A Full-Duplex Technology Based on the Doppler Effect

Hao Feng , Meng Ma and Yuping Zhao

Abstract

Abstract: Full-duplex technology can improve bandwidth and energy efficiency but has serious self-interference. In this paper, we introduce a novel full-duplex communication scheme that leverages the Doppler effect. By rotating the circular antenna array, the Doppler frequency shift is introduced into the received uplink (UL) signal, and the UL signal can be separated from the downlink (DL) signal in the frequency domain, thus eliminating self-interference. In order to maximize the interference-free bandwidth, an antenna switching criterion to maximum frequency offset interval is proposed for antenna switching control. Moreover, an antenna switching module based on the above criterion and a Doppler frequency shift compensation module are designed. Simulation results show that the proposed scheme can effectively avoid interference between UL and DL signals and achieves a substantial capacity improvement compared to conventional systems.

Keywords: Channel capacity , direction of arrival , Doppler effect , duplex technology

I. INTRODUCTION

THE full-duplex communication system facilitates simultaneous uplink (UL) and downlink (DL) transmission on the same frequency, enhancing both bandwidth and energy efficiency [1]–[5]. However, wireless signals rapidly attenuate over distance, resulting in higher interference from a node’s own transmit antenna to its receiver compared to signals from other nodes [6], [7]. Consequently, effectively mitigating this self-interference remains a primary challenge for full-duplex receivers [8], [9]. Currently, most approaches to self-interference cancellation operate in three domains: airspace [10], [11], analog [12], [13], and digital [14], [15], achieving up to approximately 100 dB of interference cancellation. However, these methods often introduce considerable complexity in practical applications.

On the other hand, the Doppler effect caused by the relative motion between the transmitter and receiver makes some frequency offset of the received signals compared to the transmitted one. Some studies have leveraged this effect for direction-of-arrival (DOA) estimation [16], [17]. In [18], researchers rotated antennas at the receiver to induce a periodic frequency offset in received signals, enabling DOA estimation by analyzing these frequency shifts. Hioka et al. even showcased a hardware demo system highlighting the advantages of this approach. In addition, a Doppler frequency shift was applied in a space division multiple access scheme for UL multiuser communication systems [19]. By rotating the receiving antenna array, varying Doppler frequency shifts were introduced in the received signals. This method effectively separates user signals from different directions in the frequency domain, significantly reducing multiuser interference.

In this paper, we leverage the Doppler frequency shift within full-duplex systems. By rotating the receiver antenna array at the central node, we induce a Doppler frequency shift in the received UL signal, effectively mitigating interference from the DL signal.

The main contributions of this paper are as follows:

· We introduce an innovative full-duplex scheme exploiting the Doppler effect. By rotating the central node’s receiver antenna array, the intended received signals are shifted to the outside of the frequency band to avoid in-band interference at the central node.

· We propose an antenna switching criterion to maximize interference-free bandwidth. This criterion selects the receive antenna with the maximum Doppler frequency shift of the received UL signals.

· We present the design of two essential modules: an antenna switching module and a Doppler frequency shift compensation module. Theoretical analysis demonstrates their performance.

· We evaluate the performance of our proposed scheme in terms of channel capacity. Simulation results showcase its effectiveness in suppressing DL interference and providing significant capacity gains compared to traditional half-duplex systems and benchmark methods.

The remainder of this paper is organized as follows. The system model of a duplex system based on the Doppler effect is introduced in Section II. The antenna switching module based on the antenna switching criterion and Doppler frequency shift compensation module are proposed in Section III. Then, the performance of the proposed scheme is analyzed in Section IV, and simulation results are presented in Section V. Finally, the main achievements and conclusions are presented in Section VI.

II. SYSTEM MODEL

Let us consider a duplex system as shown in Fig. 1. The system consists of a central node, a UL user equipment (UEa), and a DL UEb. The UEa sends signals to the central node with carrier frequency [TeX:] $$f_c$$ and bandwidth B. UEb simultaneously receives signals from the central node using the same frequency as UEa. The UL and DL channels are assumed to be quasi-static, indicating that UEa and UEb are in a static or slow-motion state.

Fig. 1.
Diagram of the proposed duplex system.

