March, 2003 IEEE P802.15-03/122
IEEE P802.15
Wireless Personal Area Networks
Project / IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs)Title / Data Whitening in Base-band to Reduce PSD of UWB Signals
Date Submitted / 3 March, 2003
Source / [Shaomin Mo]
[Panasonic -- PINTL]
[Two Research Way
Princeton, NJ 08540 ] / Voice: [ 609-734-7592]
Fax: [ 609-987-8827]
E-mail: [
Re: / IEEE P802.15 Alternative PHY Call For Proposals
IEEE P802.15-02/372r8
Abstract / Base-band processing of whitening data to reduce power spectral density of UWB signals in IEEE 802.15.3 systems.
Purpose / Proposal of base-band processing of whitening data to reduce power spectral density of UWB signals in IEEE 802.15.3 systems.
Notice / This document has been prepared to assist the IEEE P802.15. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein.
Release / The contributor acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P802.15.
1 Introduction 3
2 Analysis of Power Spectral Density of Clocked Sequences 4
3 Selective Phase Reversion 10
4 Using Linear Feedback Shift Registers to Generate Random Numbers 13
4.1 Linear Feedback Shift Registers 13
4.2 Proposed Architecture 14
4.2.1 Initial Setting with Randomly Generated Numbers 14
4.2.2 Initial Setting Using Another LFSR 15
4.2.3 Initial Setting Using Two LFSRs 15
4.3 Synchronization of LFSRs 16
4.4 Simulation 17
5 Phase Reversion for SYNC 23
5.1 Phase Reversion on the Whole SYNC 23
5.2 Phase Reversion on Symbols 23
5.3 Symbol-based Phase Reversion and Scrambling 23
6 Conclusion 29
7 References 29
8 Appendix 30
8.1 Symbol-based Phase Reversion 30
8.2 Symbol-based Scrambling 32
1 Introduction
Ultra-wideband (UWB) technology has been used for military applications for some time [1][2]. UWB technology uses base-band pulses of very short duration, thereby spreading the energy of the radio signal very thinly from near zero to several GHz. The techniques for generating UWB signals have been around for more than three decades [3]. A comprehensive reference of early work in this area can be found in a tutorial survey paper [4].
Interest in UWB has broadened, however, since the United States Federal Communications Commission (FCC) announced a ruling on February 14, 2002 that would permit the marketing and operation of certain new types of commercial products incorporating UWB technology. FCC has strongly advocated technologies that can lessen their burden in allocating frequency spectra. UWB is one of their earliest test cases for this policy. They have followed up preliminary ruling of February 14, 2002 with a reaffirmation on February 13, 2003 of their Report and Order [5]. FCC coordinated a public demonstration on UWB technologies on February 13, 2003.
As a consequence, research and development efforts as well as standardization activities have intensified [6]. UWB is now under consideration as an alternative physical layer technology for wireless personal area networking (PAN).
A key motivation for the FCC’s new decision is efficient spectrum use. Because UWB signals can in principle co-exist with other applications in the same spectrum with negligible mutual interference, they require no new spectrum allocation. A basic requirement by the FCC is that UWB systems do not generate interference to other narrowband communication systems operating in the same spectrum. Accordingly, the FCC has specified emission limits in Power Spectral Density (PSD) for UWB applications. Besides the FCC, other agencies still have some reservations about whether UWB will interfere with other wireless applications, air navigation and landing systems. Therefore, the PSD is an important issue and reducing the PSD is an important part in system design.
The use of stochastic theory to evaluate the PSD of ideal synchronous data pulse streams is well documented in the literature [7] [8]. For example, a stochastic approach to characterize the PSD of the Time-Hopping Spread Spectrum signaling scheme in the presence of random timing jitter is given in [7][8]. According to this research, the PSD of UWB signals consists of continuous and discrete components. The continuous component has lower PSD and therefore cause less interference on narrowband communication systems than the discrete component does. Thus, a basic objective in the design of UWB systems is to reduce the discrete component of the UWB power spectrum.
As shown in Section 2, “whitening data” will help to reduce the discrete component of UWB. In
traditional communication systems, scramblers are commonly used for whitening. The main purpose of the whitening is for time recovery and equalization. The scramblers utilize polynomial to randomize data and they are content dependent. Because these scramblers are not designed to reduce PSD, their performance in suppressing PSD is very limited and not sufficient. An extreme example is that when a block of data is repeated for a while, they will generate strong line spectra although inside the block data is scrambled. Therefore, traditional polynomial-based scramblers are not effective and sufficient in suppressing PSD.
Ultra-wideband technology has many potential applications in networking and communications, as well as in radar. In particular, UWB is now under consideration as an alternative physical layer of IEEE 802.15.3. In IEEE 802.15.3, TDMA is used as the access technology. A key design challenge for a UWB TDMA system is to reduce the PSD of the UWB signal while keeping the same channel capacity. In this document, we propose a mechanism of data whitening in the base-band to reduce the PSD of UWB signals used in IEEE 802.15.3.
2 Analysis of Power Spectral Density of Clocked Sequences
In this section, we provide an analysis of the PSD of a clocked random sequence.
Assume that a digitally controlled signal is used to produce random transmissions at multiples of the basic clock period Tc, shown in Figure 1.
Figure 1. Clocked random sequence
This signaling technique is modeled as [7][8]
(1)
where {an} is an unbalanced binary independent identically distributed (i.i.d.) random sequence. It is assumed that {an} is stationary with probability function of
P (2)
According to [9], we have the following expression of PSD in terms of time domain and in terms of frequency domain
(3)
Equation (3) indicates that Es of clocked random sequences is determined by w(t) and Tc, but not affected by Pr{an}. Therefore, the total PSD of clocked random sequences is determined by w(t) and Tc, but not affected by Pr{an}. If we assume that w(t) and Tc are fixed, the middle term in equation (3) becomes constant, so are the Es and the total PSD, the right term in equation (3).
