advertisement

February, 2016 IEEE P802.15-03/122r1 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 ] Re: IEEE P802.15 Alternative PHY Call For Proposals Voice: [ 609-734-7592] Fax: [ 609-987-8827] E-mail: [[email protected]] 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. Submission Page 1 Shaomin Mo, Panasonic -- PINTL February, 2016 1 2 3 4 5 6 7 8 IEEE P802.15-03/122r1 Introduction ............................................................................................................................. 3 Analysis of Power Spectral Density of Clocked Sequences ................................................... 4 Selective Phase Reversion .................................................................................................... 10 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 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 Conclusion ............................................................................................................................ 29 References ............................................................................................................................. 29 Appendix ............................................................................................................................... 30 8.1 Symbol-based Phase Reversion .................................................................................... 30 8.2 Symbol-based Scrambling ............................................................................................ 32 Submission Page 2 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 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 Submission Page 3 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 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 baseband 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. Tc Tc Tc ... t t+1 t+2 t+3 Figure 1. Clocked random sequence This signaling technique is modeled as [7][8] s (t ) a w(t nT ) n n c (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 an 1 p, P r{a n } 1 p, an 1 (2) According to [9], we have the following expression of PSD in terms of time domain and in terms of frequency domain Submission Page 4 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 N 1 E s w(n) w* (n) n 0 1 2 | W (w) | 2 dw (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 1 | W ( f ) | 2 1 (2 p 1) 2 Tc (2 p 1) 2 l l Sd ( f ) | W ( ) |2 D ( f ) 2 Tc Tc Tc l Sc( f ) (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 1 | W ( f ) |2 Tc 1 l l B( f ) 2 | W ( ) | D ( f ) Tc Tc Tc l A( f ) (5) C ( p) (2 p 1) 2 D( p) 1 (2 p 1) 2 then the expression of Sc(f) and Sd(f) can be simplified to Submission Page 5 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 S c ( f , p) A( f ) D( p) (6) S d ( f , p) B( f )C ( p) and it can be seen that max C ( p ) C (0) C (1) 1 min C ( p ) C (0.5) 0 max D( p ) D(0.5) 1 min D( p ) D(0) D(1) 0 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 A( f ) B( f ) (7) or 1 1 | W ( f ) |2 2 Tc Tc l | W ( Tc ) | l 2 D( f l ) Tc (8) or | W ( f ) |2 Submission 1 l l | W ( ) |2 D ( f ) Tc l Tc Tc Page 6 (9) Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 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. Submission Page 7 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (a): PSD of one pulse (b): PSD of pulses for p=0.25 0 10 -10 0 -20 -10 -30 -20 -40 -30 -50 0 100 200 300 400 -40 0 (c): PSD of pulses for p=0.5 20 0 10 -10 0 -20 -10 -30 -20 0 100 200 300 200 300 400 (d): PSD of pulses for p=1 10 -40 100 400 -30 0 100 200 300 400 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. Submission Page 8 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (a): Waveform of single pulses (b): Waveform of data 1 1 0.5 0.5 0 0 -0.5 -0.5 -1 0 20 40 -1 60 0 (c): PSD of single pulse 20 -20 10 -30 0 -40 -10 -50 -20 0 500 1000 200 300 400 (d): PSD of data -10 -60 100 -30 1500 0 500 1000 1500 Figure 3. PSD of a stream of block of data in TDMA systems bits inside a block X blocks in TDMA frame N frame N+1 frame N+2 frame N+3 offset m Y Figure 4. Data relationship inside a block and between blocks Submission Page 9 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 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]: 1. Generating a random sequence {bn} with the evenly distributed function of 0.5, bn 1 Pr{bn } 0.5, bn 1 (10) 2. 