The central node employs a circular antenna array with a radius of r for receiving signals from UEa, and this array is rotated to induce a Doppler frequency shift. The transmit antenna to UEb is located at the center of the antenna array. We denote the antenna array as having N equally spaced receive antennas, denoted by #1, #2, · · ·, #N, respectively. The antenna array rotates at an angular velocity ω.

The angle between the instantaneous time t as a function of the nth receive antenna and the DOA of the UEa signal is

(1)
[TeX:] $$\theta_n(t)=\omega t+\alpha_1-\frac{2 n \pi}{N}-\beta,$$

where β is the DOA of the UL signal, and [TeX:] $$\alpha_1$$ is the initial angle between the 1st receive antenna and the x-axis at t = 0. The Doppler frequency shift introduced to the UL signal on the nth receive antenna can be expressed as a periodic function

(2)
[TeX:] $$f_n(t)=f_{\max } \cos \theta_n(t), \quad 1 \leq n \leq N,$$

where [TeX:] $$f_{\max }=f_c \omega r / \mathrm{C}$$ is the maximum Doppler frequency shift, and C is the speed of light. Therefore, the instantaneous frequency of the UL signal at the nth receive antenna can be expressed as

(3)
[TeX:] $$f_n^{\mathrm{IF}}(t)=f_c+f_n(t)=f_c+f_{\max } \cos \theta_n(t).$$

The ‘antenna switching module’ is shown in Fig. 1 to select one of the most favorite antennas. The signal from the selected antenna is then fed into a filter to remove out-of-band noise, a low-noise amplifier to amplify the reception signal, and converted to a baseband signal by a down-converter. Then, the signal is processed by a ‘Doppler frequency shift compensation module’ to remove the Doppler frequency shift from the received signal, and its output can be expressed as

(4)
[TeX:] $$r_{\mathrm{o}}(t)=r_{\mathrm{d}}(t) \times e^{-j 2 \pi f_n(t)},$$

where [TeX:] $$r_{\mathrm{d}}(t)$$ is the signal after down-conversion, and [TeX:] $$r_{\mathrm{o}}(t)$$ is the output of [TeX:] $$r_{\mathrm{d}}(t)$$ multiplied by the Doppler frequency shift compensation signal. Finally, a band-pass filter is used to suppress the out-of-band DL interference and get the UL signal.

A. Antenna Switching Criterion

Based on the above analysis, if the bandwidth B is smaller than the Doppler frequency shift on the selected antenna, the UL signal and DL signal can be separated in the frequency domain, thus theoretically achieving interference-free.

In this paper, we design the antenna switching criterion to maximize the interference-free bandwidth between the UL and DL signals. Since all the movement of the receive antenna is in the tangential direction of the transmit antenna, its Doppler frequency shift is zero. Consequently, the criterion is to select the receive antenna with the maximum Doppler frequency shift, which can be expressed as

(5)
[TeX:] $$\begin{aligned} d(t) & =\max _{1 \leq n \leq N}\left|f_n(t)\right| \\ & =f_{\max } \max _{1 \leq n \leq N}\left|\cos \left(\omega t+\alpha_1-\frac{2 n \pi}{N}-\beta\right)\right|. \end{aligned}$$

It can be seen from (5) that when d(t) reaches its maximum value, there is

(6)
[TeX:] $$\omega t+\alpha_1-\frac{2 n \pi}{N}-\beta=q \pi,$$

where q is an integer. Due to the rotational symmetry of the receive antennas, the antennas should be switched periodically, and the period of antenna switching is

(7)
[TeX:] $$\Delta t=\frac{2 \pi}{N \omega} .$$

According to (6) and (7), the active duration of the nth receive antenna is

(8)
[TeX:] $$\frac{\left(q \pi+\frac{2 n \pi}{N}+\lambda\right)}{\omega}-\frac{\pi}{N \omega} \leq t\lt \frac{\left(q \pi+\frac{2 n \pi}{N}+\lambda\right)}{\omega}+\frac{\pi}{N \omega},$$

with [TeX:] $$\lambda=\beta-\alpha_1.$$

Substituting the minimum value of (8) into (2), the maximum interference-free bandwidth can be derived as

(9)
[TeX:] $$B_{\max }=f_{\max }\left|\cos \frac{\pi}{N}\right| .$$

It can be seen from (9) that [TeX:] $$B_{\max}$$ increases as the number of receive antennas increases. With the number of antennas going to infinity, the maximum interference-free bandwidth approaches to

(10)
[TeX:] $$\lim _{N \rightarrow \infty} B_{\max }=\lim _{N \rightarrow \infty} f_{\max }\left|\cos \frac{\pi}{N}\right|=f_{\max }.$$

To illustrate the impact of Doppler frequency shift on different receive antennas, the following numerical simulations are carried out with simulation parameters as shown in Tab. I.

