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Forward Spreading

All base stations radiate a common, universal code.


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 period.

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 sequences. 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, are:
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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