Development of the “software approach”

In this chapter we discuss a receiver with a baseband processor implemented on a general processor, which is usually referred to as a software receiver. GPS software receivers originated from the concept of software-defined radio (SDR), which appeared some time before 1995 in the communication field [1].

In fact, almost from the beginning all GPS receivers were SDR receivers in a general sense. An SDR receiver, as it is defined by Joe Mitola who created the SDR concept, is one that can be reprogrammed and reconfigured through software.

In the GPS field, the concept of the software receiver was assumed to be somewhat different from SDR. It originated in works by Akos [2] and Tsui [3]. The GPS software receiver concept is narrower than that of SDR in the sense that all signal processing is implemented completely in the software. This approach provided a unique perspective on our understanding of GNSS receivers and sparked a great deal of research in the receiver field that was previously available only to receiver manufacturers and large research labs. We discuss GNSS receivers from the perspective of a general SDR concept in Chapter 10.

From Cold War competition to a business model

The development of global satellite navigation was sparked by the Cold War competition between the USA and the USSR, which led to the birth of GPS and GLONASS.

The concept of satellite navigation was created in the 1960s. In 1963, Aerospace Corporation in the USA began a study on a space-based satellite navigation system. At that time, the concept of GPS had already been developed [1]. By the mid 1960s, a similar research program had started in the Soviet Union.

In a few years, both programs resulted in first satellite launches. In May 1967, the USA launched the first navigation satellite for the US Navy satellite system Timation. This satellite system provided a foundation for GPS. In November of the same year, the USSR launched the first Soviet navigation satellite, Kosmos-192, which transmitted navigation signals on 150 and 400 MHz.

In 1973, the NAVSTAR GPS program began, and in the following year the first NAVSTAR satellite was launched. The first GLONASS satellite, Kosmos-1413, was launched nine years later, in 1982. GLONASS started to be used by the international geodetic community in 1987.

The Global Navigation Satellite System comprises a constellation of satellites and a ground segment that determines the satellite coordinates. The main idea behind GNSS is to measure distances between satellites and users located on the surface of the Earth or in the lower atmosphere.

Satellites move around the Earth along precisely known orbits, so we can define a satellite’s position precisely at any given moment. GNSS satellites transmit signals on frequencies between 1 and 2 GHz. These signals can be received by using a GNSS receiver. When the receiver acquires the satellite signal, the user can estimate the time required for the signal to propagate to the user from the satellite. By referring to information about satellite orbits and measured distances to the satellites, a user can calculate receiver position as an intersection of four spheres in the four-dimensional space-time continuum. If the receiver time could be perfectly synchronized with the system or satellite time frame, only three satellites would be required to determine receiver position in three-dimensional space (Figure 3.1).

Foreword by Glen Gibbons

The Law of Unintended Consequences – case in point: the mandate for enhanced 911(E911) services for mobile devices.

In 1996, the Federal Communications Commission (FCC), a US regulatory agency with broad powers over telecom providers and services, issued its first report, order, and notice of proposed rule-making (NPRM) regarding E911. The FCC action sought to require wireless telephone companies to be able to report automatically the location of an emergency caller.

This initiative proposed to bring to the rapidly expanding wireless space a requirement previously established for wireline providers. Unlike telephones at fixed locations, the whereabouts of a mobile phone was not readily known in emergencies, often not even to the callers themselves.

In issuing the NPRM, however, the Global Positioning System – let alone other GNSS systems – was not on the minds of the FCC commissioners. Indeed, if FCC staff and officials were aware of GPS in 1996, which had only reached full operational capability the year before, it was probably as the precise timing technology providing synchronization to wireline and some wireless networks.

No, in 1996, the FCC assumed that the positioning solutions for E911 would arise from within the networks themselves, using such techniques as angle of arrival (AOA), time of arrival (TOA), and time difference of arrival (TDOA).

A GNSS signal is transmitted from a satellite in order to measure the distance between the satellite and a receiver. There are four GNSS today: GPS, GLONASS, Galileo, and BeiDou. Each GNSS has its signal transmitted on specific radio frequencies. In this book we mainly consider single-frequency devices working with frequencies in the L1 band. The reasons for this are discussed in Chapter 10. The L1 signals for all current navigation satellite systems are shown in Table 2.1. Figure 2.1 shows how the signal frequency bands are distributed. The signals on these frequencies share some specific features, which we consider in this chapter. The frequencies for the GNSS L1 signal are slightly different, but this difference is not large enough to cause any variation in their error budget. For readers interested in the position of GNSS signals in the overall electromagnetic wave spectrum, the signal description from an electromagnetic theory point of view, and the fine aspects of signal propagation through the atmosphere, which may be derived from consideration of electromagnetic theory, such as signal scintillation theory and models, we recommend [1].

