## 3.2. Conventional Pulse-Detection Techniques## 3.2.1. Energy DetectorsEnergy detectors are simple, noncoherent receivers that detect the energy of a signal and compare it with a threshold level to demodulate the data bits. Figure 3-1 shows the block diagram of an elementary energy detector receiver. ## Figure 3-1. Noncoherent energy detector receiverAs shown in Figure 3-1, energy detector receivers are composed of a squaring device, followed by a finite integrator and a decision threshold comparator. If the signal is present, its energy is calculated by squaring the signal. Once this energy passes a certain threshold, the data is demodulated as a digital bit 1. Consequently, if the data is not present or its energy does not pass the threshold, the received data will be demodulated to 0. ## 3.2.2. Classical Matched FiltersThe classical matched filter is a simple and optimal method for detecting a signal in random noise based on the correlation process. Before we go into the details of CMFs, it's worth explaining what correlation is. Correlation is a mathematical operation that provides a measure of similarity between two signals. This technique is used often in all types of pattern-recognition and signal-processing problems. The basic idea of correlation is to multiply the two waveforms at different points in time and to find the area under the curve formed by multiplication using integration in finite time. Equation 3-1 shows the mathematical expression of the correlation function. Equation 3-1 where the two signals being compared are x(t) and y(t), t is the time shift to provide sliding of y(t) on x(t), and R ## Figure 3-2. Classical matched filter block diagramAs shown in Figure 3-2, classical matched filters perform the correlation operation on the received signal r(t), which comprises the transmitted signal s(t) and channel noise w(t). The correlation operation is achieved by multiplying the received signal with a predefined template (similar to the transmitted signal), s(t), and then integrating over a finite period of time. This process maximizes the received signal's signal-to-noise ratio (SNR) and detects the desired signal from the background random noise. The following equations illustrate the matched filters operation mathematically. Equation 3-2 Equation 3-3 Equation 3-4 Expanding the integral in Equation 3-3 produces two terms in Equation 3-4. The first term represents the signal energy, E Therefore, when the filter is matched to the shape of the transmitted signal, the output of a matched filter provides sufficient statistics to detect signals in the presence of noise. It's important to emphasize that matched filters are optimal solutions only for detecting signals in the presence of additive white Gaussian noise (AWGN).
Equation 3-5 Assuming that User 1's signal is the desired signal, s Equation 3-6 Equation 3-7 As shown in Equation 3-7, although we can ignore correlation between the desired signal and random noise, the correlation between s |

Ultra-Wideband Communications: Fundamentals and Applications

ISBN: 0131463268

EAN: 2147483647

EAN: 2147483647

Year: 2005

Pages: 93

Pages: 93

Authors: Faranak Nekoogar

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