The specification establishes a strict hierarchy of the scrambling sequences. The set of all scrambling codes is divided into 512 subsets, each consisting of 1 primary and 15 secondary codes. All 512 primary codes are in turn divided into 64 groups, 8 code sequences in each one. Only one unique primary code is allocated to a specific BS. Some physical channels are allowed to use only the primary code, while others may use either primary or secondary codes.

11.4.11 Synchronization channel

11.4.11.1 General structure

The synchronization channel (SCH) possesses quite an important role in the network structure, providing initial cell search and aligning the MS clock diagram with the boundaries of frames and the slots of the received BS signal. Neither channelization nor scrambling codes participate in forming the synchronization channel, since its signal should be found and processed before the MS is aware of the scrambling code of a contacted BS. Note again that BS clocks over the UMTS network are not synchronized to each other, and the initial cell search has to be fulfilled wherever an MS switches to another BS (e.g. in the course of handover). This proved to be one of the key factors in designing the SCH architecture to fit a two-stage search procedure, which is potentially capable of saving acquisition time in comparison with an ordinary serial search (see Sections 8.2 and 8.3). As a matter of fact, the SCH is a pair of primary and secondary synchronization channels, whose signals—primary and secondary synchronization codes—are exploited at the first and second search stages, respectively. Both signals occupy 256 initial chips of every slot. The primary synchronization code sequence is identical not only over all slots but also over all BSs of the network. This makes it impossible for an MS to capture the primary synchronization signal of a predetermined BS; to which of them the MS got connected after the first search stage will become clear only as a result of the second stage. After finding the primary synchronization signal, the MS knows the boundaries of slots but not of frames. At the second stage the MS should remove this ambiguity by testing all 15 (number of slots within a frame) possible values of mismatch between the MS clock and the received BS signal for all possible versions of the secondary synchronization code. To match this task the secondary synchronization code has one frame (15 slots or 38 400 chips) period and a code structure, which is specific for a given BS. Besides, the secondary code sequence is strictly bound to the scrambling code group (one of 64) assigned to the base station. Thus, having completed the second search stage, the MS recognizes the scrambling code group of the captured BS signal, and finally, after testing eight possible primary scrambling code sequences, finds out which of them is used by the contacted BS.

11.4.11.2 Primary synchronization code

The primary synchronization code (PSC) is defined in the specification as a 16-element sequence a ¼ (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1), which is repeated 16 times with or without polarity change to produce the 256-element binary sequence:

cps ¼ ða; a; a; a; a; a; a; a; a; a; a; a; a; a; a; aÞ

Every BS directly transmits the same sequence cps implementing PSC and enabling the MS to perform the first stage of cell search. Since PSC is meant for time measurement in the multipath environment, it should have relevant autocorrelation properties (see Section 6.1). Despite PSC periodicity, most of its period is empty, so aperiodic ACF sidelobe level is an adequate criterion of PSC quality. As pointed out in Example 6.10.2 (see also Figure 6.16), aperiodic ACF of the UMTS PSC is far from prominent, which is probably a penalty for the hardware simplifications pursued by designers.

11.4.11.3 Secondary synchronization code

The secondary synchronization codes (SSC) are built on the basis of a 16-element sequence b replicating the sequence a above in the first eight elements and the negative of a (i.e. a) in the rest: b ¼ (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1). This sequence is repeated 16 times with or without polarity change to produce the 256element sequence:

z ¼ ðb; b; b; b; b; b; b; b; b; b; b; b; b; b; b; bÞ

The sequence z is then symbol-wise multiplied with every 16th row of a Sylvester-type Hadamard matrix (see Section 2.7.3) of size 256 to generate 16 orthogonal 256-ary alphabet symbols used further to generate codewords of SSC. The SSC encoding algorithm should secure low levels of all incorrect correlations, i.e. between all 15 cyclic replicas of any one word as well as between any time-shifts of different words. In the UMTS specification all 64 SSC codewords are presented as a table, but an immediate check indicates that these words are just taken from (15,3) 256-ary Reed–Solomon code. The minimum Hamming distance of any Reed–Solomon code is greater by one than the number of check symbols [31,33], i.e. in our case equals 13. This guarantees that there are no more than 2 coinciding 256-ary symbols in any SSC word and any of its 14 cyclic replicas shifted to each other by an integer number of slots. In other words, the normalized periodic ACF of any SSC codeword at such shifts has a level no higher than 2/15. The same is true for any two codewords assigned to different BSs, when only shifts by an integer number of slots are analysed. At the same time, since the BSs of the network do not rely on a common clock, synchronization codes transmitted by them slide against each other and low cross-correlation values should be preserved under arbitrary timeshifts, not only those equal to an integer number of slots. The Reed–Solomon code distance optimality cannot secure a low level of correlations under arbitrary shifts of SSC sequences, and this issue calls for further investigation.

As a common conclusion to Sections 11.3 and 11.4, we again stress that our sketchy excursion into 3G systems and standards dealt only with those solutions relevant to the context of this book, i.e. concerning practical implementation of spread spectrum and CDMA ideas. A lot of books and papers already exist, and many more are anticipated, explaining and clarifying various aspects of 3G and beyond, and covering all the layers of the system protocol stack. In particular, we refer the curious reader to [19,69,92,104,114,115,120–122] and to the 3G specifications directly.