5.2.3 Training sequences for spread bursts
25.2213GPPPhysical channels and mapping of transport channels onto physical channels (TDD)Release 17TS
In this subclause, the training sequences for usage as midambles in burst type 1, 2,3 and 4 (see subclause 5.2.2) are defined. The training sequences, i.e. midambles, of different users active in the same cell and same time slot are cyclically shifted versions of one cellspecific single basic midamble code. In the case of MBSFN timeslots there is only a single midamble and this is derived from a single basic midamble code which is not necessarily cellspecific. The applicable basic midamble codes are given in Annex A.1 and A.2. As different basic midamble codes are required for different burst formats, the Annex A.1 shows the basic midamble codes m_{PL} for burst type 1 and 3, and Annex A.2 shows m_{PS} for burst types 2 and 4. It should be noted that burst type 2 must not be mixed with burst type 1 or 3 in the same timeslot of one cell and furthermore burst type 4 shall not be mixed with any other burst type in the same timeslot of one cell.
The basic midamble codes in Annex A.1 and A.2 are listed in hexadecimal notation. The binary form of the basic midamble code shall be derived according to table 6 below.
Table 6: Mapping of 4 binary elements on a single hexadecimal digit
4 binary elements

Mapped on hexadecimal digit 

1 1 1 1 
0 
1 1 1 1 
1 
1 1 1 –1 
2 
1 1 1 1 
3 
1 1 1 –1 
4 
1 1 1 1 
5 
1 1 1 –1 
6 
1 1 1 1 
7 
1 1 1 –1 
8 
1 1 1 1 
9 
1 1 1 –1 
A 
1 1 1 1 
B 
1 1 1 –1 
C 
1 1 1 1 
D 
1 1 1 –1 
E 
1 1 1 1 
F 
For each particular basic midamble code, its binary representation can be written as a vector:
(1)
According to Annex A.1, the size of this vector is P=456 for burst types 1 and 3. Annex A.2 is setting P=192 for burst types 2 and 4. As QPSK modulation is used, the training sequences are transformed into a complex form, denoted as the complex vector:
(2)
The elements of are derived from elements of using equation (3):
for all (3)
Hence, the elements of the complex basic midamble code are alternating real and imaginary.
To derive the required training sequences (different shifts), this vector is periodically extended to the size:
(4)
Notes on equation (4):
– L_{m}:_{ }Midamble length
– K’: Maximum number of different midamble shifts in a cell, when no intermediate shifts are used. This value depends on the midamble length.
– K: Maximum number of different midamble shifts in a cell, when intermediate shifts are used, K=2K’.
This value depends on the midamble length.
Note that intermediate shifts are not used for burst type 4, i.e K=K’=1 for burst type 4
– W: Shift between the midambles, when the number of midambles is K’.
– x denotes the largest integer smaller or equal to x
Allowed values for L_{m}, K’ and W are given in Annex A.1 and A.2.
So we obtain a new vector containing the periodic basic midamble sequence:
(5)
The first P elements of this vector are the same ones as in vector , the following elements repeat the beginning:
for the subset (6)
Using this periodic basic midamble sequence for each shift k a midamble of length L_{m} is derived, which can be written as a shift specific vector:
(7)
The L_{m} midamble elements are generated for each midamble of the first K’ shifts (k = 1,…,K’) based on:
with and (8)
The elements of midambles for the second K’ shifts (k = (K’+1),…,K = (K’+1),…,2K’) are generated based on a slight modification of this formula introducing intermediate shifts:
with and (9)
with and (10)
The number K_{Cell} of midambles that is supported in each cell can be smaller than K, depending on the cell size and the possible delay spreads, see annex A. The number K_{Cell} is signalled by higher layers. The midamble sequences derived according to equations (7) to (10) have complex values and are not subject to channelisation or scrambling process, i.e. the elements represent complex chips for usage in the pulse shaping process at modulation.
The term ‘a midamble code set’ or ‘a midamble code family’ denotes K specific midamble codes ; k=1,…,K, based on a single basic midamble code according to (1).