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The special impacting filter (SIF) with IIR structure has been used to demodulate ABSK signals. The key points of SIF, including the resonance circuit's high Q value and the “slope-phase discrimination” character of the filter sideband, are demonstrated in the paper. The FIR narrow-band bandpass filtering system, which can also provide the impact-filtering effect, is proposed. A dual carrier system of ABSK signals is designed with the proposed FIR filter as its receiver. The simulation results show that the FIR filter can work well. Moreover, compared to the traditional SIF, the proposed FIR filter can not only achieve higher spectral efficiency, but also give better demodulation performance.

With the rapid development of information technology, the traditional wireless communication systems which employ wasteful static spectrum allocation can no longer take full advantage of the spectrum. Meanwhile, the radio spectrum has become more and more complicated and fragmented. Therefore numerous efficient transmission techniques have been proposed to maximize utilization of the spectrum, which could also provide remarkable economic benefits [

The Asymmetry Binary Shift Keying (ABSK) modulation [

Let

Note that the frequency response depends on the distribution of zeros and poles. The numerator and denominator mean the vectors from the zeros and poles to the point

_{1} and _{1} are the modules of the vector respectively, ψ_{1} and θ_{1} are the angles of the vector respectively. Without loss of generality, the complex factors of zeros and poles are given by:

^{j}^{[(ψ}_{1} ^{+ ψ}_{2} ^{+…+ ψ}_{m}^{)−(θ}_{1}^{+θ}_{2}^{+…+θ}_{n}^{)]} is the phase.

With ω moving along the imaginary axis, the module and angle change as well, the relationship between module and phase could be explained by the following explanation. If the circuit has high Q value and the transfer function has a couple of poles and zeros adjacent to the imaginary axis respectively, that is:

The amplitude-frequency response reach a peak and the phase-frequency response decrease rapidly when the poles approaching the point ω = ω_{i}_{j}

So we conclude that the steeper transitional band of the amplitude-frequency curves, the steeper of the phase-frequency curves [_{d}

At present the SIR which has one or more conjugate zeros and multi-poles is adopted to be used as ABSK signal receiver. The zeros are located on the unit circle; the poles are close to the imaginary axis, so the IIR impacting filter has very high Q value and steep resonance peak, as well as high frequency selectivity. The ideal phase-frequency curve of the impacting filter has its steepest slope near the carrier frequency, so as to achieve differential effects on the ABSK signal phase. The tiny change of the carrier's phase can bring about obvious amplitude changes. For an ABSK signal, if the codes “0” and “1” have the same amplitude, the ABSK signal is a PM signal. When the frequency of the carrier is located between the zeros and poles,

Based on the above description, there are two key points for the impacting effect: the “slope-phase discrimination” character and the high Q value of resonance circuit. We know that the bandwidth of transmission signal is inversely proportional to the Q value, and thus a larger Q value can lead to narrower transmission bands and better circuit selectivity. Because the FIR narrow-band filter has natural steep transmission bands, we can infer that the ABSK signal's carrier frequency can be placed on the steepest slope of the transmission bands to obtain the “slope-phase discrimination” effect. The frequency response of the FIR narrow-band filter satisfies the condition of “slope-phase discrimination”, as shown in

In order to increase the transmission rate and restrain the inter-symbol and multipath interference, the practical communication system usually use the multi-carrier parallel transmission, such as OFDM, which decomposes the data flow to several sub-data flows, and thus the sub-data flows have much lower transmission rates. A multi-carrier ABSK communication system has been proposed in [

At the transmission end, the respective data bits of the data sequence (denoted T as the symbol period, 2R bps data rate) was alternately modulated on the carrier frequency _{1} and _{2}, respectively (denoted 2T as the new symbol period, R bps data rate). Set one sub carrier time-delay T to avoid the both carrier's “1” occurs simultaneously,

At the receiving end, the FIR narrow-band filter is used as receiver, as shown in _{1} and _{2} were placed on the left and right transition bands of the steepest slope. Because of the “slope-phase discrimination” character of FIR sideband, symbol “1” can be impacted, and then the envelope detector outputs a 2R bps rate pulse, and realizes code rate doubled in one passband finally.

