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IEEE P802.22 Wireless RANs Last Revised : 200 7 - 02 - 08

Modified CAZAC Sequences Based Low PAPR Preambles. Authors:. IEEE P802.22 Wireless RANs Last Revised : 200 7 - 02 - 08.

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IEEE P802.22 Wireless RANs Last Revised : 200 7 - 02 - 08

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  1. Modified CAZAC Sequences Based Low PAPR Preambles Authors: IEEE P802.22 Wireless RANs Last Revised: 2007-02-08 Notice:This document has been prepared to assist IEEE 802.22. 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 grants a free, irrevocable license to the IEEE to incorporate material contained in this contribution, and any modifications thereof, in the creation of an IEEE Standards publication; to copyright in the IEEE’s name any IEEE Standards publication even though it may include portions of this contribution; and at the IEEE’s sole discretion to permit others to reproduce in whole or in part the resulting IEEE Standards publication. The contributor also acknowledges and accepts that this contribution may be made public by IEEE 802.22. Patent Policy and Procedures:The contributor is familiar with the IEEE 802 Patent Policy and Procedures http://standards.ieee.org/guides/bylaws/sb-bylaws.pdf including the statement "IEEE standards may include the known use of patent(s), including patent applications, provided the IEEE receives assurance from the patent holder or applicant with respect to patents essential for compliance with both mandatory and optional portions of the standard." Early disclosure to the Working Group of patent information that might be relevant to the standard is essential to reduce the possibility for delays in the development process and increase the likelihood that the draft publication will be approved for publication. Please notify the Chair Carl R. Stevenson as early as possible, in written or electronic form, if patented technology (or technology under patent application) might be incorporated into a draft standard being developed within the IEEE 802.22 Working Group. If you have questions, contact the IEEE Patent Committee Administrator at patcom@iee.org.

  2. Co-Authors:

  3. Background (1) • In Draft v0.2, two binary PN Sequences are used to generate the I and Q components of QPSK symbols which form preambles in the frequency domain (c.f. Section 8.3) • Superframe and frame preambles currently specified have high PAPR (> 7.8 dB for 2K FFT mode) • Preambles with high PAPR may be clipped by the power amplifier, leading to • lower accuracy in timing synchronization and channel estimation • degraded detection performance • To allow the transmission power of preambles to be boosted up (relative to that of data symbols), the PAPR of preambles must be a few dBs lower than that of the data symbols.

  4. Background (2) • Many effective methods (e.g. clipping, coding and companding) for reducing the PAPR of data modulating subcarriers by 3dB~5dB have been reported in the last few years. • It is important to ensure that the PAPR of preambles to be minimized as much as possible, or it may limit the system performance. • Binary preambles have undesirably higher PAPR than polyphase preambles, but can only offer marginal advantages in implementation: • Complexity is dominated by the IFFT/FFT computation rather than the sequence generators • Timing synchronization requires the time-domain samples of the preamble, which are not simpler for a binary preamble that is specified in the frequency domain

  5. Background (3) • Recently, polyphase preambles (Frank & Chu sequences) belonging to the class ofConstant Amplitude Zero Auto-Correlation (CAZAC) sequences are adopted in IEEE802.16a and IEEE802.15.3 due to their perfect autocorrelation property. • When the effect of adjacent cell interference (ACI) on preambles has to be considered (c.f. Runcom’s doc IEEE802.22-06/0223r0), a set of preambles with low time-domain cross-correlation energy is desirable. • These requirements for preambles are very similar to those for channel sounding sequences. Actually, sets of CAZAC sequences, called GCL (Chu) sequences, are also specified in Draft v0.2 as sounding sequences (c.f. Section 8.10.5.4.4). • Note that only one sequence for one preamble of a type is specified in Draft v0.2. i.e. the effect of ACI was not considered for preambles. • In this proposal, we modify the CAZAC sequences to obtain (sets of) preambles with very low PAPR and low cross-correlation energy.