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 c n a n ^b n (11) the XOR operation is shown in Table 1. Table 1. XOR operation an 1 1 -1 -1 bn 1 -1 1 -1 cn -1 1 1 -1 If the probability functions of {an} and {bn} are an 1 p, Pr{a n } 1 p, a n 1 (12) 0.5, bn 1 Pr{bn } 0.5, bn 1 (13) then the probability of {cn} can be obtained as: Pr{cn 1} Pr{a n 1, bn 1} Pr{a n 1, bn 1} (14) Because {an} and {bn} are independent, we can get Submission Page 10 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 Pr{c n 1} Pr{a n 1} Pr{bn 1} Pr{a n 1} Pr{bn 1} p * 0.5 (1 p) * 0.5 (15) 0.5 as well as Pr{c n 1} Pr{a n 1} Pr{bn 1} Pr{a n 1} Pr{bn 1} p * 0.5 (1 p) * 0.5 (16) 0.5 Therefore the probability function of {cn} is 0.5, cn 1 Pr{cn } 0.5, cn 1 (17) Based on analyses presented in Section 2, this method will change a unbalanced sequence into a balanced sequence and all the PSD of the resulting sequence will go to the continuous component of its PSD. We have performed simulations to show that applying the operation proposed in equation (10) and (11) will suppress line spectra and reduce the PSD of multiple pulses shown in Figure 3. The configuration of the simulations is shown in Figure 5. The simulations use Periodogram PSD estimators to calculate the PSD of different UWB signals. In the configuration employed, a pulse is represented by 31 samples followed by 33 samples of zero padding. A bit consists of one pulse and is represented by 64 samples.1 Frame size Tc takes 512 samples. 16384-point FFT is used on 16384 samples to evaluate the PSD. In other words, FFT is on 32 frames and each frame has seven pulses plus zero-padding on the eighth pulse. Because a single estimate usually generates a large bias in estimation and the FCC regulation sets a limit on average PSD, 200 runs are used to smooth the final PSD estimate. The results of this simulation are shown in Figure 6. As in Figure 3, panels (a) and (c) in Figure 6 are the waveform and power spectrum of single pulses, while panels (b) and (d) are the waveform and PSD of the new data cn. 1 Throughout the discussion in the remainder of the document, pulses are represented in the same way. Submission Page 11 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 FFT (16384) frame (512) frame frame pulse (31) 64 Figure 5. Configuration of simulations of selective phase reversion The results indicate that, with this method: Line spectra in data are eliminated; The peak value of PSD is reduced from about from 19 dB in Figure 3-(d) to 9 dB in panel (d); and The shape of the PSD of the new data, shown in Figure 6-(d) is very close to that of the pulse used, shown in Figure 6-(c). The proposed phase reversion can effectively reduce PSD. Phase reversion can also be used in PPM, PAM and Time-Hopping to suppress line spectra. From the analysis and simulation presented thus far, we can see that a random sequence generator is required in order to effectively eliminate line spectra and achieve good performance, or p=0.5. The simulation shown in Figure 6 used a MATLAB function for random number generation. Although this function has good performance, it is not suitable for real implementation because addition, multiplication and division are involved to generate a random number. Another issue in implementation is synchronization of random number generators in transmitters and receivers. Thus two key challenges for the design of a random number generator are simplicity of implementation and ease of synchronization. In the remainder of this paper, we describe a mechanism that is effective in suppressing the PSD of UWB signals and meets both of these design challenges, beginning with an architecture in which Linear Feedback Shift Registers (LFSRs) are integrated with the mechanisms described above to generate random numbers. Submission Page 12 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (a): Waveform of single pulses (b): Waveform of data 1 1 0.5 0.5 0 0 -0.5 -0.5 -1 0 20 40 -1 60 0 (c): PSD of single pulse 10 -20 0 -30 -10 -40 -20 -50 -30 0 500 1000 200 300 400 (d): PSD of data -10 -60 100 -40 1500 0 500 1000 1500 Figure 6. Simulation results of selective phase reversion 4 Using Linear Feedback Shift Registers to Generate Random Numbers In this section, we propose an architecture in which Linear Feedback Shift Registers (LFSRs) are integrated with the mechanisms proposed in Section 3 for generating random numbers. 