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In order to satisfy the higher and higher demand for communication systems, an Extended Binary Phase Shift Keying (EBPSK) system with very high spectra efficiency has been proposed. During the research, a special kind of filters was found, which can amplify the signal characteristics and remove utmost noise,

With the development of the information society, there is higher and higher demand for communication systems. Therefore, how to transmit the information faster and better has become very important. Recently, high efficiency modulation technologies are receiving the attention by many researchers, especially Ultra Narrow Band (UNB) [

In wireless sensor networks [

During the research, we found that as a kind of UNB system, the Extended Binary Phase Shift Keying (EBPSK) [

The rest of this paper is organized as follows. In Section 2, a scheme for EBPSK- MODEM is introduced, of which the detailed derivation of BER performance is given, and also the SNR improvement performance is analyzed in Section 3. Then, Section 4 collects some simulation results, and conclusions are given in Section 5.

EBPSK modulation [_{0}(_{1}(

It is just the classical Binary Phase Shift Keying (BPSK) modulation, so is named as the Extended BPSK. _{c}_{c}_{c}_{c}_{c}_{c}

As we know, if
_{b}_{0} is the

However, if the same optimal BPSK receiver using traditional matched filter was utilized as the EBPSK demodulator, the BER performance would be much poorer since the difference in EBPSK modulated waveforms corresponding to “0” and “1” is very tiny and hard to detect, although in

In this section, the BER performance of the impacting filter based EBPSK receiver is analyzed in an AWGN channel.

The EBPSK modulated waveform corresponding to “0” is a pure sine wave, after passing the AWGN channel and the special impacting filter at the receiver, then the envelope _{0} of the filter output is with Rice distribution [_{0} is the amplitude of the filter output, ^{2} the noise variance, and _{0}(

A similar analysis can also be done aiming at code “1”. If we only consider those periods with phase jumping during _{1} still is Rice distribution, the corresponding pdf is:

This derivation of the BER is based on the special and linear impacting filter as given in _{1} > _{0}. Let _{1} = _{0} + Δ_{0} + _{0} and

Therefore, assuming that code “0” and “1” be transmitted with equal probability and the decision threshold be _{T}_{0}(_{1}(_{0} and _{1}, respectively, and _{1}(

We will now discuss in detail how to ascertain the parameters _{0}, ^{2} and _{T}

(1) The amplitude _{0} is evaluated as follows:

In EBPSK modulation and via Fourier transform:

Let the frequency response of the filter be

So the waveform in time domain is:
_{1} = ∠_{c}_{2} = ∠_{c}_{1} = −_{2}, and |_{c}_{c}

So _{0} = _{c}_{1} = (1+_{c}

(2) The variance ^{2} is evaluated as follows:

Let the _{0} / 2, measured in ^{2} at the output of the filter should be:

(3) The threshold _{T}

Based on the binary detection model, the sketch map of the detection performance illustrated by pdf is shown in _{T}_{0}) and _{1}), _{0}) and _{1}).

(4) The parameter

According to _{0}) and _{1}),

Among all the parameters discussed above, how to select

Conceptually, the maximum of _{0} could reach the peak, say ±20_{0} might be limited by filter design and waveform selection (such as _{0} is about two times of its background, so at this situation, we may roughly get the estimation as

In this subsection we will calculate the various signal to noise ratios (SNRs) so as to evaluate the EBPSK-MODEM.

(1)

Similar as _{0} / 2, then from the autocorrelation function
_{0} / 2 is measured in

Let
_{0} / 2 is the average

(2) SNR at the output of the impacting filter

The average SNR at the output of the impacting filter for bit “0” during _{c}_{b}_{b}_{b}_{b}_{0} / 2 is still the

Therefore, the gain in

From _{neq}

Similarly as

And the gain in

In this section, in order to verify the correctness of theoretical analysis, we compare the BER results calculated by the theoretical formula with one obtained by computer simulation, as in _{c}

According to the above results, the theoretical result and simulation result just have 1 dB difference in order to obtain the same BER performance, which is caused by the detection method and the choosing of the decision threshold in the simulation.

(1) The _{e−BPSK}_{e−EBPSK}

With the increasing of _{0}) and _{1}) becomes large, so the shaded area decreases,

With the decrease of ^{2}, although the peak distance of _{0}) and _{1}) remains unchanged, their shapes are narrowing, so the shaded area, or the minimum BER, decreases also.

Therefore, under certain conditions, the BER performance of the EBPSK modulation will outperform or be inferior to that of the BPSK modulation, and the spectral efficiency of the EBPSK system is much higher than BPSK.

(2) Substituting _{1} = 18_{0}, which implies that as long as we can obtain larger value of

To sum up, aimed at a UNB system, the EBPSK-MODEM, this paper has discussed the importance of the special impacting filter, deduced the BER formula of EBPSK system, analyzed the SNR improvement performance of impacting filter, discussed the choice of optimum decision threshold, and analyzed the reason or possibility for EBPSK to outperform BPSK both in spectral efficiency and in BER performance. Research on these special filters is underway, and a detailed introduction will be given in forthcoming papers.

The authors would like to thank the National Foundation of China (60872075), the Natural Science Foundation of Jiangsu Province (BK2007103), China Postdoctoral Science Foundation (20080441015), Jiangsu Planned Projects for Postdoctoral Research Funds (0802005B) and Southeast University Planned Projects for Postdoctoral Key Research Funds.

PSD of the BPSK and EBPSK modulations, all carrier peaks are normalized at 0dB.

(a) The amplitude-frequency response of an “impacting filter”. (b) The zoomed figure of (a).

The output of the impacting filter to the EBPSK modulated input.

The sketch map of the detection performance by pdf.

The BERs comparison between calculated by theoretical formula and obtained by computer simulation.