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### UWB Synchronization

Hui-Min Yeh

Outline

- Introduction
- Code synchronization
- Typical acquisition scheme
- Typical search strategies
- Definition of ‘Hit set’

- Transmitter design
- Hybrid TH/DS signal format

- Receiver design
- Proposed search algorithms
- Joint BRS-NCS search
- Joint RPS-NCS search

- Proposed acquisition scheme

- Proposed search algorithms
- Simulation results
- Conclusions

The objective of the signal synchronization is to properly align the received signal by correctly estimating the random delay

Time

Synchronization ?

Introduction

- Code synchronization (TH code; DS code):
- To enable the lower BER of data demodulation, the template signal should be aligned with the received signal, the code alignment is so-called “code synchronization” process.

- Code synchronization can be spilt into two parts
- Code acquisition
- It is a coarse code acquisition, to resolve the code phase error within certain range.

- Code tracking
- It is a fine tuning process, to guarantee the timing error below an acceptable level.

- Code acquisition

- Acquisition strategy: The search for acquisition is based on the auto-correlation properties of the applied the codes, the auto-correlation is high if the receiver is synchronized and low in other situations [5].
- MAX criterion (Maximum selective):
- TC criterion (Threshold Crossing):
- MAX/TC criterion:

Data

Sequence for synchronization

- Before any data can be received in an UWB communication, the receiver must synchronize on the transmission.
- Receiver structures
- Noise template signal
- Reference template signal

- Packet data
- Synchronization on (known) code
- Reception and processing data

Data can have specific coding-> communication can not be tapped

Code synchronization

- Find the best fit between the code and the received signal

Typical acquisition system

- The receiver’s reference signal generator will shift and guess the code boundary of received signal, and the AWGN noise will effect the performance.

Correlator

4 & 5

3

- Why use RAKE receiver?
- More than one hypothesized phase can be considered as an estimated timing delay for a coarse acquisition

Definition of ‘Hit set’

- Hit set definition:
- The definition of ‘Hit set’ is a critical issue . When the threshold setting is low, the noise effect on the false alarm probability will increase. Oppositely, when the threshold setting is high, the mean acquisition time will increase.

- Ex: The periodicity of TH code =4, frame duration , that is Nh=128, Tc = 1 nsec, normalized pulse energy =1,CM1(noise free),
search space = 512 cells, Th=2, EGC receiver (20 fingers)

Peak value

Partial correlation energy

Hit set

N

1

2

True phase

- Rake fingers = 20, search space = 512 cells, CM1 , that is Nh=128, Tc = 1 nsec, normalized pulse energy =1,CM1(noise free),

Search strategies , that is Nh=128, Tc = 1 nsec, normalized pulse energy =1,CM1(noise free),

- What is the efficient search algorithm?
- Serial or Parallel

- Typical serial search algorithms [1]
- Linear Search (LS)
- Random Permutation Search (RPS)
- Bit Reversal Search (BRS)

- Ideal mean stopping time:

- Bit Reversal Search , that is Nh=128, Tc = 1 nsec, normalized pulse energy =1,CM1(noise free),
- The search algorithm is described by assuming that N is a power of 2.
- The order of search positions in the bit reversal search
algorithm is decided by “bit reversing”

- For example: Let the integer of N is equal to 8 (2^3)

Search locations for N = 23

‘Bit Reversing’

Reorder search locations by ‘bit reversing’

The ideal and normalized mean stopping time vs. the parameter H/N for three serial search algorithms (N=512 cells)

- Bit Reversal Search algorithm , code length=4, Nh=128, parameter H/N for three serial search algorithms (N=512 cells)
CM1(noise free), search space = 512 cells, EGC receiver (20 fingers)

Outline parameter H/N for three serial search algorithms (N=512 cells)

- Introduction
- Code synchronization
- Typical acquisition scheme
- ‘Hit’ definition
- Typical search strategies

- Transmitter design
- Hybrid TH/DS signal format

- Receiver design
- Proposed search algorithms
- Joint BRS-NCS search
- Joint RPS-NCS search

- Proposed acquisition scheme

- Proposed search algorithms
- Simulation result
- Conclusions

Transmitter design: Hybrid TH/DS signal format parameter H/N for three serial search algorithms (N=512 cells)

Next

symbol

1’s Symbol (Nds*Tf)

(TH-sequence)

(Repeat NT times)

Frame (CNth-1)

Frame (C0)

Frame (C1)

Tf

- The variation of power spectral density (PSD) between the pure time hopping sequences and hybrid TH/DS signals
- No TH coding
- The periodicity of TH code is equal to the number of pulses per symbol
- Hybrid TH/DS signal

- The hybrid TH/DS signal format method not only speeds up the code acquisition, but also improves the interference to other co-existing systems [7].

UWB signals with no Time-Hopping coding pure time hopping sequences and hybrid TH/DS signals

- Parameters: 10 symbols; number of pulses per symbol ( ) =64;pulse repetition time ( ) =10 nsec; chip duration ( ) = 1 nsec
- The transmitter power is concentrated at multiples of pulse repetition frequency.

