UWB Synchronization

1. UWB Synchronization 徐烜龍 2005/8/2

2. Outline • Introduction • Symbol-Differential UWB Systems • Frame-Differential UWB Systems • Proposed Algorithm • Simulations • Conclusions • References

3. Introduction • The synchronization schemes can be divided into two strategies as: • Serial search • It consists of successive detection tests on consecutive locations of the received signal. • This process is stopped when the correlation exceeds a predefined threshold. • Parallelsearch • This process will check all possible locations and select the maximum correlation value.

4. The features of the serial search and the parallel search: • Serial search • It has lower hardware complexity. • However, it needs more search time. • Parallel search • It has higher hardware complexity due to the receiver architecture. • It can reduce the total search time. • Thus, according to different requirements of the system, a tradeoff between the hardware complexity and the total search time for the proposed receiver can be made.

5. How to achieve synchronization? • Generally, the receiver design is based on correlator-based receivers. • By the observation of the correlation values can determine if the system achieves synchronization. • In other words, how to capture the signal energy is considerable. • The UWB impulse radio receiver design includes as: • Rake receiver • Transmitted reference receiver • Differential receiver

6. The features for three types receivers: • Rake receiver: • It can take full advantage of the available signal energy. • Although the full rake receiver can capture more signal energy, it has higher circuit complexity • It has the challenge of the template signal design. template signal correlator a(t-jTr-τ0) c0 r(t) hj “rake” combining correlator a(t-jTr-τL-1) cL-1

7. Transmitted reference receiver: • Pulses are transmitted in pairs, where the first pulse is denoted as the reference pulse and the second pulse is the data pulse. • The reference pulse acts as a template signal to correlate the data pulse. • But TR systems waste communication resources, i.e., power and time, to transmit reference signals. data bit 1 data bit 0 D

8. Differential receiver: • A differential UWB system doesn’t transmit reference signal, but instead, the data signal in the previous is used as a reference signal. • Since it does not transmit reference signals, it can reduce the transmitted power. • It does not need to design a template signal. • The differential receivers can be divided into two types: • Symbol-differential UWB receiver • Frame-differential UWB receiver.

9. Symbol differential approach • Frame differential approach symbol i symbol i+1 Delay for Ts symbol i symbol i+1 D1 D0

10. Symbol-Differential UWB System • The transmitted signal of the symbol differential scheme: • : modulating the pulse polarity ( ). • : the transmitted pulse energy. • : the normalized pulse. • : the number of frames in one symbol. • : the frame duration • : the time hopped code. • : the chip duration • Pulse polarities remain the same during each symbol, but will change in the next symbol if a -1 is transmitted.

11. +1 transmitted +1 transmitted -1 transmitted Received Signal Tf Tm Delay for Ts Ts Turning point Architecture of Symbol-Differential Receiver ( ) • Adaptive synchronization scheme can be divided into two steps: • Step 1: Symbol-level synchronization • Step 2: Frame-level synchronization

12. Symbol-Level Synchronization • To sample the integrator output twice per frame to achieve symbol-level synchronization. • These sampled values are compared to find the highest absolute one, which corresponds to the coarse symbol boundary. • Once symbol-level synchronization is achieved, the sampling rate can be decreased to be once per symbol. • Assuming that the estimated start point of symbol is at , the sampled output of this symbol can be written as:

13. When and the SNR is not very low, the inaccuracy of symbol-level synchronization can be controlled within . • Since we can not know the exact start point , what we have is only an estimate with . • So the uncertain region has a length of .

14. Frame-Level-Synchronization • To exclude the noise-only region, we need to reduce the integration time in each symbol. • Since each symbol is composed of frames. • The new integration region would also be composed of sections, which are denoted as “sub-integration-windows (SIWs)”. • Each frame has a SIW, and each SIW has a same width at one integration, which is smaller than . • Assuming that the exact start point of symbol is at , the integrator output can be expressed as the equation

15. This step splits the continuous integration region over a whole symbol into SIWs, each with a width where • Let the searching step size to be equal to • Due to the uncertain region is equal to . Thus, altogether times of search are needed. • Assuming that the search starts from the symbol, at the search, the integrator output is: • with • where is the estimated start place of the symbol.

