With recent developments in modern science technology, various types of sensors have been widely used in industry, agriculture, aerospace, aviation and other fields, to allow the production process a high level of automation. However, the interference suppression in the application of wireless sensors is a very difficult problem, which affects the control precision and accuracy of the whole system. Therefore, a variety of anti-interference measures to improve system stability and accuracy are inevitable, which has been a subject of intense research. The usual methods include shielding technology, filtering technology, isolation measure and grounding technology, etc. In some special cases, even more complicated anti-interference methods [1–4] are needed, but the performances are still not satisfactory, for example, Reference [1] proposed an interference avoidance frequency assignment method IAFA, Reference [2] studied explicit definitions of interference and proposed various models of interference to ensure the reasonable anti-interference methods, Reference [3] used the second order vibration mode to solve the co-channel interference in the silicon resonant beam microsensor, Reference [4] proposed a novel measure with nonsymmetrical excitation to eliminate the co-channel interference, etc.

This paper considers this problem in physical layer directly in order to remove the complicated anti-interference module. In our research, we have found that the Ultra Narrow Band (UNB) system [5,6] based on Extended Binary Phase Shift Keying (EBPSK) [6] modulation presents good performance of anti-interference, which may have very wide applications, and can realize high data rate transmission within an ultra narrow bandwidth. On the other hand, its modulated waveforms corresponding to “0” and “1” have a very tiny difference, if demodulating by using classical correlation detector or matched filter, it has even high demand on input SNR. In order to improve the efficiency of the EBPSK signal as much as possible, the special detection filter method [7,8] must be sought, which can amplify the signal characters as much as possible and remove utmost noise. However, traditional filter theory and conventional filter [9] design can hardly satisfy this demand. For example, after the EBPSK modulation signal is filtered by narrow classical Infinite Impulse Response (IIR) or Finite Impulse Response (FIR) digital filters, the carried information is also removed, and just pure sine wave as carrier remains in the filter center frequency. [8] proposed the impacting filter based on zero-pole point, which can cooperate with tiny waveform difference of EBPSK signal to transform the phase jumping information into amplitude impacting. Because of the special characteristics of the EBPSK modulation waveform, the co-channel interference can be thought of as useful information to add in the modulation waveform, and have no effects on the BER performance, i.e., EBPSK system itself has the better performance in canceling co-channel interference.

All in all, aiming at the interference problem in wireless sensors networks, this paper proposes a simple solving scheme of physical layer, which is based on EBPSK modulation with ultra narrow bandwidth. Simultaneously, the anti-interference performance of the EBPSK system itself is mainly discussed. When the initial phase of the co-channel interference is small, the EBPSK system has good anti-interference characteristics, which has been analyzed by intuition and proved by simulation results. While with the increasing of the initial phase, the anti-interference performance of system itself decreases, so the usual anti-interference methods can be considered to solve it.

The paper is organized as follows. The EBPSK modulation and the analysis of the related parameters are introduced in Section 2. Section 3 presents the scheme of EBPSK transmission system. The effects of co-channel interference are analyzed and verified experimentally in Section 4. Then BER simulation results are given in Section 5. Finally, Section 6 gives some conclusive remarks.

EBPSK [6] is a modulation method with high frequency spectra efficiency, which is defined as following: (1) g 0 ( t ) = A   cos   2 π f c t , 0 ≤ t < T g 1 ( t ) = { B   cos ( 2 π f c t + θ ) , 0 ≤ t < τ , 0 ≤ θ ≤ π A   cos   2 π f c t , τ ≤ t < Twhere g₀ (t) and g₁ (t) represents the waveform modulated by “0” or “1”, respectively, T = 2π N/ω_c = NT_c is the symbol width of data, T_c = 2π/ω_c = 1/f_c is the carrier cycle, namely T lasts N ≥ 1 cycles of carrier; T is the symbol width of data; θ is the phase jumping angle or modulating angle, and τ is the time length of the θ jumping lasting. The paper just considers the case of A = B = 1.

In EBPSK modulation, the modulated waveforms corresponding to “0” and “1” have a very tiny difference, and the most parts of the waveform are sine components, therefore, having compact power spectra [10], i.e., high throughput efficiency, and is difficult to detect. The problem faced is how to design a UNB receiver filter to save or improve phase jumping information. The traditional IIR or FIR filter can erase the phase information, so that “0” and “1” information cannot be distinguished. A special UNB impacting filter [8] will be used in EBPSK system, which can transform the tiny phase information into the higher impulse amplitude at the phase jumping point corresponding to code “1” than the amplitude of “0” [11], that is to say, amplify the signal characters as much as possible and remove the maximum noise and other interferences. Consequently, in the case of precise synchronization, we can use directly amplitude detection at the jumping point [12] or energy accumulation of tailing to judge “0” and “1”, which causes the structure of receiver much simplifier than that based on phase locked loop [6]. Therefore, the UNB transmission system can be digitally implemented, since the EBPSK has covered both the traditional BPSK and most UNB modulations, which is beneficial for chip integration.

The modulation waveform corresponding to code “1” can be regarded as the superposition of all-zero sequence (i.e., pure sine wave) and jumping sequence (i.e., just existing signal in EBPSK jumping point), as shown in Figure 1. In addition, the special detection filter used in EBPSK system is a linear filter, so superposition principle can be used. For simplicity, this paper takes the filter having one conjugate pole and one conjugate zero points as an example to analyze. Letting the decomposed sequences pass the filter, we can obtain the response shown in Figure 2. Obviously, the jumping response and all-zero response have almost the same phases, which enhance each other, so that the amplitude impulse is produced.

Reference [8] proposed the IIR narrowband band-pass filter with multi-poles and one zero, which can produce even much higher impact in phase jumping point than that with one pole and one zero as analyzed above, much narrower bandwidth, and greatly improve output SNR. Especially, in the case of signal submerged by noise, i.e., SNR < 0, the modulation information is emphasized with impacting shape, therefore, in the following real simulation, the filter having three conjugate poles and one conjugate zero point is taken as an example, and the transfer function can be written as following: (2) H ( z ) = 1 − 1.61817331       85991785   z − 1 + z − 2 1 + ∑ i = 1 6 a i · z − iwhere a₁ = −4.5781931992746454, a₂ = 9.6546659241157258, a₃ = −11.692079 480819313, a₄ = 8.5756341567768217, a₅ = −3.6121554794765309, a₆ = 0.70084076 00731199

In this section, computer simulation results of bit error rate (BER) are given to illustrate the good anti-interference characteristics of the EBPSK system, where the transfer function of the filter is chosen as (2), i.e., simulations are based on the filter having three conjugate poles and one conjugate zero. On the other hand, just co-channel interference is considered in this paper. In our simulation, the other parameters are chosen as follows: f_c = 930kHz, N = 20, K = 2, A = B =1, θ = π.