Amplitude

Time (ns)

UWB signals with Time-Hopping coding pure time hopping sequences and hybrid TH/DS signals

- Consider the same parameters
- The periodicity of TH code ( ) is equal to the number of pulses per symbol, that is ,
- The PSD of the signals is composed of spectral lines at the distances of
- The transmitted power is concentrated at multiples of symbol repetition frequency.

UWB signals with hybrid TH/DS signals pure time hopping sequences and hybrid TH/DS signals

- Consider the same parameters
- a) Short TH code with ; repeat NT =8
- It will increase a lot of spectral lines due to the repeat operation

- b) Short TH code with ; repeat NT =8;
- The polarity of pulses per symbol is scrambles by DS code

Outline pure time hopping sequences and hybrid TH/DS signals

- Introduction
- Code synchronization
- Typical acquisition scheme
- ‘Hit’ definition
- Typical search strategies

- Transmitter design
- Hybrid TH/DS signal format

- Receiver design
- Proposed search algorithms
- Joint BRS-NCS search
- Joint RPS-NCS search

- Proposed acquisition scheme

- Proposed search algorithms
- Simulation result
- Conclusions

- Proposed Joint Search Algorithms pure time hopping sequences and hybrid TH/DS signals
- Joint BRS-NCS Search
- Joint RPS-NCS Search

- Non consecutive search (NCS) criterion:
- The non consecutive search strategy is proposed owing to more than one HIT phase in multi-path channel models.
- The non consecutive search can achieve a rapid acquisition by testing search locations with a step size D which is greater than one cell.
- The cells in total search space are so called uncertainty region that can be divided into blocks
- This will reduce the search time required to acquire the location of hit set from an initial search cell, but it could also increase the miss probability.

LI-NCS (Linear Increasing NCS) pure time hopping sequences and hybrid TH/DS signals

- In order to avoid the miss search, we propose a linear increasing NCS (LI-NCS) approach.
- The search equation can be expressed as
- The LI-NCS approach can be described as following:
- Set initial loop =1, and check blocks. The number of test cells are
- If the correlation output of each block in this loop is lower than threshold, then go to the step (3). If the correlation output of one block in this loop is higher than threshold. then the search procedure is DONE.
- Set loop = loop + 1, and also check blocks, the number of cells are
, then go to step (2)

An example of the LI-NCS search approach pure time hopping sequences and hybrid TH/DS signals

Assume that search space N=12, hit set =[7 8 9 10 11], block size D = 4,

0

1

2

3

4

5

6

7

8

9

10

11

Joint BRS-NCS search procedure a) search space N=48, hit set H=8, b) divided into 8 blocks, each block with D = 6

Search space N

Correct

Symbol

Boundary

(a)

=: New search location

D cells

(0)

(4)

(6)

(1)

(3)

(5)

(7)

(2)

(b)

Receiver design : Acquisition scheme H=8, b) divided into 8 blocks, each block with D = 6

- Two-stage acquisition scheme
- TH code acquisition
- DS code acquisition

Find DS-boundary

(get symbol boundary)

ACQ2

(Second stage)

ACQ1

Coarse

TH-boundary

acquisition

Fine

acquisition

Received signal

(First stage)

First Stage H=8, b) divided into 8 blocks, each block with D = 6

(RAKE receiver with parallel correlators)

Z

Hit

Roughly find TH-boundary

TC #1

No Hit

Set new search location based on Joint Search Algorithm (new shift )

Template signal generator

(Coarse Acquisition)

Maximum path amplitude selective

One branch

correlator

Second Stage

(Fine Acquisition)

Fine Acquisition Procedure: H=8, b) divided into 8 blocks, each block with D = 6

- Step1:The terminating point of coarse acquisition process is the starting point of fine acquisition.
- Step2: The new search window in fine acquisition process is equal to the double Hit set size.
- Step3: The fine acquisition process searches both right and left directions from the starting pointof fine acquisition with one branch correlator to acquire the strongest path. The search range of each direction is equal to the size of hit set.
- Step4: Weutilize the maximum selective criterion to select the strongest path amplitude
- Step5: Finally, the fine acquisition process passes the parameter on to the second stage.

Left direction

Right direction

Starting point

Second Stage H=8, b) divided into 8 blocks, each block with D = 6

(RAKE receiver with parallel correlators)

Found DS-boundary

(Found symbol boundary simultaneously)

Z

Hit

TC #2

No Hit

Set step size=: time-hopping code length and new search location based on Joint Search Algorithm location (new shift )

Template signal generator

Outline H=8, b) divided into 8 blocks, each block with D = 6

- Introduction
- Code synchronization
- Typical acquisition scheme
- ‘Hit’ definition
- Typical search strategies

- Transmitter design
- Hybrid TH/DS signal format
- Power spectral density (PSD)

- Receiver design
- Proposed search algorithms
- Joint BRS-NCS search
- Joint RPS-NCS search

- Proposed acquisition scheme

- Proposed search algorithms
- Simulation results

Simulation cases H=8, b) divided into 8 blocks, each block with D = 6

- Two-stage vs. one stage
- Comparison of search strategies
- Two-step approach
- MAI case

Channel model 1&4 H=8, b) divided into 8 blocks, each block with D = 6

- The first path of CM1 we consider has the strongest amplitude gain, and the tenth path of CM4 has the strongest amplitude gain in our simulation.