4.1 Linear Feedback Shift Registers LFSRs sequence through (2n – 1) states, where n is the number of registers in the LFSR. At each clock edge, the contents of the registers are shifted right by one position. There is feedback from predefined registers to the leftmost register through an exclusive-OR (XOR) or exclusive-NOR (XNOR) gate. A value of all zeroes is illegal in the case of a NOR feedback, while a value of all ones is illegal for XNOR feedback because these states would cause the counter to lock up. Throughout the remainder of this paper, we will use a 28-bit (n=28) LFSR for purposes of illustration, as depicted in Figure 7. As the figure shows, XNOR from registers 28 and 25 is used to produce input to the register. There is a check for the illegal state of all one values and, should that state occur, the output of NXOR gate would be “0” instead of “1” to avoid lock-up. Submission Page 13 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 NXOR 1 3 2 4 25 26 27 28 Figure 7. Linear Feedback Shift Registers as random number generators 4.2 Proposed Architecture A LFSR-based random number generator works in two steps: Initial setting at the beginning of each frame; Random number generation for the data in the frame. The purpose of initial setting is to introduce randomness of generators. In this subsection, we introduce three forms of architecture that differ according to the method of initial setting, and present simulations through which their performance can be evaluated. 4.2.1 Initial Setting with Randomly Generated Numbers We have proposed the structure shown in Figure 8 for initializing LSFRs with random numbers. At the beginning of each frame, 28 random numbers are generated and loaded into the LFSR. NXOR 1 2 . 3 4 25 26 27 28 random numbers Figure 8. Structure of LFSRs with random numbers for initial setting Submission Page 14 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 4.2.2 Initial Setting Using Another LFSR For generating random numbers, the two-layer LFSR structure shown in Figure 9 is proposed. Here, sign_ctl_reg is used to generate random numbers for sign control on data in each frame, and sign_ctl_orig is for the initial setting of sign_ctl_reg at the beginning of each frame. Sign_ctl_reg is updated every bit, while sign_ctl_orig is updated every frame. NXOR sign_ctl_reg sign_ctl_orig 1 2 3 4 25 26 27 28 1 2 3 4 25 26 27 28 Figure 9. Structure of LFSRs using single LFSR for initial setting Operation can thus be summarized as follows: 1. 2. 3. 4. At the beginning of each frame, right shift sign_ctl_orig for n bits; Copy sign_ctl_orig to sign_ctl_reg; Use sign_ctl_reg to generate required sign control bits; Go to step 1 for next frame. It can be seen that the original state of sign_ctl_reg at frame n+1 is an n-bit delay of sign_ctl_reg at frame n. From the above operation, we can see that only sign_ctl_orig needs to be synchronized, because sign_ctl_orig specifies initial state of sign_ctl_reg at the beginning of each frame. 4.2.3 Initial Setting Using Two LFSRs In order to increase randomness, a second sign_ctl_orig register can be introduced, as shown in Figure 10. Operation in this case will proceed as follows: Submission Page 15 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 1. At the beginning of each frame, right shift sign_ctl_orig1 for n1 bits and sign_ctl_orig2 for n2 bits; 2. XOR sign_ctl_origa and sign_ctl_orig2, or sign_ctl_orig = sign_ctl_orig1 ^ sign_ctl_orig2; 3. Copy sign_ctl_orig to sign_ctl_reg; 4. Use sign_ctl_reg to generate required sign control bits; 5. Go to step 1 for next frame. NXOR sign_ctl_reg sign_ctl_orig1 sign_ctl_orig2 1 2 3 4 25 26 27 28 XOR XOR XOR XOR XOR XOR XOR XOR 1 2 3 4 25 26 27 28 1 2 3 4 25 26 27 28 Figure 10. Structure of LFSRs using double LFSR for initial setting 4.3 Synchronization of LFSRs Synchronization of LFSRs is required for initial access system and traffic channels. Usually devices access system channels first for registration, and after that switch to traffic channels for media exchange. In initial traffic channel access, receivers have some knowledge of the states of LFSRs and there is only limited difference between the states of LFSRs in transmitters and receivers. Therefore, sequence number can be used for synchronization in initial traffic channel access. By contrast, in initial system channel access the