September 2008doc.: IEEE 802.22-08/0251r0 Soo-Young Chang, Huawei TechnologiesSlide 1Submission NEW...

September 2008 doc.: IEEE 802.22-08/0251r0

Soo-Young Chang, Huawei TechnologiesSlide 1Submission

NEW CHIP SPREADING SEQUENCES FOR TG1 MULTIPLE ACCESSIEEE P802.22 Wireless RANs Date: 2008-9-4

Name Company Address Phone email

Soo-Young Chang Huawei Technologies Davis, CA, USA 916 278 6568 [email protected]

Authors:

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NEW CHIP SPREADING SEQUENCES FOR TG1 MULTIPLE ACCESS

Soo-Young Chang

Huawei Technologies

September 2008

Soo-Young Chang, Huawei TechnologiesSlide 2

doc.: IEEE 802.22-08/0251r0

Submission



INTRODUCTION

• In D2 (and D4), one chip sequence was introduced for chip spreading, not for multiple access. [1] [2]

• However, with only one chip sequence multiple networks (or PPDs) in an area can not be facilitated.

• The author has introduced 8 orthogonal codewords (or seuences) in D3 to accommodate this multiple access feature. [3]

• In July 2008 meeting, Steve Kuffner [1] claimed these codewords in D3 do not have good correlation characteristics for chip synchronization and less uniform spectral characteristics.

• In this document, a new set of codewords are being introduced to improve these characteristics and meet the requirements.

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D2 CHIP SEQUENCE

• The spreading sequence for 802.22.1 D2 was a complex sequence that was chosen based on its correlation properties.

• Sequence = [1-j -1-j 1+j 1-j 1-j 1-j -1+j -1-

j]

• The figure was imported from [1]. It was plotted with average values with two cases of next bits 1 and -1. It means at one moment, the actual correlations may be larger than those shown in this figure.

• Still the value should be 2 for lags of 4 and -4. (any mistake in [1] ?)

-8 -6 -4 -2 0 2 4 6 80

1

2

3

4

5

6

7

8

lag

|R(k

)|

Autocorrelation values vs chip lag

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D3 CHIP SEQUENCES

• The D3 spreading sequences were chosen to provide separability between different beacons operating in the same area on the same frequency. [3]

• The sequences in Table 26 of D3 are the inverted sense of the Hadamard8 matrix:

1 1 1 1 1 1 1 1 1 -1 1 -1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 -1 1 -1 1 1 -1

Steve Kuffner claimed that these sequences have poor auto/cross-correlation properties, and are only ensured to be orthogonal when properly time aligned. [1]

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INTRODUCTION OF NEW SEQUENCES

• A new set of four 8 chip sequences are being introduced where each element is a complex number.– Four sequences were selected so as for correlations to be less

than 5.6 out of 16.

C1: 1-j -1-j 1+j 1-j 1-j 1-j -1+j -1-j

C2: 1-j 1+j 1+j -1+j 1-j -1+j -1+j 1+j

C3: 1-j -1-j -1-j -1+j 1-j 1-j 1-j 1+j

C4: 1-j 1+j -1-j 1-j 1-j -1+j 1-j -1-j

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HOW TO CALCULATE CORRELATIONS (1)

• Received chip stream

r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16

a1 a2 a3 a4 a5 a6 a7 a8

a1 a2 a3 a4 a5 a6 a7 a8

a1 a2 a3 a4 a5 a6 a7 a8

a1 a2 a3 a4 a5 a6 a7 a8

Bit n Bit n+1

Red chips are overlapped with chips for the next bit.

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• Received chip stream

r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16

a1 a2 a3 a4 a5 a6 a7 a8

a1 a2 a3 a4 a5 a6 a7 a8

a1 a2 a3 a4 a5 a6 a7 a8

a1 a2 a3 a4 a5 a6 a7 a8

Bit n Bit n+1

Each bit may have 1 or -1.

If two adjacent bits are identical, red chips needs no inversion.

If two adjacent bits are different values, red chips needs to be inverted to have lower correlations.

In the scheme proposed, the smaller one is taken from these two cases as a correlation at a position.

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• Take a block of eight chips randomly from the received chip stream. Calculate a correlation of this block with the assigned receiver sequence.

a1 a2 a3 a4 a5 a6 a7 a8

a1 a2 a3 a4 a5 a6 a7 a8

a1 a2 a3 a4 a5 a6 a7 a8

a1 a2 a3 a4 a5 a6 a7 a8

Calculate two correlations by shifting by one chip at one time and by taking inversion and non-inversion for red chips.

Take the smaller correlation value between two values with inversion and non-inversion for the correlation of the shifted block.

For eight shifted sequences including no shift, get correlation values. The chip sequence with highest correlation value is the right one for bit synch.

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HOW TO GET BIT SYNCH

• If the receiver received chip stream which was spread with the same sequence,– Calculate a correlation between a received 8 chip sequence and

the receiver’s assigned chip sequence. Correlations calculated for a chip sequence is explained in the previous three slides.

