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The Galileo Code and Others

Working Papers explore the technical and scientific themes that underpin GNSS programs and applications. This regular column is coordinated by Prof. Dr.-Ing. Günter Hein.  Contact Prof. Hein at

GNSS signals might fairly be characterized as an enigma wrapped inside a conundrum. More than any others, two factors give the signals this quality: spread spectrum techniques and their code structure. The first hides the signals in a “cellar” below the thermal noise floor of the RF spectrum; the second disperses them into a long and apparently random sequence of digits. The advent of Europe’s Galileo system and introduction of new GPS signals stimulated a re-examination of the subject of codes, buttressed by advances in electronics that allowed new approaches to implementing codes in a GNSS receiver. This column explores the growing categories of codes, their production, and the qualities that make them suitable for use in GNSS systems. Along the way, we take a brief excursion to discover the surprising genesis of spread spectrum radio in the collaboration of a glamorous actress and an avant-garde pianist.

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Codes are a fundamental element in any code division multiple access  (CDMA) system such as GPS and Galileo, because these codes are the tool that enables a GNSS receiver to distinguish one satellite from another. In spite of their great importance, no great innovations have been made in the world of satellite navigation in this area — not since GPS used the Gold codes for the first time in its L1 C/A signal introduced nearly 30 years ago.

With GIOVE-A, however, the first Galileo test satellite is now in space. And, together with new signals and new technologies, new code concepts developed in recent years will appear in Galileo transmissions. Galileo will broadcast for the first time so-called random codes, which are codes optimized in a highly multidimensional space to make them look as random as possible.

But Galileo is not alone in bringing new concepts into the world of GNSS. Modernized GPS signals also use new structures of codes based on so-called Legendre sequences, which will be applied for the very first time in navigation.

Given the great importance that codes play in any GNSS system that relies on CDMA and more generally, on spread spectrum (SS) communications, SS techniques will be an important focus of this paper. This column, therefore, will begin by discussing various techniques that rely on codes and the history behind them. Then we will concentrate on the many possibilities that exist to generate pseudorandom codes, giving special attention to those code structures that GPS and Galileo will be implementing in the near future.

. . .

Spread Spectrum Communications
Spread spectrum radio communications stem from the work of Hollywood actress Hedy Lamarr and the pianist George Antheil who described in 1941 a secure radio link to control torpedos and received for that U.S. patent number 2,292,387. (See the sidebar, “Player Pianos, Sex Appeal, and Patent No. 2, 292, 387”.) Although the idea was not taken seriously at the beginning and was even forgotten, the scientific community rediscovered it in 1957 at the Sylvania Electronic Systems Division.

Today, spread spectrum radio has become one of the most important modulation techniques, covering completely different applications ranging from 3G mobile telecommunications, W-LAN, and Bluetooth to satellite positioning systems such as GPS and Galileo.

. . .

Not So Simple
The SS principle seems simple and evident, but its implementation is complex. In order to accomplish this objective, different SS techniques are available, but they all have one thing in common: they perform the spreading and despreading operation by means of a pseudo random noise (PRN) code attached to the communication channel. The manner of inserting this code into the transmitting chain before the antenna is actually what defines the particular SS technique in question.

. . .

Not So Random Noise
Codes are digital sequences that, in order to achieve the benefits that we have described, must be as long and as random as possible. That is equivalent to saying they must appear as “noise-like” as possible. This is of major importance because the robustness of the spreading and despreading operations depends on the quality of the code.

. . .

PRNGs: A Brief History
The first works on computer-based PRNGs were published in 1946 by John von Neumann, who proposed an approach for generating PRN codes, known as the “middle square method.” The idea of this method is as follows: take any number, square it, remove the middle digits of the resulting number as your “random number,” then use that number as the seed for the next iteration.

. . .

Pseudorandom Noise Codes
Now that we have seen the broad palette of algorithms that exist to generate pseudorandom sequences, we will analyze the properties of the most commonly used codes in CDMA systems, paying special attention to those that GPS and Galileo use now or will use in the near future.

Because codes comprise a very wide field, only some of the most popular sequences are listed here, and only the first six families will be described in detail in this article. Of special interest, then, to CDMA-based systems are the following PRN codes:

•    Maximal length sequences or m-sequences
•    Gold Codes
•    Kasami Codes
•    Weil Codes
•    Random Codes – Memory Codes
•    Bent Codes and Bent-function Sequences

. . .

Codes are a fundamental element in any GNSS system. Indeed, the final performance a receiver will experience depends much on the quality of the selected family of codes. Gold codes and truncated codes have been the most used solutions in the past but in the last years with the optimization of GPS and the birth of Galileo radically different approaches with better properties have come into play. This is not a static field of study at all and a quick look in the literature shows that much work has been done and remains to be done.

As we have seen in this paper, optimizing codes is not an easy task. In fact, the desirable properties a family should present depend highly on the application the code is intended to serve. What use we will make of GNSS in the future is something that only time will tell, and thus the goodness of the codes for every certain application will definitely not be uniform.

For the complete article, including figures and graphs, please download the PDF at the top of the page.

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