All base stations radiate a common, universal
If all base stations radiate a common, universal
code, then the mobiles need no prior knowledge of where they
are in order to know what to search for - they always search
for the same code. Second, search time is roughly proportional
to the number of timing hypotheses that must be tested.
Does a common, universal code work? The answer is
yes. Don't the stations interfere with each other so that
they cannot be distinguished from one another? The answer
is no, and for the same reason that communication works in
this environment. The autocorrelation of an m-sequence from
a Linear Feedback Shift Register has the form shown in Figure
1. The off-time correlations will be further reduced by random
carrier phasing, which has been disregarded in this figure.
The desired signal on-time correlation will exceed that of
the off-time correlations by a factor which is roughly the
length of the code divided by the effective number of interferers.
Figure 1. Discrete autocorrelation of m-sequences, N=sequence
Base stations are distinguished by the phase
of the universal code.
If all base stations are synchronized to a universal system
time, then phases of the universal codes can be coordinated.
In particular, stations can be assigned different phases in
order make them distinguishable by the mobiles.
The minimum separation of code phases is related to the largest
cells that may be present in a system. The separation must
be larger than the propagation delay that can be incurred
by a usable base station. The air interface standards call
out a separation increment of 64 chips (about 15.6 km of one-way
propagation delay) between stations. This gives 512 possible
base station pilot phases. The 9-bit index that represents
the pilot phase in call processing messages is called the
pilot index. However each operator is free, if they
choose, to use a larger separation. Use of larger separations
leads, of course, to fewer possible pilot offset assignments.
This is similar to the ambiguity problem that exists in AMPS
systems caused by failure of the SAT code system, but in that
case there is only a space of three identities. Here the number
is much larger and not likely to be troublesome.
The universal code is the Short
Code. The universal code,
or Short Code, has period 215,
which is 80/3 = 27.667 ms at the 1.2288 MHz spreading rate.
This length is a compromise between search time, and the number
of available code phases.
The Short Code is composed of not just one sequence, but actually
two. The spreading modulation, in both forward and reverse
directions, is quadrature. This ensures that the mutual interference
is always homogeneous in phase. There is thus one short code
for the I-channel and another for the Q-channel. They have
different generators and low cross correlation.
The fact that the short code period is an even power of two
represents a slight compromise in the design. Maximal length
LFSR sequences always have period 2N-1,
N an integer. Even if the period is not actually a prime number
(215-1 = 32767 = 7*31*151 is not), the factors
are odd numbers, making them inconvenient at best. The underlying
short code sequences are indeed from 15-bit LFSRs, but they
are augmented by stuffing an extra zero at a particular place
in the sequence. This makes the number of ones and zeros equal,
among other things. While the stuffing "spoils"
the autocorrelation property, it doesn't spoil it very much,
and makes life a whole lot easier in other ways. See our Short
Code page for more details.
Each base station radiates a family of 64 orthogonal
cover code channels.
Because each base station must serve in the neighborhood of
40 mobiles (see CDMA Revolution
there must be some way of creating independent communication
channels. Moreover, because these channels all come from the
same site, they can share precise timing, and must
somehow share the common Short Code spreading. This is easily
accomplished because the number of spreading chips per code
symbol is fairly large. Suppose for example, that the FEC code
rate is r. Code rates from perhaps r=1/3 to r=3/4 are good design
choices in most terrestrial communication systems. Toll-quality
vocoders now exist that can operate at data rates from R=8 to
R=16 kbps. Then the symbol rate from the FEC encoder, R/r, assuming
a binary alphabet, ranges from about 10 ksps to 50 ksps. with
the 1.2288 MHz chip rate, there are about 25 to 125 chips per
code symbol. This suggests an orthogonal cover technique that
can be applied to each symbol.
The orthogonal cover technique is based on the so-called Hadamard-Walsh
. These are binary sequences, powers-of-two long,
that have the property that the "dot product" of any
two of them is zero. The Walsh sequences of order 8, for example,
If we represent each + as a positive amplitude, and each - by
a negative amplitude, then take the dot product of any two rows
as the sum of the products of the amplitudes in corresponding
columns, that dot product is zero for any two distinct rows.
Walsh functions of order 64 are used in the Forward CDMA Channel
to create 64 orthogonal channels. There is exactly one period
of the Walsh sequence per code symbol: 64 * 19.2 ksps = 1.2288
Mcps. These channels are readily generated by the binary logic
shown in Figure 2. The "impulse modulators" generate
a discrete ±1 outputs in response to binary (0, 1) inputs.
Figure 2. Forward spreading logic.
Summing the code symbols, the Walsh cover, and the two short
code sequences (see Figure 2), and changing to the bipolar
±1 representation, results in a quadrature (I, Q) sequence
of elements from the set (±1, ± j). These elements
drive a modulator that generates the appropriately bandlimited
analog output. See the Forward CDMA
Channel for further details.
The pilot code, one of the 64 channels, is the
universal search target of the mobiles.
One of the Walsh codes, numbered zero by tradition, has all
64 symbols the same. By the logic of Figure 3, this is just
the "bare" short code spreading. It is the universal
pilot sequence that all mobile use as their search target. Those
searches are done for several purposes:
- Initiation of Handoff
- Initial Acquisition of an appropriate serving station
- Rake finger assignment
The common, universal, pilot code facilitates the implementation
of all these processes.
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