The strongest path

The strongest path

SNR vs. Detection probability for the second stage in CM1 H=8, b) divided into 8 blocks, each block with D = 6

- Assume that the first stage finds the correct boundary.

Mean stopping time of two acquisition schemes as a function of threshold parameter A

- Simulation parameters:

- The mean stopping time of Joint BRS-NCS /Joint RPS-NCS method versus threshold setting for step size D=4, D=8, and D is approximated to hit set.

- Comparison of performance in terms of Mean stopping time versus threshold setting for proposed search algorithms and bit reversal search algorithm.

A statistical number as function of offset value for 5000 trials, a) SNR = 10 dB, coarse acquisition result, b) considering fine acquisition result, in CM1

Single-user

Multi-user

SNR = 20 dB, 5000 trials, CM4 trials, a) SNR = 10 dB, coarse acquisition result, b) considering fine acquisition result, in CM1

Single-user

Multi-user

MAI vs Detection probability (CM1) trials, a) SNR = 10 dB, coarse acquisition result, b) considering fine acquisition result, in CM1

- Simulation results for detection probability of the UWB channel model (CM1), as a function of the number of interfering users Nu-1

MAI vs Detection probability (CM4) trials, a) SNR = 10 dB, coarse acquisition result, b) considering fine acquisition result, in CM1

- Simulation results for detection probability of the UWB channel model (CM4), as a function of number of interfering users Nu-1

- Simulation results of detection probability for different lengths of in UWB channel model (CM1), as a function of interfering users (Nu-1), SNR=20dB

Conclusions lengths of in UWB channel model (CM1), as a function of interfering users (N

- The mean stopping time of two-stage acquisition scheme is simulated and it is evident to see that the two-stage acquisition scheme outperforms the conventional one stage acquisition scheme.
- By simulation results, we can see that the “Joint Search Algorithms” have lower mean stopping time.
- We propose a two-step approach which is composed of coarse step and fine step to achieve a fine code acquisition in first stage.
- Adding more users to the systems is investigated by computer simulations.

References lengths of in UWB channel model (CM1), as a function of interfering users (N

[1] E. A. Homier and R. A. Scholtz, “Rapid acquisition of ultra-wideband signals in the dense multipath channel,” Proceeding of2002IEEE Conference Ultra Wideband Sys. Tech, (Baltimore, MD), pp. 105-109, 2002.

[2] J. Oh, S. Yang, and Y. Shin, “A Rapid Acquisition Scheme for UWB Signals in indoor wireless channels,” IEEE WCNC ’04, Wireless Commun. and Networking Conference, vol. 2, 2004.

[3] S. Gexici, E. Fishler, F. Kobayashi, H. V. Poor, and A. F. Molisch, “A rapid Acquisition Technique for Impulse Radio,” in Proc. IEEE Pacific Rim Conference Commun., Comput., Signal Process., pp. 627-630, Aug 2003.

[4] L. Reggiani, G. M. Maggio,”Rapid Search Algorithms for Code Acquisition in UWB Impulse Radio Communications,” IEEE Commun. Journal, vol. 23, pp. 898-908, May 2002.

[5] G. E. Corazza, “On the MAX/TC criterion for code acquisition and its application to DS-SSMA systems,” IEEE Trans. on Commun., vol. 44, pp. 1173-1182, Sept. 1996.

[6] M. Z. Win, R. A. Scholtz, “Impulse Radio : How It Works,” IEEE Commun. Letters, vol. 2, No. 1, pp. 36-38, Jan. 1998.

[7] S. Aedudodla, S. Vijayakumaran, T. F. Wong, “Rapid Ultra-wideband Signal Acquisition,” IEEE Wireless Commun. and Networking Conference, vol. 2, pp 1148-1153, March 2004.

[8] O. S. Shin and K. B. Lee, “Utilization of multi-paths for spread-spectrum code acquisition in frequency-selective rayleigh fading channels” IEEE Journal Trans. on Commun., Apr. 2001.

[9] S. L. Han, S. O. Hyun, E. K. Chang, “Code acquisition for the DS-CDMA RAKE receiver in a multi-path fading channel,” Proceeding of IEEE Singapore International Conference, pp. 215-219, July 1995.

[10] V. Saravanan, F. W. Tan,”Equal gain combining for acquisition of UWB signals,” MILCOM ’03, IEEE Military Commun. Conference, vol. 2, pp.880-885, Oct. 2003.

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