  6. Unified Construction of M-Phase CAZAC Sequences(1) • The preambles proposed in this contribution are based on a very general construction of M-phase CAZAC (in the M-PSK format), i.e. the unified perfect roots-of-unity sequences (PRUS) [1]. [1] W.H. Mow, “A new unified construction of perfect root-or-unity sequences,”Proc. IEEE 4th International Symposium on Spread Spectrum Techniques and Applications (ISSSTA'96), Germany, September 1996, pp. 955-959. • It includes the Frank, Chu, Milewski, and GCL sequences and more. • It was proved by an exhaustive search that the unified PRUS construction includes all M-phase CAZAC sequences with M 15, sequence length L 20 and LM  1111.  • It was conjectured that no more unknown M-phase CAZAC sequences exist [2]. [2] H.D. Lüke, et al. “Binary and quadriphase sequences with optimal autocorrelation properties: a survey,” IEEE Transactions on Information Theory, Vol. 49, Dec. 2003, pp.3271-3282.

  7. Unified Construction of M-Phase CAZAC Sequences(2) • The unified CAZAC sequence sCAZAC of length L = sm2 is • By modifying a properly selected sCAZAC and optimizing the parameters s, m, α(l), β(l), (l), low PAPR sequences can be obtained.

  8. Generation of Modified CAZAC Sequences with M = 2n phases • Storage requirement for a 2n-phase preamble is nNused bits, where Nused = no. of usable subcarriers. E.g. a 32-phase preamble requires 5 bits per used subcarrier. • Initial generation of the proposed preamble involves 2 steps: • Generate the integer phase indices based on Equation (1) → requires 1 multiplication and 2 additions per index 2. Perform table lookup to obtain the corresponding I and Q representations → only need to store M/4 = 2n-2 pairs of I/Q values (i.e. phase angles in [0, π/4)) as multiplication by ±1 or ±j can be computed with little complexity. This lookup table can be shared for generating IFFT/FFT coefficients and/or M-phase sounding sequences. • Proposed sequences can be extended to form a sequence set with low cross-correlation energy for use as a set of ACI-resistant preambles. • Require only 2 additional cyclic shift operations to generate another sequence in the set. • Need to store 2 cyclic shift values per sequence • There is no additional complexity at the transmitter, once the allocated preamble is generated and stored.

  9. Receiver Complexity: Polyphase vs. Binary Preambles(1) • The choice of a polyphase or binary preamble has little impact on the timing sync processing, because after taking FFT, the time samples of the preamble used in the correlator are complex-valued anyway. It onlymakes a difference in the channel estimation block of the receiver. • Channel estimation requires 1 complex multiplication per used subcarrier with polyphase preambles, while a negation is needed with binary preambles.

  10. Receiver Complexity : Polyphase vs. Binary Preambles(2) • To estimate the extra # complex multiplications incurred, let us consider the processing ofa frame in 2K-FFT mode • There are 26 OFDM symbols per frame since Frame duration = 10 ms (c.f. Section 6.7.1.1.1) and symbol duration = 373.33 µs (c.f. Section 8.1.2.3.1) • Channel estimation is performed only using the long frame preamble, so it is only performed for 1/26= 3.85% of all OFDM symbols in a frame • FFT is performed for all 26 OFDM symbols (i.e. for both preambles and data). • An N-point FFT requires (N/2)log2(N) complex multiplications and Nlog2(N) complex additions. For N=2048, 11,264 complex multiplications per OFDM symbol are performed. • Channel equalization for the 24 data symbols requires 1 complex multiplications per used sub-carrier • With polyphase preamble, channel estimation for the preamble requires 1 complex multiplication per used sub-carrier

