The Alignment Procedure

We shall limit ourselves here, initially, to the simplistic frame format illustrated within Fig. 6-4. In Sec. 6.2.2 we shall show that our analysis may be extended and applied to distributed multiframe alignment schemes with only minor alterations.

Synchronous Time Division 121 Suppose that F digits are used to specify the FA W, and that N digits occupy one complete frame. In this case the number of digits given to information carrying equals N - F. We may assume that these information digits exhibit a purely random behavior since we shall impose no control over the channel messages. Thus the probability of a logical 1 at each digit position is 0.5.

Since the information digits may take any form it is likely that the FA W is imitated during the frame by some sequence of F message digits. Furthermore, once the equipment has been aligned, transmission errors can cause either a corruption of an occasional FA W, which may be ignored, or a more severe perturbation that demands the realignment of the system. For these reasons it is necessary to define a state-transition diagram such as shown in Fig. 6-5, and the following alignment states:

State a = Full alignment, system in lock

States b, c, and d = Provisional alignment, system in check mode State e = Out of alignment, system in search mode States

f

and g = Waiting state, system in search/check mode

There are many different alignment techniques. However, the easiest concept to visualize, and the most commonly used is the step by step, or serial frame alignment procedure. It is instructive to consider an example, using the technique discussed below.

Suppose that the demultiplier is not aligned (state e) at a point in time x (Fig.

6-4); the moment when the equipment is switched on. The alignment procedure

a I n frame synchron ization

b Frame code not detected in frame number n c Frame code not detected in frame number n + 1 d Frame code not detected in frame number n + 2 e Out of frame synchronism (search mode)

f Frame code detected in frame number 0 (waiting state) g Frame code detected in frame number 1 (waiting state)

Fig. 6-5 The frame alignment state· transition diagram.

122 Multiplexing

begins by examining the first F digits after point X, and comparing them against the FA W. If the digits do not match the FA W, the system slips one digit and interrogates the next sequence of F digits, and so on until a match occurs, whereupon state f is recorded. This process is conventionally referred to as frame searching. the state-transition diagram (see Fig. 6-5). If, on the other hand, the FA W continues to be confirmed each frame, state a will be reached and maintained.

It is interesting, and indeed important to the described process that the imitations 12, and 13 have no effect. Once partial synchronism has been established the system ceases to continue searching for the FA Wand merely checks the FA W at one-frame intervals. Systems based on this concept of serial searching operate at high bit rates, and are cheap to implement. However, some reduction in the overall mean search marking the location of all sequences that match the FA W, and immediately ignoring those that do not repeat at one-frame intervals. After several frames have elapsed all imitations have been ignored, and the position of the FA W is known with certainty.

The technique is illustrated within Fig. 6-6.

In this example the FAW is matched at locations 1, 3, 7, 12, 15, and 19 within the first frame. However, since the sequence is not repeated at locations 1 and 9 within the second frame these locations do not contain the FA W, and are consequently ignored. occurs when distributed framing structures are employed.

At first sight it may appear that the problem of imitations can easily be solved by using a very long FA W that is not likely to be simulated by random data. Unfortu-nately this is undesirable, since the FA W is more easily corrupted by transmission errors (see Sec. 6.2.2).

Tolerance to occasional transmission errors within the FA W is extremely important once the system has achieved full alignment. It should not be necessary to reenact

Synchronous Time Division 123

Alignment procedure

Location number Parallel Serial

1 2 3 4 5 6 7 8 9 10 1112 1314 1516 1718 1920

~ Indicates frame code presence within the given location

Fig. 6·6 Frame alignment by parallel searching. uniformly over a period of time. These bursts have a duration of a few milliseconds only, and are due to such terrestrial phenomena as lightning strikes, car ignition systems, etc. The number of steps required to lose alignment, that is the momentum of the flywheel, should be such that the worst error bursts are accommodated.

At this point it is appropriate to consider the described alignment processes quantitatively.! We have already identified the following parameters:

• The number of digits used to specify the FA W

=

F

1 H. Haberle, "Frame Synchronization PCM Systems," ITT Electrical Communications, voL 44, 1969, p. 280; and O. Brugia and M. Decina, "Reframing Statistics of PCM Multiplex Transmission," Electronic Letter, voL 5, no. 24, 1969, p. 623.

124 Multiplexing

stream one frame later before continuing the search. Since we may assume that there is no correlation between the test and check cycle in the case of imitations, then P(F)xN tests need to be made before the authentic FA W is detected.

The time taken to discard each imitation T equals the time occupied by one frame;

provided, of course, a second imitation does not occur exactly one frame after the first. The probability of a second imitation not occurring is given by S(F), thus the time spent locking to nonrepeated imitations TI is given by

P(F)xN

T1=

-S(F) frame rate ^(6.3)

We shall assume that multiple imitations spaced at one-frame intervals do not occur. In this case the total frame search time TF is given by

TF = TI

+

time spent slipping xN digits TF

=

¹ (P(F)XN

+

x)

frame rate S(F) (6.4)

If the synchronization word of length F digits is detected in purely random data, then the probability of a logical 1 or a logical

a

occurring at each time slot is 0.5.

Thus the probability of a sequence of F digits simulating the FA W is given by

P(F) = (0.5)F=

J..

_2F (6.5)

Substituting Eqs. (6.2) and (6.5) into Eq. (6.4) and rearranging terms gives:

TF= x

(N

- - + 1

)

frame rate 2 F - 1 ^(6.6)

This is an important result and is used extensively in determining the adequacy of proposed frame formats, from the alignment point of view. The curve defined by Eq. (6.6) is plotted in Fig. 6-7, where x has been assumed equal to one; and the FA W length Fis expressed in terms of a, the fraction of the total transmitted informa-tion used for synchronizainforma-tion. Therefore,

a=-F

N (6.7)

The plotted curves exist between two boundaries. The upper boundary defines the limiting case where only one digit per frame is given to synchronization F

=

1;

alignment cannot be achieved for values of F less than one. The lower boundary indicates that the shortest possible synchronization time must be at least equal to the time occupied by one frame. A shorter time is not possible since we have assumed x equal to unity.

Analysis of Fig. 6-7 leads us to the following generally valid conclusions:

1. The alignment time decreases as the percentage of digits given to synchroniza-tion increases (frame length

=

constant).

2. The alignment time is dependent on the frame length if the percentage of digits given to synchronization remains fixed. This is particularly true for small values of a.

Synchronous Time Division 125

Frame length, in bits (N)

Fig.6-7 Approximate mean synchronization time as function of the frame length. (From H. Haberle, "Frame Synchronization PCM Systems," ITT Electrical Communications, vol. 44, no.

4, 1969.)

3. The alignment time has a minimum value corresponding to some particular value of frame length (a

=

constant).

Suppose that a frame format is required for the transmission of PCM coded voice signals. Normally, sUbjective testing must first be carried out to determine a suitable value for the frame alignment time, say 2 ms. The smallest value of a that satisfies the required alignment time may then be read directly from one of the curves shown in Fig. 6-7. The minimum value of the selected curve defines the optimum frame length, while the optimum length of the FA W is obtained using Eq. (6.7).

Im Dokument and DIGITAL TRANSMISSION SYSTEMS (Seite 135-140)