The dual-carrier ABSK signal's frequency spectrum is shown in

In our work, the EBPSK modulated signal is chosen as the transmit signal (set A = B = 1, θ = π) [

Let us consider the following specifications of the system:

Bit rate R = 1 M bps (symbol period T = 10^{−6} s);

Carrier frequency _{c}

The bit-rate of each sub-channel EBPSK signal is 0.5M bps, the parameters of the two modulated EBPSK signal are given by: _{c1} = 400 MHz, K_{1}:N_{1} = 2:400; _{c2}_{i}_{c1} + Δ_{c}_{i}_{c1} = 0.002HMz, Δ_{c2} = 0.004 MHz, Δ_{c3} = 0.006 MHz, Δ_{c4} = 0.01Hz, the duty K_{2}_{i}_{2}_{i}_{c2}_{i}

“Slope-phase discrimination” is mainly manifested in the dramatic changes of magnitude brought by the phase changes, so the construction of extremely steep narrow transition bands of the FIR filter is very necessary. The realization of the construction is through comprehensive selection of the pass-band frequency _{pass}, stop-band frequency _{stop} and pass stop-band attenuation coefficient _{pass} and _{stop}. Here, we present one design example of FIR narrow-band filter to demonstrate the effectiveness of the proposed principle. Set _{c1} = 400 MHz, _{c24} = 400.01 MHz, according to the above principles, Kaiser Window is chosen to realize the FIR filter, set _{s} = 1.2 GHz, transition bandwidth 0.005 MHz, pass stop-band fluctuations 0.01. Specific parameters: _{stop1} = 399.999 MHz, _{pass1} = 400.004 MHz, _{pass2} = 400.006 MHz, _{stop2} = 400.011 MHz, _{pass}= −1 dB, _{stop1} = _{stop2} = −100 dB; the frequency response of the FIR narrow-band filter is shown in

Let the two independent signals and their superposition signals pass the designed FIR narrow-bandpass filter, and the filtering results are shown in

Without channel coding and bandpass shaping in the additive white Gaussian noise (AWGN) channel, the ADC sampling frequency of receiver is 1.2 GHz, and the proposed FIR narrow-band filter is used to filter the received signal. The BER performance of the EBPSK dual-carrier system is shown in

As shown in _{c1} and _{c2}_{i}^{−5}. Even for the other three smaller carrier frequency spacing, the required SNR is no more than 4 dB.

_{g}. The system demodulates the two channels of signal respectively, which suppresses the one channel to demodulate another. The frequency interval between the dual-carrier is 0.1 MHz, and the t_{g} of the second channel gets 0, 0.5 K_{1}/_{c1}, K_{1}/_{c1} respectively. As shown in _{g} = 0, but the structure of the former is much simpler.

Simulation results show that the proposed FIR narrowband filter used in the receiver can not only achieve high spectral efficiency, but also give excellent demodulation performance, compared to the previous IIR digital filter bank. The proposed filter also has the following advantages:

Enhanced system stability: the receiver structure has been greatly simplified [

Compared to the SIF, the proposed filter can quickly transit to the steady state with short transient waveform tail, so the FIR filter can reduce the inter-symbol interference and achieve higher bit rate;

No feedback loop could discard the starting oscillation, which greatly enhance the transmission of small data packet communications efficiency;

We will next design a multi-rate narrowband FIR filter to achieve the performance of an elliptic IIR filter. To further improve the spectral efficiency, we consider using the comb filter at the receiver end to achieve greater capacity for intensive multi-carrier communication.

The authors would like to thank the support of the National Natural Science Foundation of China (NSFC), under the Grant 61271204 and 61302096. The work is supported by the National Key Technology R&D Program under the grant 2012BAH15B02.

Zhimin Chen and Lenan Wu conceived and designed the study. Zhimin Chen and Jiwu Wang performed the experiments and wrote the paper. Zhimin Chen reviewed and edited the manuscript. All authors read and approved the manuscript.

The authors declare no conflict of interest.

The vector of zeros and poles.

Frequency response of zeros and poles adjacent to

Magnification of one segment of the SIF's frequency response.

Frequency response of the FIR narrow-band filter.

The impacting effect of the FIR narrow-band filter. (

Dual-carrier ABSK communication system.

Frequency spectrum of the dual-carriers. (

Amplitude-frequency response of the FIR narrow-bandpass filter.

The output waveforms of the FIR narrow-bandpass filter.

BER performance of the ABSK dual-carrier system.

The BER performance of dual-carrier EBPSK system with SIF.