}378. Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536

18 536 Z. GHASSEMLOOY AND A. R. HAYES 9. Moreira AJ, Tavares AM, Valadas RJ, Oliveira Duarte AM. Modulation methods for wireless infrared transmission systems: performance under ambient light noise and interference. Proceedings of SPIE2¹he International Society for Optical Engineering, vol. 2601, Philadelphia, PA, U.S.A., 23}25 October 1995; 226} Audeh MD, Kahn JM. Performance simulation of baseband OOK modulation for wireless infrared LANs at 100 Mb/s. IC=C+92, 1992; 271} IrDA serial infrared physical layer link speci"cation*version Park H, Barry JR. Modulation analysis for wireless infrared communications. IEEE International Conference on Communications, vol. 2. Seattle, WA, U.S.A., 18}22 June 1995; 1182} Park H, Barry JR, John R. Performance analysis and channel capacity for multiple-pulse position modulation on multipath channels. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC, vol. 1. Taipei, Taiwan, 15}18 October 1996; 247} Kaluarachchi ED. Digital pulse interval modulation for optical communication systems. PhD ¹hesis, She$eld Hallam University, U.K., Hayes AR, Ghassemlooy Z, Seed NL. Optical wireless communication using digital pulse interval modulation. Proceedings of SPIE on Optical =ireless Communnications, vol ; 61} Gibson JD. Principles of Digital and Analogue Communications (2nd edn). Macmillan: New York, Shiu D, Kahn JM. Di!erential pulse-position modulation for power-e$cient optical communication. IEEE ¹ransactions on Communications 1999; 47(8):1201} Hayes AR, Ghassemlooy Z, McLaughlin R, Seed NL. Baseline wander e!ects on systems employing digital pulse interval modulation. IEE Proceedings2Optoelectronics, October 1999, submitted for publication. 19. Proakis JG. Digital Communications (3rd edn). McGraw-Hill: New York, Couch LW. Digital and Analogue Communication Systems (5th edn). Prentice-Hall: Engleword Cli!s, NJ, Audeh MD, Kahn JM. Performance evaluation of -pulse-position modulation on non-directed indoor infrared channels. Conference Record2International Conference on Communications, vol. 2. New Orleans, LA, U.S.A., 1}5 May 1994; 660}664. AUTHORS' BIOGRAPHIES Z. Ghassemlooy received his BSc (Hons) degree in Electrical and Electronics Engineering from Manchester Metropolitan University in 1981, and his MSc and PhD from the University of Manchester, Institute of Science and Technology, in 1984 and 1987, respectively. In 1987}88 he worked as a Post-doctoral Research Fellow on optical sensors at the City University, London. He then joined She$eld Hallam University as a Lecturer in 1988, where he is now a Professor of Communication Engineering in the School of Engineering. He is the Group Leader for Communication Engineering and Digital Signal Processing and also heads the Optical Communications Research Group. He is a member of the IEEE Consumer Electronics Society's Publication Review Committee. He is the founder and the Secretary of the International Symposium on Communication Systems, Network and Digital Signal Processing (CSNDSP). He has published extensively and is a co-editor of an IEE book on &Analogue Optical Fibre Communications', special issue of the IEE Proceeding J. 1994, the proceedings of the CSDSP'98 and "rst International Workshop on Materials for Optoelectronics 1995, U.K. His research interests are in the areas of modulation techniques, high-speed optical network systems, optical wireless communications as well as optical "bre sensors. He has published more than 100 papers and is a co-ordinator and joint grant holder for numerous research grants. He is a Chartered Engineer and a member of IEE and IEEE. A. R. Hayes received a BEng (Hons) degree from the University of Hull in From 1993 to 1997 he worked as a design engineer for Pioneer Electronics Technology (U.K.) Ltd. He is now a research student in the School of Engineering at She$eld Hallam University, where he is working towards his PhD on Optical Wireless Communication Systems. He is an associate member of the IEE and a student member of the IEEE. Copyright 2000 John Wiley & Sons, Ltd. Int. J. Commun. Syst. 2000; 13:519}536