Complementary code keying

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Complementary Code Keying (CCK) is a modulation scheme used with wireless networks (WLANs) that employ the IEEE 802.11b specification. In 1999, CCK was adopted to replace the Barker code in wireless digital networks.

Complementary codes, first introduced by Golay in 1961 are sets of finite sequences of equal length, such that the number of pairs of identical elements with any given separation in one sequence is equal to the number of pairs of unlike elements having the same separation in the other sequences.

The complementary codes first discussed by Golay were pairs of binary complementary codes and he noted that when the elements of a code of length N were either [-1 or 1] it followed immediately from their definition that the sum of their respective autocorrelation sequences was zero at all points except for the zero shift where it is equal to K*N. (K being the number of code words in the set).

CCK is a variation and improvement on, M-ary Orthogonal Keying and utilises ‘polyphase complementary codes’. They were developed by Lucent Technologies and Harris Semiconductor and were adopted by the 802.11 working group in 1998. CCK is the form of modulation utilised when 802.11b operates at either 5.5 or 11 Mbit/s. CCK was selected over competing modulation techniques as it utilised approximately the same bandwidth and could utilise the same preamble and header as pre-existing 1 and 2 Mbit/s wireless networks and thus facilitated interoperability.

Polyphase complementary codes, first proposed by Sivaswamy, 1978, are codes where each element is a complex number of unit magnitude and arbitrary phase, or more specifically for 802.11b is one of [1,-1, j,-j].

Wireless networks using the 802.11b specification employ CCK to operate at either 5.5 or 11 Mbit/s in the radio-frequency (RF) band at 2.400 GHz to 2.4835 GHz. Networks using the 802.11g specification employ CCK when operating at 802.11b speeds. At higher speeds (up to a theoretical maximum of 54 Mbit/s), 802.11g WLANs use a more sophisticated modulation scheme called orthogonal frequency division multiplexing (OFDM). This is the modulation method used by 802.11a WLANs in the RF band at 5.725 GHz to 5.850 GHz.

[edit] Mathematical Description

The CCK modulation used by 802.11b transmits data in symbols of eight chips, where each chip is a complex QPSK bit-pair at a chip rate of 11Mchip/s. In 5.5 Mbit/s and 11 Mbit/s modes respectively 4 and 8 bits are modulated onto the eight chips of the symbol c0,...,c7, where

\mathbf{c}=(c_0,\ldots,c_7)=( e^{j(\phi_1+\phi_2+\phi_3+\phi_4)}, e^{j(\phi_1 +\phi_3+\phi_4)}, e^{j(\phi_1+\phi_2 +\phi_4)}, -e^{j(\phi_1 +\phi_4)}, e^{j(\phi_1+\phi_2+\phi_3 )}, e^{j(\phi_1 +\phi_3 )}, -e^{j(\phi_1+\phi_2 )}, e^{j \phi_1 })

and \phi_1,\ldots,\phi_4 are determined by the bits being modulated.

In other words, the phase change φ1 is applied to every chip, φ2 is applied to all even code chips (starting with c0), φ3 is applied to the first two of every four chips, and φ4 is applied to the first four of the eight chips. Therefore, it can also be viewed as a form of generalized Hadamard transform encoding.

[edit] References

  • IEEE Std 802.11b-1999, §18.4.6.5
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