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### Gold Codes and Scrambing

Gold codes are used to scramble data in the uplink communication of WCDMA. The purpose of scrambling is to separate the signals from different mobile stations. Gold code is generated by two m-sequences. So let us first review m-sequence and then present Gold sequences.

The maximum length shift sequence, or m-sequence for short, is probably the most widely known PN sequence. It is generated by n cell shift register and has the length of m = 2n – 1 bits, meaning that they are as long as the shift register can produce. Maximal-length sequences have a number of interesting properties, which several are listed in the following :

·        A m-sequence contains one more one than zero. The number of ones in the sequence is (n+1)/2.

·        The modulo-2 sum of a m-sequence and any phase shift of the same sequence is another phase of the same sequence (shift and add property).

·        The statistical properties of ones and zeros are well defined and always the same. Relative positions vary, but the number of each run length does not vary.

·        Every possible state of the shift register exists at some time in a complete m-sequence (except the all zeroes state, which is not allowed).

·        The periodic autocorrelation function R(k) is two valued and is given by

R(k) =

Where l is any integer and n is the sequence period.

The autocorrelation function R(k) is illustrated , where the length of  the m-sequence is 124 , generated by polynomial 1 + x2 + x5 with sequence period 31.

Gold sequences are used especially for code division multiple access. Their idea is to reduce the interference caused by a user to another user. For this reason Gold sequence has also good cross correlated properties. Gold sequences are generated by taking the modulo-2 sum of two m-sequences. The autocorrelation and cross-correlation between two Gold sequences is shown in Fig as one of example. The Gold sequences are generated by two m-sequences which are from polynomials 1 + x3 + x7 + x20 + x25 and 1 + x + x2 + x3 + x25 .

Uplink scrambling codes help to maintain separation among different mobile stations. Either short or long scrambling codes can be used in the uplink. Short scrambling codes are recommended for base stations equipped with advanced receivers employing multiuser detection or interference cancellation.

Mobile communication is affected by multipath fading in addition to shadow fading.  Multipath fading is caused by atmospheric scattering and refraction, or reflection from building and other objects. The multipath channel is classified by 2 types of multipath channel: discrete multipath channel and the diffuse multipath channel. Discrete multipath channel consists of resolvable multipath components. Diffuse multipath channel consists of unresolvable multipath components. Multipath fading affects the signals in two ways: dispersion (time spreading or frequency selectivity) and time variant behaviour. The time spreading of the symbol duration within the signal is equivalent to filtering and bandlimiting. A time-variant behaviour of the channel is due to motion of the receiver or changing environment such as movement of foliage or movement of reflectors and scatters. This means the impulse response of mobile radio channel is time variant  .

P(r)| has a Rayleigh distribution:

p(r) =  exp

where p(r) is the total power in the multipath signal.

Figure 5.6

In the most general case the channel is modeled as linear time –variant system. This is described by its time-variant impulse response, . This gives the response of the channel at time t to an impulse at time t. It therefore gives the channel impulse response and shows how it varies with time, also related to three other functions, which gives the same information in a different form. Fig.  shows the relationship among the functions in which the F denotes Fourier transformation with respect to the subscripted variable .