UWB system based on energy detection of derivatives of the Gaussian pulse

Abstract

A new method for energy detection ultra-wideband systems is proposed. The transmitter of this method uses two pulses that are different-order derivatives of the Gaussian pulse to transmit bit 0 or 1. These pulses are appropriately chosen to separate their spectra in the frequency domain. The receiver is composed of two energydetection branches. Each branch has a filter which captures the signal energy of either bit 0 or 1. The outputs of the two branches are subtracted from each other to generate the decision statistic. The value of this decision statistic is compared to the threshold to determine the transmitted bit. This new method has the same bit error rate (BER) performance as energy detection-based pulse position modulation (PPM) in additive white Gaussian noise channels. In multipath channels, its performance surpasses PPM and it also exhibits better BER performance in the presence of synchronization errors.

M-ary energy detection of a Gaussian FSK UWB system

“…The longer integration interval will capture more energy. Due to the randomness of the channel parameters, there is no direct equation to calculate the value of λ [4]. We can follow the method in [4] to achieve the value of λ.…”

“…Due to the randomness of channel parameters, there is no direct equation to express ρ according to ε [4]. We can follow the method in [4] to achieve the value of ρ. The SER must be averaged over many channel realizations.…”

“…If the decision variable is greater than decision threshold, the transmitted bit is 1, otherwise it is 0. The abovementioned is the brief description of the transmitter and receiver of the energy detection GFSK UWB system in [4]. In this paper, we will develop the M-ary system as follows: The transmitter of the M-ary system is…”

“…Before we develop the M-ary Gaussian FSK system, we will briefly summarize the system model of binary modulation in [4]. The Fourier transform X f and center frequency f c of the kth-order derivative are given by where k is the order of the derivative and f is the frequency.…”

“…When UWB signals pass through the channel, the long channel delay leads to a very large 2TW value and Gaussian approximation can achieve accurate result. The application of Gaussian approximation in energy detection UWB systems can be seen in [2][3][4][9][10][11][12][13][14]. The chi-square variable can be approximated as Gaussian variables [4,15].…”