Reverse Spreading

There are two different criteria that apply to the reverse link spreading. When a mobile is engaged in user traffic, i.e., in a conversation, it is desirable that that mobile use a unique code that is distinct from all others. A mobile-unique code, rather than a base-station-associated code, facilitates handoff. With a mobile-unique code, nothing needs to change about the mobile's modulation or coding when handoff occurs.

The second situation occurs when a mobile is attempting to gain the attention of a base station. Initially the base station has no knowledge that any particular mobile is in its service area. It is wildly impractical for each base station to search simultaneously for millions of potential subscriber codes. For these initial accesses, or any other non-traffic uses of the air interface, it is desirable to have some Reverse Spreading codes that are base station-associated. If there are only a few associated codes for each base station, then it is practical for the base station to search for them continuously and simultaneously, awaiting the arrival of any user who wants service.

Traffic Channel Spreading

Spreading is based on a single, universal 42-bit Long Code LFSR sequence. In a sense, the reverse spreading code borrows an idea from the Forward Spreading. Rather than completely unique codes, a single, universal 42-bit LFSR sequence is used. This sequence is known as the Long Code. Again, phase of the long code is used to distinguish stations. All 2⁴²-1 possible phases are available as logical addresses.

The distinct phases of the Long Code are generated by a simple means that takes advantage of one of the curious properties of maximal-length LFSR sequences. A 42-bit Long Code Mask (LCM) selects particular cells of the generator register. The output is the modulo-2 sum of the contents of the selected cells. It turns out, oddly, that any such linear combination of any cells of the generator runs through the same sequence, but with a different phase. All 2⁴² -1 phases that can be generated by a non-zero 42-bit mask are distinct (the all-zero mask gives a constant zero output). The LCM for each mobile station is based on the mobile manufacturer's identity and the serial number of that unit. The LCM is, effectively, a logical address of the Reverse CDMA Channel.

The period of the long code, for what it's worth, is 3.6 million seconds, or about 41 days!

Short code is added to resolve ambiguities.

Even though there are a large number of Long Code phases, without some modification, there is potential ambiguity between units that have similar LCMs. Timing errors in real systems will be of the order of a round trip delay to the farthest cell, in practice perhaps in excess of 100 microseconds. This would make groups of LCMs ambiguous if the Long Code were the only component to the spreading. A delay of X microseconds would be indistinguishable from a long code that was offset by X microseconds. For this reason the Long Code is modified by adding the Short Code. Each mobile, when it acquires a candidate base station, synchronizes its Short Code and its Long Code generators to System Time. The mobile applies its unique LCM to the long code generator, and modulo-2 adds the output, that is the unique-phase long code, to the universal short code. As in the Forward CDMA Channel, the spreading modulation is quadrature, so as to homogenize the phase of the interference. Again, both short code sequences are used. See Figure 1.

Figure 1. Reverse CDMA channel spreading logic.

Astute readers might note that the addition of the Short Code to the Long Code is not without residual ambiguity. The combined "supersequence" code is still periodic, but with a larger period. The periods of the short and long codes are relatively prime, so the period of the supersequence is the product of the original periods: (2⁴² -1)*2¹⁵ = approximately 2⁵⁷, or about 3700 years. Any offset long code sequence, added to the short code sequence, is some different phase of the supersequence. Why is this not a problem? Although the supersequence has period 2⁵⁷, we are only ever using, at most, 2⁴² -1 of the possible phases of it. We have constructed the spreading sequence generator in such a way that the smallest code phase separation between users is one short code period. One is more than enough. The mobile will have system time in error by at most a fraction of one millisecond due to propagation delays. Although everyone is using the same supersequence, their phases are so far apart that they will never be confused by the base stations. This is the contribution of the short code to the process: it changes the time ambiguity from one chip displacement to 2¹⁵ chips displacement.

The number of Long Code phases, 2⁴²-1, is about 4.4 * 10¹², so the number of available addresses should suffice for the near future! Actually, because of the way they are assigned, which includes space for the access channels, the available addresses are a bit less than this, but there is still plenty of space. See Long Code Mask for further details.

Access Channel Spreading Access channel spreading is generated by the same logic as the mobile-unique traffic channel spreading. The difference is that the Long Code Mask is associated with the base station, not the mobile that is using it. The LCM for an access channel is derived from a prefix that basically says "this is an access channel", the base station identity, and an integer index. The index selects one of the several possible access channels that are supported by this station. The LCMs that are assigned to each base station are shared by all mobiles. That is, any mobile station desiring to use that base station must use one of the base station's assigned LCMs.

Each base station must support an access channel on at least one RF carrier of each sector. Each station is permitted, but not required, to support more than one access channel per sector. If more than one access channel is available then the one that a mobile uses is chosen through a Resource Hashing algorithm. The hashing ensures that the load on the available channels is statistically uniform.

A mobile attempting to gain access to a base station first identifies the base station by decoding the Sync Channel message and later acquires the information it needs to do system accesses by reading the Access Parameters Message on a paging channel. These message contains all information needed to construct the appropriate long code mask, including the identity of the base station and the number of access channels that it supports. See System Access for further details.

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Copyright © 1996-1999 Arthur H. M. Ross, Ph.D., Limited