TABLE I
SIMULATION PARAMETERS.

The instantaneous frequency of the UL signal on each receive antenna is calculated by (3), and the results are shown in Fig. 2. Due to no relative movement between the transmit antenna and the receive antenna, the UEb Doppler frequency at the receive antenna is zero (see the red dashed line). The instantaneous frequency curves of the UL signal on different receive antennas are in the same shape but with a delay of [TeX:] $$\Delta t=2 \pi / \omega N=5$$ ms between adjacent antennas.

Fig. 2.
The instantaneous frequency of the UL and DL signal from the active receive antenna.

To select the receive antenna with maximum Doppler frequency shift, the receive antenna should be switched in a round-robin fashion, each with a duration of [TeX:] $$\Delta t \text {. }$$ Take Fig. 2 as an example, antenna #1 is activated from 0 to [TeX:] $$\Delta t \text {, }$$ antenna #2 is activated from [TeX:] $$\Delta t \text { to } 2 \Delta t,$$ and so on. The solid blue line represents the instantaneous frequency of the UL signal on the selected receive antenna.

The central frequency of the received signal at the output of the Doppler frequency shift compensation module is plotted in Fig. 3. It can be seen that the Doppler effect has been removed from the UL signal, and its frequency no longer varies with time.

Fig. 3.
The frequency of the UL and DL signal after Doppler frequency shift compensation.
B. The Properties of Proposed Antenna Switching Criterion

To summarize, the proposed antenna switching criterion has the following properties:

(a) According to (7), the switching period is [TeX:] $$\Delta t=2 \pi / \omega N.$$

(b) Due to the circular symmetry of the antenna array, the antennas should be switched in a round-robin fashion.

(c) During the active period, the frequency curve of the UL signal is even symmetric (because of (6), (7), (8)).

III. PROPOSED ANTENNA SWITCHING MODULE AND DOPPLER FREQUENCY SHIFT COMPENSATION MODULE

In this section, we design an antenna switching module based on the antenna switching criterion and a Doppler frequency shift compensation module.

A. Proposed Antenna Switching Module

The block diagram of the designed antenna switching module is depicted in Fig. 4. To facilitate the synchronization process, the signal is designed as two parts: pilot and data. The pilot part is a sine wave signal, and the data part is a signal with a bandwidth of B. Without loss of generality, it can be assumed that the initial phase is zero; thus, the pilot signal [TeX:] $$x_{\mathrm{p}}(t)$$ that UEa transmits to the central node can be expressed as

(11)
[TeX:] $$x_{\mathrm{p}}(t)=A_{\mathrm{p}} \cos \left(2 \pi f_{\mathrm{p}} t\right),$$

where [TeX:] $$A_{\mathrm{p}}$$ is the amplitude of the pilot signal, and [TeX:] $$f_{\mathrm{p}}$$ is the frequency of the pilot signal.

Fig. 4.
Block diagram of proposed antenna switching module.

According to (2), the frequency of the pilot signal on the nth receive antenna can be expressed as

(12)
[TeX:] $$f_n^{\prime}(t)=f_{\mathrm{p}}+f_n(t)=f_{\mathrm{p}}+\frac{f_c \omega r}{\mathrm{C}} \cos \theta_n(t).$$

From (12), the instantaneous phase of the pilot signal on the nth receive antenna is

(13)
[TeX:] $$\begin{aligned} \Phi_n(t) & =2 \pi \int_0^t f_n^{\prime}(\tau) d \tau+\phi_n \\ & =2 \pi f_{\mathrm{p}} t+2 \pi \int_0^t \frac{f_c \omega r}{\mathrm{C}} \cos \theta_n(\tau) d \tau+\phi_n, \end{aligned}$$

where [TeX:] $$\phi_n$$ is the initial phase of the pilot signal on the nth receive antenna when t = 0. The pilot signal on the nth receive antenna can be expressed as

(14)
[TeX:] $$\begin{aligned} r_n(t) & =A_{\mathrm{p}}^{\prime} \cos \left(\Phi_n(t)\right) \\ & =A_{\mathrm{p}}^{\prime} \cos \left(2 \pi f_{\mathrm{p}} t+2 \pi \int_0^t \frac{f_c \omega r}{\mathrm{C}} \cos \theta_n(\tau) d \tau+\phi_n\right), \end{aligned}$$

where [TeX:] $$A_{\mathrm{p}}^{\prime}$$ is the amplitude of the received pilot signal.

