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IEEE P802.22 Wireless RANs Last Revised : 200 7 - 02 - 01

Modified CAZAC Sequences Based Low PAPR Preambles. Authors:. IEEE P802.22 Wireless RANs Last Revised : 200 7 - 02 - 01.

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IEEE P802.22 Wireless RANs Last Revised : 200 7 - 02 - 01

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  1. Modified CAZAC Sequences Based Low PAPR Preambles Authors: IEEE P802.22 Wireless RANs Last Revised: 2007-02-01 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 • Simplest sequence generation:store nNused bits, where Nused = no. of usable subcarriers. • More memory-efficient implementation • generate the integer phase indices based on Equation (1) • 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 to reduce the implementation cost for generating other M-phase preambles and/or M-phase sounding sequences. • Generation of integer phase indices requires 1 multiply and 3~4 additions per index. • Proposed sequences can be extended to form a set with low cross-correlation energy for use as a set of ACI-resistant preambles. • After generating the proposed sequence, it requires only two additional cyclic shift operations to generate another sequence in the set.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. Modified CAZAC Sequence Set (2)

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

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

  17. 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 implementation complexity of using the proposed polyphase preambles is very affordable, and is only marginally higher than that of the binary preambles when the IFFT/FFT computation is also taken into account. • 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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