receivers have no knowledge about the states of LFSRs in transmitters. In this case, then, different mechanisms can be used for initial system channel access in the different systems that were illustrated in Figures 8, 9 and 10. Submission Page 16 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 For systems of the sort shown in Figure 8, instead of generating a set of random numbers at each frame, a set of random numbers can be generated in advance and stored into an array that we will call the LFSR Initial Vectors. The same array is kept in both transmitters and receivers. A random number is generated as an index to the LFSR Initial Vectors and this same number is also put into the data block for transmission. Synchronization between transmitters and receivers can thus be established and maintained through this number. For systems of the sort shown in Figure 9, synchronization can be accomplished by putting the state of registers into the data. For registers with length of n, n bits would be needed. However, if fewer bits are reserved for register states to transmit (i.e., only 4 bits of data), only the status of registers 1-4 is put into the data. Even so, after seven frames, the state of the whole sign_ctl_orig can be obtained as shown in Figure 11. After initial synchronization, data in this field can be used to check whether sign_ctl_orig registers remain synchronized between transmitters and receivers. Insert into data Frame N 1 2 3 Frame N-1 4 5 6 7 Frame N-5 8 21 22 23 Frame N-6 24 25 26 27 28 Figure 11. Synchronization for LFSRs with two layer LFSRs Note that, from this implementation, we can see that longer LFSRs will need either more frames or more data fields for synchronization. Finally, for systems of the sort shown in Figure 10, synchronization is similar to that for the system in Figure 9 but with twice the size of data reserved for transmission because bits from two registers need to be transmitted. 4.4 Simulation We have performed simulation to evaluate performance of LFSRs of different lengths as random number generators. The configuration of the simulations is shown in Figure 12. The simulation uses Periodogram PSD estimators to calculate the PSD of different UWB signals. Frame size is 1024*128; 1024x1024-point FFT is used on 1024x1024 samples to evaluate the PSD. In other words, FFT is on eight frames, and each frame has 2044 pulses plus zero-padding on the last 4 pulses. Two hundred runs are conducted to smooth the final PSD estimate. Three simulations were performed, using 15-bit LFSRs (shown in Figure 13), 28-bit LFSRs (shown in Figure 14), and 100-bit LFSRs (shown in Figure 15). Submission Page 17 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 In each of these figures, the three columns show the results from snapshots taken at 10, 50 and 200 runs. Rows in the figures represent the following four cases that were used in each simulation: 1. Single sign_ctl_orig is used to generate initial vector for LFSR, shown on the first row in above three figures. It shifts by 2 bits for each frame, or n=2; 2. Double sign_ctl_orig is used to generate initial vector for LFSR, shown on the second row in above three figures. Sign_ctl_orig1 shifts by 2 bits and sign_ctl_orig2 shifts by 1 bit for each frame, or n1=2 and n2=1; 3. Initial vector is generated using MATLAB function RAND, shown on the third row in above three figures. 4. Random number is generated by MATLAB function RAND and is used to control phase reversion, shown on the fourth row in above three figures. Because RAND function has very good performance, this case can be served as a reference of low bound of PSD. FFT (1024x1024) frame (1024*128) frame frame data (1024*128-256)) 2044 pulses Figure 12. Configuration of simulation using LFSRs as random number generators Note that the difference between cases 3 and 4 is that in case 3, MATLAB is used to generate initial vectors while in case 4, MATLAB generates a random number for real control of phase reversion. In case 3, the total number of random numbers is equal to the length of the LFSR for each frame. In case 4, the total number of random numbers equals the number of bits in a frame. The results showed that cases 1 and 2, which use another LFSR for initial vector setting, are sensitive to the length of LFSR. With shorter LFSRs, line spectra exist; with longer LFSRs, ripples appear