Evaluación del prototipo físico

The research design (types of studies undertaken) and the methodology followed in this thesis are subsequently discussed.

1.5.1

Research design

1.5.1.1 Theoretical and empirical analyses

The design of new detection and estimation algorithms require both mathematical analysis and empirical tests or numerical evaluation of components of these algorithms. The eval- uation of the detection and estimation performances, and the computational complexities also require mathematical and numerical analyses.

1.5.1.2 Statistical modelling

Development and evaluation of the algorithms to be implemented in the intercept re- ceiver require statistical models of the transmitted data and noise. For simplicity of mod- eling and algorithm development, it will be assumed that the data is uniformly and the noise normally distributed [7, 23]. Data and noise sequences can be generated experimen- tally using established software implementations of pseudo-random sequences, such as the Mersenne-Twister pseudo-noise (PN) generator implemented in the GNU scientific library (GSL) [24].

1.5.1.3 Computer simulation

Closed-form mathematical analysis of digital communication techniques and algorithms is often not possible due to the level of complexity involved [5, 25]. Monte-Carlo computer simulation provides a solution with a high measure of control, which can be used to predict the performance of communication and receiver systems in the real world under different scenarios. The approach followed in this thesis to determine the performance of each detection algorithm and the effects of several parameters such as the SNR relies on Monte-Carlo analysis of computer models (and mathematical analysis where applicable), which include the receiver architecture, detection algorithms, and channel effects.

Figure 1.5: Software simulation model of the communication system and intercept re- ceiver.

1.5.2

Research methodology

The research design was executed mainly through computer simulation. The DSSS com- munication platform and intercept receiver were implemented in C using the basic linear algebra subprograms (BLAS) and GSL libraries [24]. Using this lower-level programming approach provides an execution speed advantage, as performance evaluation of digital communication systems typically requires a very large number of data samples in order to obtain reliable statistics [25].

1.5.2.1 Software simulation model

The baseband simulation model of the DSSS communication system and single-channel intercept receiver shown in Fig. 1.5 were used to evaluate existing and newly developed detection and estimation algorithms. Several assumptions are made in the model to sim- plify the design, including the fact that no carrier is used and only additive white Gaussian noise (AWGN) channel effects are considered (see also Appendix A).

The data generator shown in Fig. 1.5 produces a binary phase shift keying (BPSK) data signal d(t) with uniformly distributed samples with values _±1. The data is spread by multiplying d(t) with the spreading code c(t), and the result is amplified by a factor ks

to produce the spread spectrum signal xs(t).

are amplified by a factor kn to produce the noise signal xn(t). AWGN is thus introduced

by adding xn(t) to xs(t) to produce the received signaly(t). The values ofks and kn are

chosen according to the desired SNR (at the input of the receiver) defined as

SNR = k 2 s k2 n . (1.1)

The intended DSSS receiver recovers an estimate ˆd(t) of the original data from the received signal y(t) using a synchronised copy of c(t). To confirm that the DSSS transmitter and receiver structures are implemented correctly, the error probability Pe is calculated by

comparing d(t) with ˆd(t) over a range of SNR values. The measured Pe vs. SNR is then

compared with the theoretical performance curve of BPSK DSSS in AWGN, which can easily be derived mathematically [26].

The intercept receiver executes the detection or estimation algorithm under evaluation using the received signaly(t) as main input. Other possible inputs include the transmitted DSSS signal xs(t), the correct value of a parameter to be estimated θ, and the detection

threshold γ. The performance indicators provided as outputs are the probabilities of detection PD, false alarm PF A, and correct estimation Pce.

1.5.2.2 Detection performance

Following the NP approach [5], PD can be measured (experimentally or in simulation)

over a range of SNR values using the threshold γ, calculated from a set PF A value. PF A

can also be measured and compared with the set value. The resultant PD vs. SNR curve

can then be compared with reference performance curves, such as energy detection (ED).

To calculate the optimal value for γ, perfect knowledge of the data and noise statistics are assumed. Prior knowledge of whether xs(t) is transmitted or not, is also assumed to

calculate PD and PF A.

1.5.2.3 Estimation performance

Estimation accuracy is defined in terms of the difference or error between the actual parameter valueθ and the estimated parameter value ˆθ[15]. A similar measure, the prob- ability of correct estimation value Pce, was used in this thesis to evaluate the performance

Table 1.2: Parameter summary to evaluate different scenarios.

Parameter Value/Type

Channel effect AWGN Modulation BPSK

Spreading code Barker-11, m-sequence-63, Walsh-64 SNR range As required such that PD, Pce ∈[0,1]

PF A 0.1 to 10−6

Receiver architecture Single channel

1.5.2.4 Computational cost analysis

Computational complexity can be derived mathematically in terms of the total number of elementary arithmetic operations (+,₋,_×,_÷), or the equivalent number of additions and multiplications, required to execute an algorithm [27]. The execution time (or equivalently the number of clock cycles) can also be determined in software.

1.5.2.5 Scenario selection

To evaluate different detection and estimation algorithms, a number of different scenarios must be considered. Each scenario depends on environmental effects, the type of DSSS transmission, and the configuration of the intercept receiver.

Table 1.2 contains a summary of the parameters and their values or types that are con- sidered in this thesis. Representative spreading code types used in communication sys- tems [26, 28] are considered, including a short code (Barker-11), and longer orthogonal (Walsh) and non-orthogonal (m-sequence) codes. ThePF Arange is chosen to include large

values that can easily be verified experimentally, and smaller values in line with practical detection system design [5].