16. For Example: • 1 Ts = 3 Tf • 1 Tf = 4 Tc • Th codes = [ 0 2 1] Ts • Step 1 : Symbol-level synchronization • Assuming that the symbol-level synchronization has been achieved. • Step 2 : Frame-level synchronization • The uncertain region = • To split the continuous integration region over a whole symbol into SIWs. • To find the highest integration output value. Tf Tc

17. Ts = 3 Tf, Tf = 4 Tc, Th codes = [ 0 2 1] Tf The estimated start place of the symbol 1st search 2nd search 3rd search 4th search 5th search 6th search 7th search

18. Frame-Differential UWB System • What is frame-differential UWB system ? • Each data symbol is modulated by . • A known random sequence is differentially modulated on the time-hopped pulses, where . • What is differential modulation scheme ? For example: symbol i symbol i+1

19. Here, super-imposing the user data and the frame-level binary code, the differentially modulated pulse-polarities are obtained as and For example: symbol i symbol i+1

20. For example: symbol i symbol i+1 • The transmitted signal is written • as the transmitted pulse shape • The time-instants of the pulses : • Important for this scheme are the time shifts between consecutive pulses.

21. The time shifts between consecutive pulses, written as • and • The time hopped sequences are all the same for each symbol. • If we know any one of the pulse position, we can find the following pulses according to the time shifts between each pulse. • In my proposed algorithm, we let symbol i symbol i+1

22. Proposed Algorithm: Receiver Architecture Decision Delay Delay Delay Delay Delay Delay Delay Delay Delay Delay Delay Delay

23. The output value of the first branch can be expressed as: where • Therefore, each output value over any branch can be expressed as: for

24. Uncertain Region • Since time hopped sequences are defined as • where : the number of chips within one frame duration • The maximum value of : • Where

25. Decision Rule • The observation window of each branch is equal to one symbol duration. • The uncertain region is equal to . • We set the searching step size to be • Thus, altogether times of search are needed. • Each search has output values acquired from branches. • Choosing the maximum output value between these output values. • Finally, choosing the maximum output value between all searches.

26. A Reduced Complexity Scheme • Since total correlators and delay elements are needed in this receiver architecture, we will try to reduce the number of them. • In reduced complexity case, each branch needs correlators and delay elements. Generally, A < 1. • If A is equal to one, it is the same as the previous stated search scheme. • It can save correlators and delay elements. Reduced complexity

27. Simulations • Simulation cases: • Multi-user environments • Different shift step sizes • Different width of SIWs • A reduced complexity scheme • Comparison with symbol differential synchronization scheme

28. Code correlation • Each pulse energy = 1/Nf = 1/20 = 0.05

29. Channel model 1 (CM1) • We can capture 92% total energy, it only takes 20ns.

30. Channel model 4 (CM4) • We can capture 92% total energy, it takes about 66ns.

31. SIW = 20, Shift = 20 SNR = 0 dB SNR = 10 dB

32. SIW = 20, Shift = 10 SNR = 0 dB SNR = 10 dB

33. SIW = 10, Shift = 10 SNR = 0 dB SNR = 10 dB

34. SIW = 10, Shift = 2 SNR = 0 dB SNR = 10 dB

35. DER • The “detection error” can also be called as the “decision error”, which describes the situation when the inaccuracy of estimated symbol boundary exceeds the SIW/2. SIW/2 SIW/2 0 Timing offset

36. DER • Purpose: • To compare the DER with different number of users (Nu = 1, 5 and 10). • Parameters: • CM1 • SIW = 20 (chips) • Shift step size = 10 (chips) • By the observation: • When the number of user is increased, it will get the worse DER.

37. DER • Purpose: • To compare the DER with different widths of shift step size (Shift = 20, 10 and 5). • Parameters: • CM1 • Nu = 1 • SIW = 20 • By the observation: • When the width of shift step size is smaller, it has the better performance.