GNSS signals

The description of GNSS signals is given in the corresponding Interface Control Documents (ICD): for GPS L1/L2 in IS-GPS-200 [2], for GPS L1C in IS-GPS-800 [3], for GLONASS L1/L2 [4], for Galileo [5], and for BeiDou [6].

Common approach for receiver design

In Chapter 6 we discussed a “software approach” to GNSS receivers in comparison with a traditional “conventional” approach. In this chapter we consider a common approach taken in the implementation of a receiver, or more precisely in the implementation of a baseband processor. The “common components” refers then to the realization of those components, that are independent of the “conventional” or “software” approach. For example, a realization of an RF front end does not depend on whether a receiver is implemented with either a “conventional” or “software” approach in mind. The same is true for a navigation processor, as its implementation is always via software.

The difference between the “conventional” and the “software” approaches is that in the latter case the baseband processor is implemented in software on a general processor. This led to a definition of the “GPS software receiver,” which is a more narrow definition than software-defined radio (SDR). We discuss the details in Chapter 10, Section 10.3. The software approach [1] effectively allowed researchers in the GPS field to look at the receiver from a different perspective. It was essential in order to change the approach to receiver development. It has also introduced a set of new (for this area) instruments, in particular fast Fourier transform.

Digest of GNSS receiver operation

A GNSS receiver estimates position by measuring distances to a few satellites. When it measures the distance to the satellite, it in fact measures a signal propagation time from the satellite to the antenna. The satellite signal bears a time mark, which indicates when the signal was transmitted.

First, we look at the GPS L1 C/A signal. The signal can be considered to consist of three layers, namely the carrier layer, the code layer, and the navigation data layer (see Figure 5.1). These three layers have different time resolutions. Other signals may have additional layers. The GLONASS L1 SP signal, for example, has an additional meander sequence. Galileo, BeiDou, modernized GPS, and GLONASS have additional code layers. The length of the navigation message bit for the GPS L1 C/A signal is 20 ms. One can multiply this time interval by the speed of light to calculate the length of the navigation bit. For a GPS L1 C/A signal, the code sequence has 1023 bits, and this repeats itself each millisecond. For mobile devices, we are mostly interested in code positioning only. The 1 ms time is approximately equal to 300 km. The length of one code chip is therefore 300 km divided by 1023 code chips, i.e. about 300 m. In order to achieve positioning accuracy of a few meters, a receiver must be able to measure the code phase with an accuracy of one-hundredth of a code bit. A receiver can measure a code phase by aligning the incoming signal from a satellite with an internal code replica.

In the previous chapter, we described LP and illustrated its application to solve some interesting problems in wireless networks. In this chapter, we describe convex programming [11], which is a popular tool to solve a wide range of problems in wireless networks. In terms of problem space, LP can be viewed as a special case of convex optimization. To facilitate our description, we define the following terms:

1. Convex set: A set is convex if for any two of its elements z1 and z2 and for any λ ∈ [0, 1], λz1 + (1 − λ)z2 is also an element of this set. For example, the set {(x, y): x2 + y2 ≤ 1} is a convex set but the set {(x, y) : 1 ≤ x2 + y2 ≤ 2} is not a convex set.

2. Convex and concave functions: A function f (x) is a convex function if for any x1 and x2 and any λ ∈ [0, 1], f (λx1 + (1 − λ)x2) ≤ λf (x1) + (1 − λ)f (x2), where x can be a single variable or a vector of variables.

Problem complexity vs. solution complexity

The previous two chapters focus on developing optimal polynomial-time solutions following formal optimization methods from operations research (OR). For some problems, such an approach may not be always effective, and could lead to nonpolynomial-time solutions. For these problems, a customized approach following algorithm design from computer science (CS) could be more effective and lead to a polynomial-time solution.

It is important to distinguish a (solution) algorithm's complexity from the underlying problem's complexity. A problem's complexity determines the potential complexity of any algorithm that is designed to solve this problem. That is, for a problem not in P, unless P = NP, any algorithm that can find an optimal solution to this problem must have nonpolynomial-time complexity. In contrast, if an algorithm (design to solve the problem) has a nonpolynomial-time complexity, we cannot claim that this problem is not in P. Another algorithm designed by someone else may well solve the problem with a polynomial-time complexity.

In this chapter, we illustrate the above approaches and ideas with a case study. This case study is concerned with an optimal relay node assignment problem that arises in cooperative communications (CC) [139]. We first formulate the problem as a mixed-integer linear programming (MILP), following OR's optimization approach.