in the PSD. Submission Page 18 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 By contrast, using MATLAB to generate initial vectors (case 3) gives performance very close to that of case 4 as long the LFSR is long enough. From an implementation point of view, storing a set of initial vectors meets the simplicity challenge. Therefore, the structure depicted in Figure 8 for initial setting with randomly generated numbers (section 4.2.1) is the solution we recommend. Submission Page 19 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (1-a): PSD of 1: 10 (2-a): PSD of 1: 50 (3-a): PSD of 1: 200 40 40 40 30 30 30 20 20 20 10 10 10 0 0 30 5 10 (1-b): PSD of 2: 10 4 x 10 0 0 30 5 10 (2-b): PSD of 2: 50 4 x 10 0 20 20 10 10 10 0 0 0 0 30 5 10 (1-c): PSD of 3: 10 4 x 10 -10 0 20 5 10 (2-c): PSD of 3: 50 4 x 10 -10 10 10 10 0 0 0 -10 -10 0 5 10 (1-d): PSD of random: 10 4 x 10 20 -20 0 5 10 (2-d): PSD of random: 50 4 x 10 20 -20 10 0 0 0 -10 -10 -10 -20 0 5 10 -20 0 5 4 10 5 10 (3-c): PSD of 3: 200 4 x 10 5 10 (3-d): PSD of random:200 4 x 10 10 10 -20 0 20 20 -10 5 10 (3-b): PSD of 2: 200 4 x 10 30 20 -10 0 -30 0 0 4 x 10 5 10 4 x 10 x 10 Figure 13. Bit-based phase reversion with LFSR of length 15 Submission Page 20 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (1-a): PSD of 1: 10 (2-a): PSD of 1: 50 (3-a): PSD of 1: 200 30 30 30 20 20 20 10 10 10 0 0 0 -10 0 20 5 10 (1-b): PSD of 2: 10 4 x 10 -10 0 20 5 10 (2-b): PSD of 2: 50 4 x 10 -10 10 0 0 0 -10 -10 -10 -20 0 20 5 10 (1-c): PSD of 3: 10 4 x 10 -20 0 20 5 10 (2-c): PSD of 3: 50 4 x 10 -30 10 0 0 0 -10 -10 -10 -20 0 5 10 (1-d): PSD of random: 10 4 x 10 20 -20 0 5 10 (2-d): PSD of random: 50 4 x 10 20 -30 10 0 0 0 -10 -10 -10 -20 0 5 10 -20 0 5 4 10 5 10 (3-c): PSD of 3: 200 4 x 10 5 10 (3-d): PSD of random:200 4 x 10 10 10 -20 0 10 10 -20 5 10 (3-b): PSD of 2: 200 4 x 10 10 10 -20 0 -30 0 0 4 x 10 5 10 4 x 10 x 10 Figure 14. Bit-based phase reversion with LFSR of length 28 Submission Page 21 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (1-a): PSD of 1: 10 (2-a): PSD of 1: 50 (3-a): PSD of 1: 200 30 30 30 20 20 20 10 10 10 0 0 0 -10 0 20 5 10 (1-b): PSD of 2: 10 4 x 10 -10 0 20 5 10 (2-b): PSD of 2: 50 4 x 10 -10 10 10 0 0 0 -10 -10 -10 0 20 5 10 (1-c): PSD of 3: 10 4 x 10 -20 0 20 5 10 (2-c): PSD of 3: 50 4 x 10 -20 10 0 0 0 -10 -10 -10 -20 0 5 10 (1-d): PSD of random: 10 4 x 10 20 -20 0 5 10 (2-d): PSD of random: 50 4 x 10 20 -30 10 0 0 0 -10 -10 -10 -20 0 5 10 -20 0 5 4 10 5 10 (3-c): PSD of 3: 200 4 x 10 5 10 (3-d): PSD of random:200 4 x 10 10 10 -20 0 10 10 -20 5 10 (3-b): PSD of 2: 200 4 x 10 20 10 -20 0 -30 0 0 4 x 10 5 10 4 x 10 x 10 Figure 15. Bit-based phase reversion with LFSR of length 100 Submission Page 22 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 5 Phase Reversion for SYNC SYNC, also called preamble, is designed for synchronization. Usually a prefixed pattern is assigned to a SYNC for this purpose. But if randomized phase reversion is applied to SYNCs, the prefixed pattern no longer exits, making synchronization impossible. Three methods can be used to SYNC in this case: phase reversion on the whole SYNC, phase reversion on symbols, or symbol-based phase reversion and scrambling. They differ in their simplicity and performance. 5.1 Phase Reversion on the Whole SYNC The simplest and easiest method is to apply phase reversion to the whole SYNC. In this case, either SYNC or S Y N C is transmitted, which is controlled by a random number. The results of our detailed analysis (see Appendix 8.1 for a full discussion) show that this method results in the disappearance of line spectra associated with SYNC [10]. Since SYNC occupies a very small percentage of a data block, applying phase reversion on the whole SYNC should be sufficient for suppressing the PSD associated with SYNC. If greater suppression of PSD is required, phase reversion on symbols can be used instead. 5.2 Phase Reversion on Symbols Although phase reversion can eliminate line spectra, it cannot smooth ripples in the PSD of SYNC (see Appendix 8.1 for more detailed explanation). For this, a SYNC can be divided into small groups called ‘symbols’ and phase reversion applied to each symbol. This approach can smooth ripples to some extent but if further suppression of PSD is pursued, the scheme known as symbol-based phase reversion and scrambling can be employed for best performance. 