- Research Article
- Open Access

# Pulse Interval Modulation for Ultra-High Speed IR-UWB Communications Systems

- Marijan Herceg
^{1}Email author, - Tomislav Švedek
^{1}and - Tomislav Matić
^{1}

**2010**:658451

https://doi.org/10.1155/2010/658451

© Marijan Herceg et al. 2010

**Received:**16 February 2010**Accepted:**21 July 2010**Published:**5 August 2010

## Abstract

This paper analyzes performances of the Pulse Interval Modulation (PIM) scheme for impulse radio ultra-wideband (IR-UWB) communication systems. Due to the PIM anisochronous nature, a tap delay line (TDL) coded division multiple access (CDMA) scheme based on strict optical orthogonal codes (SOOC) is proposed. This scheme is suitable for multiuser high-speed data asynchronous transmission applications because the average symbol length is shorter than in Pulse Position Modulation (PPM) schemes and it needs only chip synchronization. The error probability over the additive white Gaussian noise (AWGN) channel is derived in the single- and multi-user environment and compared with other modulation schemes.

## Keywords

- Additive White Gaussian Noise
- Code Division Multiple Access
- Packet Error Rate
- Additive White Gaussian Noise Channel
- Pulse Amplitude Modulation

## 1. Introduction

Trends in modern communication systems place high demands on low power consumption, high-speed transmission, and anti-interference characteristics. Therefore, impulse radio ultra-wideband (IR-UWB) [1] systems have recently gained increased popularity. Since IR-UWB symbols are transmitted by short pulses ( 2 ns), energy has spread over the frequency bands of up to 10 GHz. These pulses have to follow strict regulations concerning power and spectrum restrictions defined by local authorities, like the Federal Communications Commission (FCC) [2] in the USA. Because of power and spectral properties of the transmitted IR-UWB pulses, different types of orthogonal pulse shapes are used to provide a higher spectral efficiency [3, 4]. Derivation of the Gaussian pulse and modified Hermite pulses (MHPs), usually called Hermites [5], provides a wide range of various pulse combinations for IR-UWB transmission and for that reason they are most commonly used as pulse shapes. The state of art in IR-UWB systems is presented by many applicable modulation techniques like Pulse Amplitude Modulation (PAM), PPM, Pulse Shape Modulation (PSM), on-off-keying (OOK), and biphase modulation (BPM). A combination of the exposed modulation techniques (hybrid techniques) can provide system improvements in terms of the error probability, a higher data rate, a less complex receiver, or less power consumption. Many hybrid techniques for IR-UWB communication systems have been applied recently, such as Pulse Position Amplitude Modulation (PPAM) [6], Biorthogonal Pulse Position Modulation (BPPM) [7], OOK-PSM [8], PPM-PSM [9], and hybrid Shape-Amplitude Modulation [10, 11]. Regarding pulse amplitudes, positions, and shapes, three types of modulations can be distinguished. In PAM and OOK modulation information is contained in the amplitude of the signal, PPM uses the position of the pulse to convey information, whereas in PSM, information is conveyed in the shape of the pulse.

PIM was first introduced in [12] for wireless optical communication systems. It is interesting because it displays a higher transmission capacity by eliminating unused time chips within each symbol and does not require both chip and symbol synchronization, but only chip synchronization, since each symbol is initiated with a pulse. Different anisochronous and synchronous pulse time modulation (PTM) techniques for optical short-range wireless communications are compared in [13].

This paper is organized as follows. Section 2 describes basic properties of the PIM scheme. In Section 3, the proposed system model is described, while in Section 4 error performance analysis is made over the AWGN channel. Section 5 gives simulation results while some conclusions are given in Section 6.

## 2. PIM Scheme Basics

Mappings between source bits and transmitted chips for 4-PPM and 4-PIM (Example).

Source bits | 4-PPM chips | 4-PIM chips |
---|---|---|

00 | 1000 | 1(0) |

01 | 0100 | 1(0)0 |

10 | 0010 | 1(0)00 |

11 | 0001 | 1(0)000 |

## 3. The Proposed System Model

*M*-bit data sequence and then loaded in the latch. Simultaneously with loading, the counter is reset and it starts to count with chip clock frequency. The outputs of the counter and latch are compared, and when outputs match, the comparator goes high which implies starting of the new symbol generation. Then, the new

*M*-bit data sequence is loaded into the latch and the counter is reset/started. The comparator drives the pulse generator which generates a Gaussian monocycle when its input goes high and extra ( ) redundant empty chips are added. After that, the PIM sequence is fed into the TDL encoder. TDL consists of

*w*parallel tap-delay elements, where each element delay is determined by the codeword of the signature sequence. The signature sequence is obtained using an SOOC [15] defined by ( ), where is code length, is code weight, and and are unity auto- and cross-correlation constraints, respectively. The overall transmitted signal of the th user is given as follows:

*k*th user data sequence representing data coded into PIM. Due to the added redundant chips, the overall achievable data rate is decreased, and from (2) it can be written as follows:

where
is the number of users,
is time delay of the *k* th user (assumed to be the integer multiple of
), and
is an AWGN component with zero mean and variance
/2.

