and duration reduces the signal power spectrum density, hiding it under the background spectrum of the natural thermal noise.

Example 3.2.1. Consider the system transmitting sporadically and rather infrequently one of 64 messages using orthogonal signals. To provide error probability no worse than 10 3 it needs to use SNR around 7 dB per one bit, or 15 dB per 6-bit message (see Figure 2.9). Thus q2 is 15 dB and transforming the interceptor’s (voltage!) SNR (3.9) into decibels we have:

ðqi ÞdB ¼ 2ðq2ÞdB 20 lg 2 10 lg WT

If the system employs spread spectrum signals with processing gain WT ¼ 1000 the interceptor’s SNR turns to be (qi )dB ¼ 6 dB or qi ¼ 1/2, which is not at all sufficient for reliable detection of the intended system’s presence on the air in one session. If, for instance, the interceptor tolerates a probability of false alarm of pf ¼ 10 3 then according to (3.7) the detection probability pd 5 10 3, i.e. is extremely small and exposes no serious threat to the intended system.

Finishing this section, note that the discussed advantage of spread spectrum is widely utilized today not only by the military or special services. The fact that a spread spectrum signal may be practically unnoticeable for the equipment that monitors the state of the radio air has serious implications for licensing policy. In particular, the range of commercial systems that may actively operate on the air without applying for a licence becomes broader, and in some regions special spectral zones are currently allocated for such licence-free use.

3.3 Signal structure secrecy

Continuing the line of the previous section, let us remember once more that the only reason for an interceptor to resort to such an ineffective detection instrument as an energy receiver is lack of information about the structure of the detected signal, i.e. its modulation law. As a result, the interceptor cannot process the signal in the manner used by the intended receiver (matched filtering). Of course, if the signal structure is not complicated enough and the interceptor is aware that it was chosen from only a few alternatives he may try them all. Appropriate equipment for doing so may be a bank of parallel matched filters or a single filter (several filters) reconfigured to fit the candidate signal structures serially in time, if the signal is known to be received for an adequate duration. Therefore, another aspect of the strategy of the intended system in its conflict with an interceptor consists in making a signal structure practically unbreakable.

A similar task is characteristic of military or commercial systems that do not tend to make the fact of their operation a mystery, e.g. if they function continuously, but are very keen to avoid unauthorized access to services addressed only to classified consumers, or forging of the transmitted information. The satellite-based global navigation system GPS is a convincing example of this kind. It has two positioning channels (see Section 11.2): open (or clear access, abbreviated C/A) and special (or protected, P). The signal transmitted over the second channel allows super-high precision of positioning, and the US government, which runs the system, does not permit unconditional access

to this channel. In order to protect it from unauthorized use some special measures are undertaken concerning the signal modulation.

In disciplines dealing with information security, the extent of data protection is measured by a number of competitive equiprobable keys, which an enemy cryptanalyst (eavesdropper) should try to crack the ciphertext, i.e. encrypted data. In application to the signal structure, each of those keys is just a modulation law, which is typically repeated with some period T. Suppose that a signal is built of chips (see the example in Section 2.7.3) on the basis of an M-ary alphabet, i.e. using M different symbols to manipulate chips. If the bandwidth allocated to the system is W then the total signal space has dimension measured as WT (ignoring bandpass doubling; see Sections 2.3–2.5), i.e. a modulation law may be thought of as being constructed of WT chips. It is clear, then, that MWT is the total number of possible modulation laws, i.e. competitive keys, and the system designer concerned with secrecy of the modulation format in the developed system should employ signals with rather large processing gain WT.

Example 3.3.1. The signal of the P-channel (P-code) in GPS is binary (M ¼ 2) with the bandwidth W 10 MHz. Its structure is quite regular and repeated with the period T ¼ 7 days. Being hidden under the thermal noise, this signal cannot be retrieved by symbol-wise reception and only knowledge of its fine structure permits it to be cleared with highest efficiency off the AWGN. To prevent an unauthorized interceptor from accessing the P-code, a secret binary key (W-code) is modulo 2 added to it, masking the structure of the resulting Y-code. A single symbol of the W-code spans 20 symbols of the P-code; therefore, to break this mask by a trial and error method, up to 2WT /20 alternatives should be tested. Since WT ¼ 7 86 400 107 > 1012, the number of tried keys is greater than 2 to the power of ten billion, which is fully beyond any imagination. For this reason the Y-code is believed to be unbreakable and no reports have emerged in nearly 10 years of its history on any successful cryptanalytical attack on it.

We conclude the section with another declaration on the advantages of spread spectrum: this technology is very conducive to cryptographic protection of a signal structure.

3.4 Electromagnetic compatibility

The problem of electromagnetic compatibility (EMC) is one of the most topical in modern wireless engineering. EMC implies friendly co-existence of different systems on the air despite each of them receiving not only its proper signal but also the signals of the other systems. Certainly, it is impossible to root out entirely mutual disturbance when several systems are operating simultaneously within a relatively small area. Any active system, i.e. emitting electromagnetic waves, inevitably affects all neighbouring ones and a system designer should try to minimize this potentially harmful influence.

There are two parties playing the EMC game. The first, which may be called ‘emanating’, tries to minimize the interference created by its emitted power to other nearby, so-called ‘susceptible’, systems [15]. The motivation for this is not only ethical