– Calculate another correlation by shifting the received chip stream by one chip.

– Using the above procedure, eight correlations are calculated.– Synchronize the chip stream with the highest correlation.

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CORRELATION PROPERTIES

• Auto-correlations– Correlations with the same sequence– For eight different lags (or shifts), correlations can be calculated.

• Cn(0)Cn*(k): correlation of Sequence n between with 0 shift and with k chip shift, where k=0, 1, …., 7

– High correlation means more possibility to have bit synchronization.

• Cross-correlation– Correlations with different sequences– For eight different lags (or shifts), correlations can be calculated.

• Cn(0)Cm*(k) : correlation between Sequence n with 0 chip shift and Sequence m with k chip shift, where k=0, 1, …., 7

– These correlations should be smaller not to synchronize with wrong sequences.

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Submission



AUTO-CORRELATIONS FOR D2 SEQUENCE

• For D2, average values are plotted. It means that actual values can be larger than these values.

– For ex., for lag1, correlation value can be 4 with the probability of ½.

• By applying the procedure to calculate correlations of received sequences introduced in this document, less correlations are taken for unsynchronized sequence.

-8 -6 -4 -2 0 2 4 6 80

1

2

3

4

5

6

7

8

lag

|R(k

)|

Autocorrelation values vs chip lag

Only two non-zero correlations for unsynchronized sequences by proposed procedure

Original average correlation values for D2

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Submission



AUTO-CORRELATIONS OF NEW SEQUENCES (1)

Lag

seq

0 1 2 3 4 5 6 7

C1 16 0 0 0 4j 0 0 0

C2 16 0 0 0 4j 0 0 0

C3 16 4 0 -4+4j

(5.6)*

4 -4-4j

(5.6)*

0 0

c4 16 -4 0 4-4j

(5.6)*

4 4+4j

(5.6)*

0 4

* Absolute correlation values: |Rnm(k)|

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Submission



AUTO-CORRELATIONS OF NEW SEQUENCES (2)

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D2 CROSS-CORRELATIONS

• No need to have cross-correlations for original D2 sequence because there are not multiple sequences.

• With this sequence, multiple PPDs (or networks) can not be implemented.

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CROSS-CORRELATIONS OF NEW SEQUENCES (1)

Lag

seqs

0 1 2 3 4 5 6 7

C1C2 0 4 0 4-4j

(5.6)*

4 4-4j

(5.6)*

0 4

C1C3 0 -4 -4+4j

(5.6)*

4j 4 4 4+4j

(5.6)*

8

C1C4 0 8 4+4j

(5.6)*

4 4 4j -4+4j

(5.6)*

4

C2C3 0 8 4+4j

(5.6)*

-4 4 -4j -4+4j

(5.6)*

4

C2C4 0 4 -4+4j

(5.6)*

-4j 4 -4 4+4j

(5.6)*

-8

C3C4 0 0 0 0 4 0 0 0

* Absolute correlation values: |Rnm(k)|

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CROSS-CORRELATIONS OF NEW SEQUENCES (2)

September 2008


lag



SPECTRAL CHARACTERISTICS

• D2 spectral characteristics– From Steve Kuffner’s document [1], the D2 spreading sequence

spreads the energy out relatively uniformly across the chip rate bandwidth.

– This sequence is exactly the same as Sequence 1 of the new sequences proposed in this document. Therefore the spectrum of D2 sequence is the same as that of Sequence 1 of the new sequences.

• Spectral characteristics of new sequences– Spectra of new sequences are plotted using simulations in the

following slides.

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D2 SPECTRAL PROPERTIES• From Steve Kuffner’s

document, the D2 spreading sequence spreads the energy out relatively uniformly across the chip rate bandwidth. [1]

• This sequence is exactly the same as Sequence 1 of the new sequences proposed in this document. Therefore the spectrum of D2 sequence is the same as that of Sequence 1 of the new sequences.

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SPECTRAL PROPERTIES OF NEW SEQUENCES

Seq 1 Seq 2

Seq 4Seq 3

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CONCLUSIONS

• In this document, a new set of four sequences is introduced and a new procedure to calculate correlations for bit synchronization is proposed.

– A new set of sequences are selected with a criterion of maximum correlation of 5.6 out of 16.

• With these four sequences, up to four PPDs (or networks) can be operated in an area simultaneously.

– This feature should be implemented.• A new procedure to calculate correlations enables us to have smaller

correlations for unsynchronized and unmatched sequences.• The four sequences proposed have almost the same level of correlations

and spectra as D2 (and D4) sequence has:– Auto-correlation: D2: 4/16 max new sequences: 5.6/16 max– Cross-correlation: 8/16 max– Spectra: almost the same spectrum envelope across the chip rate bandwidth

• These feature will improve the performance.

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Submission



REFERENCES

[1] IEEE 802.22-08/0119r0, Steve Kuffner, May 2008.

[2] P802.22.1/D2, October 2007

[3] P802.22.1/D3, April 2008

September 2008


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