no reliable knowledge about signal attenuation in the uplink, and the first transmission of preamble goes at low power. As long as no message comes from the BS confirming connection, the MS randomly selects new access slots and makes new attempts, each time increasing the signal power. After receiving BS confirmation, the MS transmits the message itself covering one or two frames (10 or 20 ms). There is no closed power control loop in PRACH, since the connection sessions on it are quite short.

The structures of the physical CPCH (PCPCH) and PRACH are in general similar; however, the message segment of the PCPCH may occupy a larger number of frames and the preamble segment is followed by one more part: the collision detection preamble, which helps to recognize simultaneous attempts of several MSs to use PCPCH. Due to the longer duration of PCPCH packets the presence of a closed power control loop in it appears to be reasonable in contrast to PRACH.

In the same way as in the dedicated channels, quadrature multiplexing is used in the common channels to combine information and service components of transmitted data. Separation of common and dedicated physical channels is performed by channelization codes, which are considered in the next subsection.

11.4.5 Uplink channelization codes

As stated above, an individual MS uses several types of channels to be separated in the BS receiver. Since the same clock controls all the physical channels of the MS, synchronous code division is a good option to arrange separation between physical channels (multiple DPDCH, DPCCH, PRACH, PCPCH). Note that we are now discussing only the separation of channels of an isolated MS, signals of different mobiles remaining separated by asynchronous CDMA, as in cdmaOne and cdma2000.

In the UMTS documents the channelization coding format is described by the binary tree establishing an iteration procedure. At every iteration any word of the preceding iteration generates two new words of double length by appending either itself or its negation. Let ck be some code vector obtained at the kth iteration. Then two code vectors of double dimension ckþ1 ¼ (ck, ck) and c0kþ1 ¼ (ck, ck) are its descendants at the next iteration. In this way, starting with a trivial word (1) of length one leads after k iterations to 2k channelization codewords of length N ¼ 2k (Figure 11.8 shows this for the case k ¼ 3). One can easily see that this algorithm differs from the Sylvester rule of constructing the Hadamard matrix (see Section 2.7.3) only in reordering the resulting matrix rows, so that the codewords obtained are nothing but Walsh functions. Nevertheless they appear in the UMTS specifications under a special name, orthogonal variable spreading factor (OVSF) codes.

The uplink OVSF tree is built using k ¼ 8 iterations, so that codewords have maximal length N ¼ 256 chips. The word of this length consisting of all ones is allocated to the dedicated control channel DPCCH, whereby a subsequent scrambling secures DPCCH spreading factor 256, mentioned in Section 11.4.3. Choice of channelization code of the same length for DPDCH (spreading factor 256) allows transmitting data at the rate 15 kbps. If a greater rate is on demand, the data symbol becomes shorter, i.e. the spreading factor drops (the chip rate never changes, remaining 3.84 Mcps!). Appropriate DPDCH channelization words are then taken from the intermediate (kth, SF ¼ 2k being

(1, 1, 1, 1, 1, 1, 1, 1)

(1, 1, 1, 1)

(1, 1, 1, 1, –1, –1, –1, –1)

(1, 1)

(1, 1, –1, –1, 1, 1, –1, –1)

(1, 1, –1, –1)

(1, 1, –1, –1, –1, –1, 1, 1)

(1)

(1, –1, 1, –1, 1, –1, 1, –1)

(1, –1, 1, –1)

(1, –1, 1, –1, –1, 1, –1, 1)

(1, –1)

(1, –1, –1, 1, 1, –1, –1, 1)

(1, –1, –1, 1)

(1, –1, –1, 1, –1, 1, 1, –1)

Figure 11.8 Tree of OVSF codes of length 8

the required spreading factor) iteration of the OVSF code tree. If a necessary rate is attainable within a single DPDCH its channelization word number is fixed by the specification as SF/4 ¼ 2k 2, counting top-down on the tree and numbering the uppermost word by zero. Such a choice always preserves orthogonality between DPDCH and DPCCH independently of DPDCH spreading factor. When a single DPDCH (with spreading factor 4) cannot provide the necessary data rate, the multicode transmission mode involves several DPDCH, all having always the same minimum spreading factor 4. There are three codewords of length 4 orthogonal to each other and to the word of DPCCH, so, allowing for the chance of using the same word for two DPDCH in quadrature multiplexing (Figure 11.7), up to 6 multicode DPDCH may be arranged.

