M-ary energy detection of a Gaussian FSK UWB system
© Cui and Xiong; licensee Springer. 2014
Received: 9 December 2013
Accepted: 25 April 2014
Published: 29 May 2014
The energy detection M-ary Gaussian frequency-shift keying (FSK) system is proposed in this paper. The system performance is analyzed in additive white Gaussian noise channels, multipath channels, and in the presence of synchronization errors. The numerical results show that the M-ary modulation achieves the higher data rate than the binary modulation. However, it also results in performance degradation.
Energy detection (ED) is a popular technology in ultra-wideband (UWB) communication systems. When compared to Rake receivers, ED has as many advantages, such as simple receiver structure [1, 2], robustness to synchronization errors, and no channel estimation requirement. The popular ED schemes include on-off keying (OOK) and pulse position modulation (PPM) . In our previous publication , a new ED scheme based on using different-order derivatives of the Gaussian pulse was proposed. This new scheme is called Gaussian frequency-shift keying (GFSK) energy detection UWB. It was proved that this new scheme has better bit error rate (BER) performance than an energy detection PPM UWB system in multipath channels and in the presence of synchronization errors.
In , the energy detection Gaussian FSK system is based on binary modulation so we extend the research into M-ary modulation in this paper.
Although there exist some M-ary UWB methods, our method is different to these methods. In , the M-ary modulation is achieved by using the orthogonality of modified Hermite polynomials . Where n is the order of the polynomials and n=0,1,|…, and −∞<t<∞. In , the waveform is obtained from the Battle-Lemarie wavelet , where g l and c k are coefficients, and β n (t) is a B-spline function of order n. In , the author uses the pulsed sinusoidal waveform as carrier to realize the M-ary FSK modulation. In this paper, we will construct the M-ary FSK waveforms using different order derivatives of the Gaussian pulse. The spectra of these different-order derivatives of the Gaussian pulses are separated entirely in frequency domain so the orthogonality is achieved. Our M-ary FSK system still transmits baseband pulses without inducing carrier modulation. UWB is carrier-less system, so our method conforms to UWB regulation. At the receiver, the demodulation can be achieved by using filters with different passband frequencies to separate the pulses directly. This makes it very simple and easy to implement the demodulation procedure.
The structure of this paper is as follows: Section 2 introduces the system models. Section 3 evaluates system performance in additive white Gaussian noise (AWGN) channels. Section 4 evaluates system performance in multipath channels. The effect of synchronization errors on system performance is analyzed in Section 5. In Section 6, the numerical results are analyzed. Section 7 is the conclusion.
2 System models
where p1(t) and p2(t) denote the pulses of different-order derivatives with normalized energy and E p is the signal energy. The j th transmitted bit is denoted by b j . The frame period is denoted by T f . The modulation is carried out as follows: when bit 1 is transmitted, the value of b j and 1−b j are 1 and 0, respectively, so p1(t) is transmitted. Similarly, the transmitted pulse for bit 0 is p2(t). The above transmitter considers a single user only, and a bit is transmitted once. The receiver includes two branches, and each branch is a conventional energy detection receiver. The only difference between the two branches is the passband frequency ranges of filters. The filter in the first branch is designed to pass the signal energy of p1(t) and reject that of p2(t), and the filter in the second branch passes the signal energy of p2(t) and rejects that of p1(t). Finally, the captured energies of two branches are subtracted to generate a decision variable and then this variable is compared with decision threshold to determine the transmitted bit. 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 .
3 SER performance in AWGN channels
3.1 SER performance of GFSK in AWGN channels
Equation 18 is the SER of binary GFSK in AWGN channels, and it is the same as that in .
4 SER performance in multipath channels
where δ(t) is the Dirac delta function, and αk,l is the tap weight of the k th component in the l th cluster. The delay of the l th cluster is denoted by T l and τk,l is the delay of the k th multipath component relative to T l . The phase ϕk,l is uniformly distributed in the range [ 0,2π].
Equation 23 is SER of binary GFSK in multipath channels, and it is the same as in .
5 Performance analysis in the presence of synchronization errors
It is the same as that in .
6 Numerical results, analysis and discussions
The SER equations for binary GFSK are proven validated in . From the above analysis, we can know that the M-ary SER equation can be converted to the SER equation for binary modulation when the value of M=2. So, the SER equations of the M-ary modulation are general equations which can be applied to any M-ary modulation including the binary modulation. In the following, we will compare the performance of binary and M-ary modulation using both the simulated and analytical SER curves. We use the SER equations to generate analytical SER curves directly. In this paper, we use 4-ary as an example to compare with binary modulation. We consider the pulses in Figure 1. The filter bandwidth is 1.66 Ghz.
From above numerical analysis, we can know that binary GSFK achieves a consistent 0.4-dB improvement under different integration intervals T0 or synchronization errors. However, the 4-ary can deliver a speed that is twice that of the binary modulation. It is significant that the 0.4-dB loss of performance can achieve a double speed. There is always a trade-off between binary and M-ary modulations. The M-ary can deliver higher data rate but it causes performance loss. The designers should consider the actual applications to decide what kind of modulation to choose. If the speed is the primary requirement, the M-ary is a better option. If the performance is the most important condition to consider, binary is more suitable.
The implementation of high-order derivatives of the Gaussian pulse can be achieved by two approaches. The first one is the digital approach. The discreet points of waveforms are stored in the memory of application-specific integrated circuit (ASIC) or field programmable gate array (FPGA) chips. These points are sent to digital to analog converter (DAC), and then the DAC outputs the analog waveform of the pulse. This approach is straightforward and easy to achieve the waveform accurately. UWB pulses usually have large bandwidth, so it needs high sampling rate of the digital signal to recover the analog signal. The DAC needs to work in high clock rate. The burden of digital implementation is added on DAC. If we implement the pulse waveform by analog approach, it will not need high-speed DAC. The system will send the control signal to activate the corresponding pulse generator respective to the specific data. The design of analog pulse generator is not so straightforward as the digital approach. There are many analog research achievements on UWB pulse generators. In , a 7th-order pulse generator is proposed. In , the pulse generator arrives to the 13th order. The pulse generator in  can generate the pulse with a center frequency at 34 GHz. The higher the order of the pulse is, the higher the center frequency is. The pulse generator in  has the ability to generate pulse with higher center frequency than the range of 3.1 to 10.6 GHz set by FCC. These research achievements have already provided feasible solutions for analog implementation of high-order derivative of the Gaussian pulse. We do not provide any specific circuit design in this paper and it is left for the hardware engineers or researchers.
The M-ary energy detection GFSK UWB system is proposed. The system performance is analyzed in AWGN channels, multiple channels, and in the presence of synchronization errors. The M-ary system can achieve higher data rate than binary system. However, it causes the performance loss.
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