5.3 Symbol-based Phase Reversion and Scrambling Detail of symbol-based phase reversion and scrambling can be found in Appendix 8.2. This scheme can be extended to the whole data. We conducted simulations on the whole data using LFSRs with length of 7, 9, 11, 15, 28 and 100. The simulations are used to evaluate performance of the mechanisms when different lengths of LFSRs are employed as random number generators. The configuration of the simulations are the same as that shown in Figure 12. The results showed that the introduction of scrambling made LFSRs of different lengths perform robustly. Even shorter LFSRs provide reasonably good performance. The tradeoff to this approach, however, is in system complexity. Submission Page 23 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (1-a): PSD of 1: 10 (2-a): PSD of 1: 50 (3-a): PSD of 1: 200 30 30 30 20 20 20 10 10 10 0 0 0 -10 0 20 5 10 4 (1-b): PSD of 2: 10 x 10 -10 0 20 5 10 4 (2-b): PSD of 2: 50 x 10 -10 10 10 0 0 0 -10 -10 -10 0 20 5 10 4 (1-c): PSD of 3: 10 x 10 -20 0 20 5 10 4 (2-c): PSD of 3: 50 x 10 -20 10 10 0 0 0 -10 -10 -10 0 20 5 10 (1-d): PSD of random: 10 4 x 10 -20 0 20 5 10 (2-d): PSD of random: 50 4 x 10 -20 10 0 0 0 -10 -10 -10 -20 0 5 10 -20 0 5 4 10 5 10 4 (3-c): PSD of 3: 200 x 10 0 5 10 (3-d): PSD of random:200 4 x 10 10 10 -20 0 20 10 -20 5 10 4 (3-b): PSD of 2: 200 x 10 20 10 -20 0 -30 0 5 4 x 10 10 4 x 10 x 10 Figure 16. Symbol-based phase reversion and scrambling with LFSR of length 7 Submission Page 24 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (1-a): PSD of 1: 10 (2-a): PSD of 1: 50 (3-a): PSD of 1: 200 30 30 30 20 20 20 10 10 10 0 0 0 -10 0 20 5 10 4 (1-b): PSD of 2: 10 x 10 -10 0 20 5 10 4 (2-b): PSD of 2: 50 x 10 -10 10 10 0 0 0 -10 -10 -10 0 20 5 10 4 (1-c): PSD of 3: 10 x 10 -20 0 20 5 10 4 (2-c): PSD of 3: 50 x 10 -20 10 10 0 0 0 -10 -10 -10 0 20 5 10 (1-d): PSD of random: 10 4 x 10 -20 0 20 5 10 (2-d): PSD of random: 50 4 x 10 -20 10 0 0 0 -10 -10 -10 -20 0 5 10 -20 0 5 4 10 4 x 10 x 10 5 10 4 (3-c): PSD of 3: 200 x 10 0 5 10 (3-d): PSD of random:200 4 x 10 10 10 -20 0 20 10 -20 5 10 4 (3-b): PSD of 2: 200 x 10 20 10 -20 0 -30 0 5 10 4 x 10 Figure 17. Symbol-based phase reversion and scrambling with LFSR of length 11 Submission Page 25 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (1-a): PSD of 1: 10 (2-a): PSD of 1: 50 (3-a): PSD of 1: 200 30 30 30 20 20 20 10 10 10 0 0 0 -10 0 20 5 10 4 (1-b): PSD of 2: 10 x 10 -10 0 20 5 10 4 (2-b): PSD of 2: 50 x 10 -10 10 10 0 0 0 -10 -10 -10 0 20 5 10 4 (1-c): PSD of 3: 10 x 10 -20 0 20 5 10 4 (2-c): PSD of 3: 50 x 10 -20 10 10 0 0 0 -10 -10 -10 0 20 5 10 (1-d): PSD of random: 10 4 x 10 -20 0 20 5 10 (2-d): PSD of random: 50 4 x 10 -20 10 0 0 0 -10 -10 -10 -20 0 5 10 -20 0 5 4 10 4 x 10 x 10 5 10 4 (3-c): PSD of 3: 200 x 10 0 5 10 (3-d): PSD of random:200 4 x 10 10 10 -20 0 20 10 -20 5 10 4 (3-b): PSD of 2: 200 x 10 20 10 -20 0 -30 0 5 10 4 x 10 Figure 18. Symbol-based phase reversion and scrambling with LFSR of length 15 Submission Page 26 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (1-a): PSD of 1: 10 (2-a): PSD of 1: 50 (3-a): PSD of 1: 200 20 20 20 10 10 10 0 0 0 -10 -10 -10 -20 0 20 5 10 (1-b): PSD of 2: 10 4 x 10 -20 0 20 5 10 (2-b): PSD of 2: 50 4 x 10 -20 10 0 0 0 -10 -10 -10 -20 0 20 5 10 (1-c): PSD of 3: 10 4 x 10 -20 0 20 5 10 (2-c): PSD of 3: 50 4 x 10 -30 10 0 0 0 -10 -10 -10 -20 0 5 10 (1-d): PSD of random: 10 4 x 10 20 -20 0 5 10 (2-d): PSD of random: 50 4 x 10 20 -30 10 0 0 0 -10 -10 -10 -20 0 5 10 -20 0 5 4 10 4 x 10 x 10 5 10 (3-c): PSD of 3: 200 4 x 10 5 10 (3-d): PSD of random:200 4 x 10 10 10 -20 0 10 10 -20 5 10 (3-b): PSD of 2: 200 4 x 10 10 10 -20 0 -30 0 0 5 10 4 x 10 Figure 19. Symbol-based phase reversion and scrambling with LFSR of length 28 Submission Page 27 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (1-a): PSD of 1: 10 (2-a): PSD of 1: 50 (3-a): PSD of 1: 200 30 20 20 20 10 10 10 0 0 0 -10 -10 -10 0 20 5 10 (1-b): PSD of 2: 10 4 x 10 -20 0 20 5 10 (2-b): PSD of 2: 50 4 x 10 -20 10 10 0 0 0 -10 -10 -10 0 20 5 10 (1-c): PSD of 3: 10 4 x 10 -20 0 20 5 10 (2-c): PSD of 3: 50 4 x 10 -20 10 0 0 0 -10 -10 -10 -20 0 5 10 (1-d): PSD of random: 10 4 x 10 20 -20 0 5 10 (2-d): PSD of random: 50 4 x 10 20 -30 10 0 0 0 -10 -10 -10 -20 0 5 10 -20 0 5 4 10 4 x 10 x 10 5 10 (3-c): PSD of 3: 200 4 x 10 5 10 (3-d): PSD of random:200 