It has been shown [7][8] that the continuous component Sc(f) and the discrete component Sd(f) of the PSD of s(t) are
(4)
Equation (4) indicates that the PSD is determined by three factors, i.e.,
· W(f) – pulse shape and transmission power
· Tc – clock period or pulse rate
· p – distribution of an
(3) and (4) indicate that although distribution of an does not affect the total PSD, but it does affect the PSD, changing p only changes distribution of the PSD between continuous and discrete component, but the total PSD will keep unchanged. In this proposal, we will focus on the relationship between the p and the PSD. To make the analysis simpler and clearer without losing generality, we assume W(f) and Tc are fixed.
Now let us define
(5)
then the expression of Sc(f) and Sd(f) can be simplified to
(6)
and it can be seen that
Based on above results, we can derive the following:
· Sc(f, 0) = 0 and Sd(f, 0) = B(f) when p=0.
In this case, Sd(f) reaches maximum and all PSD goes to the discrete component no matter what waveform is used for pulses;
· Sc(f, 1) = 0 and Sd(f, 1) = B(f) when p=1.
In this case also, Sd(f) reaches maximum and all PSD goes to the discrete component no matter what waveform is used for pulses;
· Sc(f, 0.5) = A(f) and Sd(f, 0.5) = 0 when p=0.5.
In this case, Sc(f) reaches maximum and all PSD goes to the continuous component no matter what waveform is used for pulses.
From the above analysis, we can see that if the total PSD is kept constant, the distribution of the random sequence will determine the distribution of the PSD between the continuous and discrete components.
Now let us look the relationship between A(f) and B(f). Because the total PSD is the same for p=0 and p=0.5, [i.e., S(f, 0) = S(f, 0.5)], we have
(7)
or
(8)
or
(9)
The above equation tells us:
· The total PSD on the left side – continuous component is equal to the total PSD on the right side – discrete component;
· The PSD on the left side is distributed on all frequencies while the PSD on the right side is distributed on those discrete frequencies separated by 1/Tc. This means that the PSD on the left side is more widely distributed than the PSD on the right side;
· Because of above two facts, the magnitude on left side is smaller than the magnitude on the right side.
From the above analyses, we can conclude that objective of a good design for a UWB TDMA system is to reduce or eliminate discrete component of PSD. In our example, we chose p=0.5 and in this case all the PSD goes into continuous component. Because of this analysis, we will focus on how to suppress discrete component of PSD in the rest of this document.
Figure 2 gives the PSDs of clocked random sequences with different probabilities of distribution p. This figure is used to illustrate that different p will change the distribution of the PSD between continuous and discrete component and the discrete component exhibits higher PSD than the continuous component. In this figure, panel (a) is the power spectrum of a single pulse, while panels (b) – (d) are the PSDs of clocked pulse streams with different p in their probability functions. In particular, (b) gives the PSD of p=0.25, (c) of p=0.5 and (d) of p=1.0. It is clear that when p=1.0, only line spectra exist; when p=0.5, only the continuous component exists and when p=0.25, both continuous and discrete components exist. This figure confirms the conclusion derived from formula (4).
In this figure and all simulations in this document, the value of the PSD is nominal because the absolute value of PSD is closely related to RF and pulse rate. However for base-band processing, we are interested only in relative value, i.e., how much in PSD we can reduce.
Figure 3 gives waveforms and PSDs of clocked data that consist of multiple pulses. This figure is used to illustrate that if pulses are not evenly distributed between 1 and –1, line spectra appear. In this figure, (a) and (c) are the waveform and Power Spectrum of single pulses, while (b) and (d) are the waveform and PSD of data with multiple pulses. It is assumed that the data change randomly and independently. However, they are not necessarily distributed evenly, and p is not always equal to 0.5. It can be seen that the data generate both continuous and discrete spectra because p is not always 0.5.
Figure 2. PSD of clocked random sequences with different p
Figure 4 illustrates the problem schematically. In this figure, the X direction represents bits in one block of a TDMA system and the Y direction represents bits with the same offset from the beginning of the block. In traditional communication systems, data streams are randomized by polynomial-based scramblers in the X direction for timing recovery, equalization, etc. As Figure 2-(c) shows, only when pulses are randomly and evenly distributed in Y direction can line frequencies be suppressed. However polynomial-based scramblers are content dependent and cannot guarantee such condition. An extreme example is that when a block of data is repeated for a while, it will generate strong line spectra although inside the block data is scrambled. Therefore, traditional polynomial-based scramblers are not effective and sufficient in suppressing PSD.
In the next section, we will propose a mechanism of selective phase reversion to achieve line spectra suppression.
Figure 3. PSD of a stream of block of data in TDMA systems
Figure 4. Data relationship inside a block and between blocks
3 Selective Phase Reversion
Based on the preceding analysis of the PSD of clocked random sequences, we have proposed the following mechanism of selective phase reversion to eliminate line frequencies [10]:
- Generating a random sequence {bn} with the evenly distributed function of
(10)
- Performing an exclusive OR (XOR) operation on sequences {an} and {bn} to produce a new sequence {cn}. The {cn} is used as the new data for transmission.
Since
(11)
the XOR operation is shown in Table 1.
Table 1. XOR operation
an / bn / cn1 / 1 / -1
1 / -1 / 1
-1 / 1 / 1
-1 / -1 / -1
If the probability functions of {an} and {bn} are
(12)
(13)