38. DER • Purpose: • To compare the DER with different number of SIWs included in each branch during one symbol duration. • Parameters: • CM1 • Nu = 1 • SIW = 20 • Shift step size = 5 • By the observation: • When the number of SIWs is reduced, the DER will be worse.

39. DER • Purpose: • To compare the DER with symbol differential scheme. • Parameters: • CM1 • Nu = 1 • SIW = 20 • By the observation: • The performance of my proposed algorithm is better than the performance of symbol differential scheme.

40. BER • Purpose: • To compare the BER with different number of users (Nu = 1, 5 and 10). • Parameters: • CM1 • SIW = 10 (chips) • Shift step size = 2 (chips) • By the observation: • When the number of user is increased, it will get the worse BER.

41. BER • Purpose: • To compare the BER with different width of shift step size (Shift = 2 and 5). • Parameters: • CM1 • Nu = 1 • SIW = 10 (chips) • By the observation: • When the width of shift step size is smaller, it has the better performance.

42. BER • Purpose: • To compare the BER with symbol differential scheme. • Parameters: • CM1 • Nu = 1 • SIW = 10 (chips) • Shift step size = 2 (chips) • By the observation: • The performance of my proposed algorithm is better than the performance of symbol differential scheme.

43. BER • Purpose: • To compare the BER with different width of SIWs in the corresponding synchronization inaccuracy. • Parameters: • CM1 • Nu = 1 • SNR = 5 dB • By the observation: • When the width of SIW is smaller, it get the worse performance.

44. BER -10

45. BER • Purpose: • To compare the BER with different number of SIWs for each branch during one symbol duration. • Parameters: • CM1 • Nu = 1 • SNR = 5 dB • By the observation: • When the number of SIWs is reduced, the BER will be worse.

46. Conclusions • The differential receiver has an advantage that it does not need to spend extra efforts designing the template signal. • An effective synchronization algorithm for multi-user environment is proposed in this thesis. • In the architecture of proposed receiver, the uncertain region is smaller than two frame durations . It is helpful to reduce the search time. • It is a tradeoff between the performance and the circuit complexity. • The BER of our proposed algorithm is better than the symbol-differential synchronization algorithm.

47. References • The references about this slides: • A.-J. van der Veen, A. Trindade, QH Dang, and G. Leus,“Statistical Analysis of a Transmit-Reference UWB Wireless Communication System,” ICASSP, Mar. 2005. • N. He and C. Tepedelenlioglu, “Adaptive synchronization for non-coherent UWB receivers,” ICASSP, Montreal, CA, May 2004. • M. Ho, V. S. Somayazulu, J. Foerster, and S. Roy, “A differential detector for an ultra-wideband communications system,” in IEEE Vehicular Tecnology Conference, VTC, Spr. 2002. • K. Witrisal and M. Pausini, “Equivalent system model of ISI in a frame- differential IR-UWB receiver,” in IEEE Global Telecommunications Conference, GLOBECOM, Dallas, Dec. 2004. • K. Witrisal, M. Pausini, and A. Trindade, “Multiuser interference and inter-frame interference in UWB transmitted reference systems,” in International Workshop on Ultra-Wideband Systems, IWUWBS, Kyoto, May 2004.

48. References • Suggested readings for UWB synchronization research: • J. Oh, S. Yang, Y. Shin, “A rapid acquisition scheme for UWB signals in indoor wireless channels,” in IEEE Wireless Communications and Networking Conference, WCNC, Mar. 2004. • L. Reggiani, GM Maggio, “A reduced complexity acquisition algorithm for UWB impulse radio,” UWBST, Reston (VA, USA), Nov. 2003. • E. A. Homier and R. A. Scholtz, “Rapid acquisition of ultra-wideband signals in the dense multipath channel,” in IEEE Conference on UWB systems and Technologies, May 2002. • S. Aedudodla, S. Vijayakumaran, and T. F. Wong, “Timing Acquisition in Ultra-wideband Communication Systems,” IEEE Transactions on Vehicular Technology, 2005. To appear.