4 x 10 10 10 -20 0 10 10 -20 5 10 (3-b): PSD of 2: 200 4 x 10 20 10 -20 0 -30 0 0 5 10 4 x 10 Figure 20. Symbol-based phase reversion and scrambling with LFSR of length 100 Submission Page 28 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 6 Conclusion In this document, we have proposed a mechanism in base-band processing to reduce the PSD of pulses in UWB communication systems. This mechanism consists of (1) phase reversion, (2) an architecture that uses Linear Feedback Shift Registers to generate random numbers, and (3) synchronizing LFSRs in transmitters and receivers. The mechanism can be applied to PAM, PPM and Time-Hopping systems to achieve PSD suppression. Our simulations show that the proposed approach is effective in suppressing the PSD of UWB signals. In addition, it satisfies the important practical criteria of being both simple and easy to implement. 7 References [1]. Moe Z. Win and Robert A. Scholtz, “Impulse radio: How it works,” IEEE Commun. Lett., vol. 2, no. 2, pp. 36-38, Feb. 1998. [2]. Moe Z. Win and Robert A. Scholtz, “Comparisons of analog and digital impulse radio for multiple-access communications,” in Proc. IEEE Int. Conf. on Commun., June 1997, vol. 1, pp. 91-95, Montreal, Canada. [3]. Gerald F. Ross, “The transient analysis of certain TEM mode four-post networks,” IEEE Trans. Microwave Theory Tech., vol. MTT-14, pp.528, Nov. 1966. [4]. C. Leonard Bennett and Gerald F. Ross, “Time-domain electro-magnetics and its applications,” Proc. IEEE, vol. 66, no. 3, pp.299-318, Mar. 1978. [5]. FCC AFFIRMS RULES TO AUTHORIZE THE DEPLOYMENT OF ULTRAWIDEBAND TECHNOLOGY, ET Docket No. 98-153, February 13, 2003. [6]. Jeff Foerster, Evan Green, Srinivasa Somayazulu, David Leeper, “Ultra-Wideband Technology for Short- or Medium-Range Wireless Communications”, Intel Technology Journal Q2, 2001. [7]. Moe Z. Win, “On the power spectral density of digital pulse streams generated by Mary cyclostationary sequences in the presence of stationary timing jitter,” IEEE Tran. on Commun., vol. 46, no. 9, pp. 1135-1145, Sep. 1998. [8]. Moe Z. Win, “Spectral Density of Random Time-Hopping Spread-Spectrum UWB Signals with Uniform Timing Jitter”, Proc. MICOM ‘99, vol. 2, pp. 1196-1200, 1999. [9]. John G. Proakis and Dimitris G. Manolakis, “Chapter 4 Frequency Analysis of Signals, Introduction to Digital Signal Processing”, Macmillan Publishing Company, 1988. Submission Page 29 Shaomin Mo, Panasonic -- PINTL February, 2016 [10]. IEEE P802.15-03/122r1 Shaomin Mo, Alexander D. Gelman and Jay Gopal, “Frame Synchronization in UWB Using Multiple SYNC Words to Eliminate Line Frequencies”, To appear at IEEE Wireless Communications and Networking Conference 2003, New Orleans, AL, March 17-20, 2003. 8 Appendix 8.1 Symbol-based Phase Reversion In this section, we provide a detailed investigation of the PSD of a clocked random sequence of symbols, shown in Figure 21. Tc t Tc Tc t+1 t+2 Tc t+3 t+4 Figure 21. Clocked random sequence of symbols Assume that the rectangle in the figure represents a symbol that consists of J bits. Symbol time is denoted by Tc and bit time is denoted by Tb. Similarly to the analysis presented earlier in Section 2, a symbol can be modeled generically as: S s (t ) J 1 a n j 0 n, j w(t nTc jTb) (18) where JTb Tc (19) Applying the operations introduced in Section 3, we get a new sequence {cn} S s (t ) c w (t nTc) n n (20) s where ws is the waveform of a symbol. The probability function of {cn} is Submission Page 30 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 0.5, cn 1 Pr{cn } 0.5, cn 1 (21) In this way, an unbalanced sequence becomes a balanced sequence and all PSD goes to the continuous component of the PSD. Comparative simulations are performed to show that symbol-based phase reversion eliminates line spectra generated by a SYNC. The results of the simulations are presented in Figure 22. In this figure, panels (a) and (b) are the waveform and power spectrum, respectively, of a SYNC with seven pulses, while panel (c) is the PSD of a SYNC without processing and panel (d) is the PSD of a SYNC that has been processed following the scheme described in Section 3. Comparing panels (c) and (d) we can see that using the scheme in section 3 can effectively suppress the discrete component of the PSD of symbols, thereby reducing the peak value of the PSD by about 15dB. (a): Waveform of one symbol (b): PSD