At the input of the receiver, is passed through the TDL decoder, where by tuning the delay elements a higher amplitude pulse can be formed by each of the pulses in the signature sequences. The decoded signal is then fed into the correlator-based matched filter which multiplies the signal by the template waveform. The decision which chip is empty and which chip contains a pulse is made on the basis of autocorrelation properties of the Gaussian monocycle at the threshold detector. At the output of the threshold detector, the transmitted PIM data encoded stream is estimated by removing redundant ( ) chips. The pulse at the start of the PIM symbol is then used to load the output of the counter in the latches and to reset the counter.

*N*are the desired PIM sequence, self-interference, interference due to the multi-user interference (MUI), and AWGN interference, respectively, given as follows:

## 4. Error Performance Analysis

- (a)
Channel model is an AWGN channel (no multipath components).

- (b)
MUI is approximated as a Gaussian random variable.

- (c)
There is a perfect synchronization and power control between the transmitter and the receiver.

*N*is the AWGN interference, that is, a Gaussian random variable with zero mean and variance /2 and is the MUI in the

*m*th symbol given as

*M*is the number of bits per symbol. Probability density function (PDF) of is

The decision variable can then be modeled as a Gaussian random variable with mean and variance

*m*th symbol is

*m*th symbol. The probability of one pulse interference in a single chip due to self-interference also has a binomial distribution and it is given from [16] as follows:

*P*( ) or

*B*data bits is considered, then the number of symbols and hence the number of transmitted pulses in a packet is

*B*/

*M*. Assuming that there is no guard slot in the symbol, the average number of empty slots per packet is /(2

*M*)

*.*Therefore, the probability of the packet error is given by

where is the channel bandwidth and is the bit rate defined in (2), (3).

## 5. Simulation Results

*B*= 128. It can be seen that the derived error probability matches simulation results for 4-PIM and 8-PIM, while for 2-PIM there is a slight difference for large .

*B*= 512 bits,

*w*= 1, and PER performance of PIM is obtained using (18), (24), (25) and the results are shown in Figure 6. In the simulation, the number of modulation levels is

*L*= 2, 4, 8. In the case of

*L =*2, PIM has a 6 dB and 3 dB worse performance than 2-PAM and 2-PPM, respectively. With the increase of the modulation level to

*L*= 4, PIM has a 0.8 dB better performance than 4-PAM and 3 dB worse than 4-PPM, while for

*L*= 8 PIM performance is 7 dB better than 8-PAM and 3 dB worse than 8-PPM. Generally, it can be seen that if the modulation level increases, PIM and PPM performance increases while PAM decreases significantly.

*B*= 512 bits,

*w*= 1 and Results are shown in Figure 7. In the simulation the number of modulation levels is

*L*= 2, 4, 8. In the case of

*L =*2, PIM has a 4 dB lower PER than 2-PPM. With the increase of the modulation level to

*L*= 4, 8 PIM performance decreases compared with PPM.

*w*= 10. It can be seen that the optimal threshold is at It results from the fact that in an 8-PIM symbol there is only one chip where a pulse occurs and on average 4.5 empty chips, so the probability that a false pulse will be detected is higher than the probability that a correct pulse will not be detected.

*w*on PER performance for 8-PIM with set to an optimal value. It can be seen that 8-PIM with

*w*= 11 has a slightly better performance than 8-PIM with

*w*= 10, and 2.3 dB better than 8-PIM with

*w*= 9.

*w*= 10 and dB. It can be seen that for the optimal threshold the PER performance improves significantly.

*w*influence on 8-PIM in presence of the MUI for optimal is analyzed and shown in Figure 11. It can be seen that with an increase of code weight, PER is improved, which is a result of more correlated pulses at the receiver. This advantage is at the cost of the data rate shown from (6) in Figure 11.

## 6. Conclusion

This paper proposes an anisochronous PIM scheme for IR-UWB communication systems. The basic principles and characteristics of anisochronous PIM scheme are outlined. Unlike PPM, PIM requires no symbol synchronization, which results in a much simpler receiver structure (only one correlator). The proposed multiple access method based on SOOC-TDL-CDMA allows a totally asynchronous transmission and it needs only chip synchronization which significantly reduces hardware complexity, while classical time-hopping IR-UWB needs both frame and chip synchronization which increase hardware complexity. It is shown that an increase of code weight can decrease PER at the cost of hardware complexity (more delay elements at TDL) and the influence of in both single- and multi-user environment is analyzed. The major disadvantage of anisochronous PIM techniques is that they have a variable symbol length, and hence the time required to transmit a data packet containing a fixed number of bits is not constant. Employing some form of a source coding scheme, packet length variation can be limited still maintaining the increase in information capacity over isochronous modulation techniques. Simpler receiver complexity and very high achievable bit-rates make PIM modulation very attractive for IR-UWB short-range communication systems.

## Authors’ Affiliations

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This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.