  11. Receiver Complexity: Polyphase vs. Binary Preambles(3) • Assuming that 1680 subcarriers are all used, the percentage increase in # complex multiplications due to the use of polyphase preambles is • The extra complexity incurred is actually much less than 0.5% because the following have not been considered in the above analysis. • The no. of used subcarriers at CPE is generally <<1680 and can be as small as 18. • Packet detection: 2 real multiplications and 3 real additions per time sample • Viterbi decoding of the 64-state convolutional code for each data OFDM symbol

  12. Receiver Complexity: Polyphase vs. Binary Preambles(4) • Last but the least, the complex multiplications required for channel estimation with a polyphase preamble are only phase rotation, which can be very efficiently implemented without any real multiplication by applying the famous shift-and-add-onlyCORDIC algorithm. • Reference: http://www.dspguru.com/info/faqs/cordic.htm • In conclusion, the use of the proposed polyphase preambles only incurs negligible extra complexity at the receiver, compared with the binary preambles.

  13. Results on Low PAPR Preambles(1) • Results are presented for the setting: • 2K, 4K and 6K FFT modes, null subcarriers [L=184n, DC, R=184n-1] (n = no. of bonded TV channels) • Decimation factor = 2 or 4 • Number of bonded TV channels = 1, 2 or 3 • Here, all PAPR values are estimated for continuous-time waveforms using an oversampling factor of 4.  Without oversampling, the computed PAPR values may be over-optimistic.

  14. Results on Low PAPR Preambles (2) • The following table lists the PAPR values of the proposed modified CAZAC sequences for different modes of preambles in draft v0.2 with 32 and 128 phases, respectively. • The proposed preambles can be used to replace preambles in the current draft with a PAPR gain of at least 5.87dB.

  15. Results on Low PAPR Preambles (3) • The following table lists the PAPR values of the modified CAZAC sequences for frame preambles when the number of bonded TV channels n = 2 or 3.

  16. Results on Low PAPR Preambles (4) • PAPR reduction as compared to the preambles based on PN sequences in the current Draft v0.2 is at least 5.87 dB. • By reducing M from 128 to 32 and hence the lookup table size from 32 to 8 pairs of I/Q values, the resultant PAPR values are still very low and the worst-case PAPR is only increased mildly from 1.93dB to 2.14dB. • Still, the memory requirement for the proposed 128-phase preambles are very affordable.

  17. Modified CAZAC Sequence Set (1) • When adjacent cell interference is a concern, we propose a set of modified CAZAC sequences with low PAPR and low cross-correlation levels as preambles (and sounding sequences). • The average energy of the time-domain cross-correlation functions is as low as that of the GCL (Chu) set specified in Draft v.0.2, leading to same adjacent cell interference power. • Next, the PAPR values of a set of 114 modified CAZAC sequences are evaluated. • The worst case PAPR of the proposed set is 2.55dB, which is about 2.2dB better than the Chu set.

  18. Modified CAZAC Sequence Set (2)

  19. CDF CDF of PAPR of Sequence #114 in the Modified CAZAC Set

  20. CDF of PAPRs of the 114 Sequences in the Modified CAZAC Set

  21. Summary • We propose the use of modified CAZAC sequences to replace the existing preambles specified in draft v0.2. • The proposed polyphase preambles can attain very low PAPR (≤1.93dB for 2K, 4K and 6K FFT) so that the detection performance will not be limited by the preambles, even if some advanced method is applied to reduce the PAPR of data modulating subcarriers by 3dB. • It was demonstrated that sets of modified CAZAC sequences can also attain very low PAPR (≤2.55dB for 2K, 4K and 6K FFT & set size = 114), while having the same time-domain cross-correlation energy as that of the GCL (Chu) set specified in Draft v0.2. • The extra implementation complexity of using the proposed polyphase preambles is very affordable and is practicallynegligible, when compared with the binary preambles. • Low PAPR results for the proposed type of preambles have been obtained for various decimation factors 1,2,4 (corresponding to 1, 2 and 4 repetitions of sequences) and for various FFT sizes. These confirm that the desirable properties of the proposed preambles can be maintained independent of the choice of preamble structures.

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