of one symbol 1 10 0 0.5 -10 0 -20 -0.5 -1 -30 0 100 200 300 -40 400 0 (c): PSD of symbol: p=1 20 30 10 20 0 10 -10 0 -20 0 500 1000 1000 1500 (d): PSD of symbol: p=0.5 40 -10 500 1500 -30 0 500 1000 1500 Figure 22. Comparison of PSD of a SYNC with/without phase reversion However, what panel (b) indicates is that, as the basic element in the signal sequence, {cn} does not keep the same spectral shape as {an}. The presence of numerous ripples in the PSD of {cn} means that phase reversion can eliminate line spectra but not ripples in PSD. No matter what was Submission Page 31 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 done on the {cn}, we were unable to match the PSD shown Figure 2-(a). In other words, with this technique we cannot get the PSD closer to the power spectrum of the pulse used in the UWB communication systems. 8.2 Symbol-based Scrambling Consider first the spectra of words with four pulses representing the following values (with one pulse representing one binary digit): 0: 1: 2: 3: 0000 0001 0010 0011 4: 5: 6: 7: 0100 0101 0110 0111 Different waveforms have different spectra shapes, which leads to the hypothesis that combining them will smooth the resulting spectrum. To evaluate this, let us make the following assumptions with regard to the symbols: 1. A frame consists of N symbols 2. A symbol consists of four pulses 3. The total number of pulses in a frame is 4N. Frame N: 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, ... Frame N+1: 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, ... X Frame N+2: 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, ... Frame N+3: 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, ... Frame N+4: 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, ... Frame N+5: 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, ... Frame N+6: 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, ... Frame N+7: 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, ... Frame N+8: 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, ... Frame N+9: 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, ... Y Figure 23. Scrambling in both X&Y directions Submission Page 32 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 As illustrated schematically in Figure 23, imagine that a Scramble Word is arranged in the X direction and changes in the Y direction. In this figure, each number denotes the value for a symbol. The X axis represents symbols in each frame while the Y axis denotes frames at different instants in time. In this figure, the Scramble Words used in frame N+8+j is the same as in frame N+j. After symbols are scrambled with the Scramble Words, phase reversion is then applied to the symbols. We conducted simulations to show that symbol-based phase reversion plus scrambling can smooth ripples as well as eliminating line spectra in the PSD, and its performance is very close to that of pulse-based phase reversion. The same configuration is employed as that used in Figure 22. The results of simulations using this scheme are shown in Figure 24. The left side of the figure plots the PSDs of the proposed scheme and the right side shows the PSDs of randomly and independently generated pulses. Rows in the figure give snapshots at 10 runs, 50 runs and 200 runs. The PSD of randomly and independently generated pulses can be considered as the statistical low bound of the PSD. It is used in the simulation as a reference to evaluate the performance of the proposed scheme. Comparing the results shown in Figure 22-(c) for original SYNC, Figure 22-(d) for phase reversion on SYNC and Figure 24-(3-a) for phase reversion & scrambling on SYNC, we can see the PSD of the proposed scheme has the lowest peak and is very close to that of the reference. Submission Page 33 Shaomin Mo, Panasonic -- PINTL February, 2016 IEEE P802.15-03/122r1 (1-a): PSD using 8 symbols: 1 (1-b): PSD of random pulses: 1 20 20 10 10 0 0 -10 -10 -20 -20 -30 0 1000 2000 -30 3000 0 (2-a): PSD using 8 symbols: 10 10 0 0 -10 -10 -20 -20 -30 -30 0 1000 2000 -40 3000 0 (3-a): PSD using 8 symbols: 50 10 0 0 -10 -10 -20 -20 -30 -30 0 1000 2000 3000 1000 2000 3000 (3-b): PSD of random pulses: 50 10 -40 2000 (2-b): PSD of random pulses: 10 10 -40 1000 -40 3000 0 1000 2000 3000 Figure 24. Spectra of SYNC with symbol-based phase reversion & scrambling Submission Page 34 Shaomin Mo, Panasonic -- PINTL