The technique of allocation of codewords to PRACH and PCPCH set up by the specification also provides their orthogonality to the dedicated channels over the whole range of DPDCH data rates.

11.4.6 Uplink scrambling

The final step in forming the MS signal is its DS spreading by a user-specific signature to realize asynchronous CDMA separation of signals of different MSs in the BS receiver. According to the UMTS thesaurus, this operation, as well as a similar operation in the downlink, is called scrambling. This usage of the term is slightly different to that in the cdmaOne and cdma2000 documents (see Sections 11.3.3.3 and 11.3.3.4). There are two types of uplink scrambling codes predetermined by the standard: either long or short codes apply to scramble dedicated channels.

x þ x þ x þ 1 form two m-sequences, of which the second may also be obtained by decimation of the first with the index relevant for Gold codes. The modulo 2 addition of

the offset second m-sequence to the first gives a Gold sequence which is then truncated and mapped to the f 1g alphabet. The ‘pure’ truncated Gold sequence fcig determines the real component of the MS QPSK signature. To obtain the imaginary part the original (before truncation) Gold sequence is first offset by 16 777 232 chips and then truncated and mapped to produce the f 1g sequence fc0ig. After this, the negative of every even element of the latter sequence replaces the following odd element and the result is chip-wise multiplied with fcig. The last operation halves the number of elements in the resulting QPSK sequence whose polarities are opposite to the preceding. Indeed, the equation describing a QPSK signature ai thus obtained is:

where c(i) and c0(i) are just more convenient designations for the elements ci and c0i. One can observe now that in passing from an even position i ¼ 2l to the next odd i ¼ 2l þ 1 the real and imaginary part cannot change simultaneously, meaning that maximal phase jumps are only 90 , never 180 , so a chip polarity may change into the opposite only during transitions from odd to even chips. Reduced frequency of the opposite transitions is typically desirable for battery lifetime, since power amplifier during them dissipates higher energy.

The final step of QPSK scrambling consists in multiplication of the MS multiplexed signal taken from the branches of the scheme of Figure 11.7 with scrambling sequence. This operation, which is performed by an ordinary QPSK modulator, was discussed at length in Section 7.1.2.

A scrambling sequence is precisely synchronized to the MS clock beginning in any frame from the same symbol (chip).

Note that the key advantage of Gold codes—minimax periodic correlation proper- ties—cannot justify their choice for uplink scrambling, because truncation corrupts correlations drastically. An alternative reasoning is ease of generation of many (no fewer than 225 þ 1) pseudorandom sequences.

Short scrambling sequences have length 256 and are planned for employment when a BS receiver is capable of running multiuser algorithms (see Section 10.1). In the case of asynchronous CDMA, the complexity of this type of receiver typically grows with the length of spreading code. The rule of forming short scrambling codes set by the specification includes generating a linear recurrent quaternary sequence of length 255, modulo 4 summation of it with two binary recurrent sequences of lengths 51 and 85, extension of the resulting sequence by one element up to length 256, mapping quaternary symbols onto the QPSK alphabet, and transformation of the obtained complex sequence by rule (11.1).

11.4.7 Mapping downlink transport channels to physical channels

Information conveyed by the network to a specific MS at the transport layer is organized as a single dedicated channel, which is then mapped to two downlink physical channels similar to those in the uplink: data (DPDCH) and control (DPCCH) dedicated channels.

The list of downlink common transport channels is much wider compared to the uplink. It contains, specifically, the already mentioned broadcast channel BCH transmitting