The selected antenna index during [TeX:] $$t_{k-1} \leq t\lt t_k$$ is

(15)
[TeX:] $$m=\left(m_0+k\right) \bmod N,$$

where [TeX:] $$t_k$$ denotes the moment that the kth receive antenna is switched on, [TeX:] $$m_0$$ is the initially selected antenna index, and mod represents the modulo operation.

By substituting n = m into (13), the instantaneous phase of the pilot signal on the mth receive antenna [TeX:] $$\Phi_m(t)$$ can be derived. The pilot signal at the output of the antenna switching module can be expressed as

(16)
[TeX:] $$\begin{aligned} r_{\mathrm{p}}(t) & =A_{\mathrm{p}}^{\prime} \cos \left(\Phi_m(t)\right) \\ & =A_{\mathrm{p}}^{\prime} \cos \left(2 \pi f_{\mathrm{p}} t+2 \pi \int_0^t \frac{f_c \omega r}{\mathrm{C}} \cos \theta_m(\tau) d \tau+\phi_m\right). \end{aligned}$$

After being processed by the filter, the low-noise amplifier, and the down-converter, as shown in Fig. 1, the pilot signal can be expressed as

(17)
[TeX:] $$r_{\mathrm{d}}(t)=A_{\mathrm{d}} \cos \left(2 \pi \int_0^t \frac{f_c \omega r}{\mathrm{C}} \cos \theta_m(\tau) d \tau+\phi_m\right),$$

where [TeX:] $$A_{\mathrm{d}}$$ is the amplitude of the output signal after the down-converter. Then [TeX:] $$r_{\mathrm{d}}(t)$$ is fed into the frequency discriminator, as shown in Fig. 4, and the frequency at the output of the frequency discriminator is

(18)
[TeX:] $$f_{\mathrm{d}}^{(k)}(t)=q_{\mathrm{d}} \frac{f_c \omega r}{\mathrm{C}} \cos \theta_m(t),$$

where [TeX:] $$q_{\mathrm{d}}$$ is the scale factor.

From Fig. 4, VCO1 generates a sine wave s(t) with frequency [TeX:] $$f_{\mathrm{V} 1}^{(k)}.$$ The output frequency of VCO1 can be expressed as a linear function of the control voltage [TeX:] $$V_k$$

(19)
[TeX:] $$f_{\mathrm{d}}^{(k)}(t)=q_{\mathrm{d}} \frac{f_c \omega r}{\mathrm{C}} \cos \theta_m(t),$$

where [TeX:] $$f_0$$ is the free oscillation frequency, and A is the voltage control sensitivity. The duration of the kth receive antenna switching cycle can be expressed as

(20)
[TeX:] $$\Delta t_k=\frac{1}{N f_{\mathrm{V} 1}^{(k)}},$$

which can be adjusted by [TeX:] $$f_{\mathrm{V} 1}^{(k)}.$$ The kth receive antenna switching moment can be expressed as

(21)
[TeX:] $$t_k=\sum_{i=1}^k \Delta t_i=\frac{1}{N f_{\mathrm{V} 1}^{(k)}}+t_{k-1},$$

where [TeX:] $$t_{k-1}$$ is the moment when the k − 1th receive antenna is activated, and [TeX:] $$t_0=0.$$

The sine wave signal s(t) is fed into N frequency multiplier, and then into the sawtooth generator to obtain a sawtooth signal as

(22)
[TeX:] $$f_{\mathrm{r}}^{(k)}(t)=q_{\mathrm{r}}\left(t-t_{k-1}-\frac{t_k-t_{k-1}}{2}\right), t_{k-1} \leq t\lt t_k,$$

where [TeX:] $$q_r$$ is the amplitude of the sawtooth signal.

The sawtooth signal is then multiplied by [TeX:] $$f_{\mathrm{d}}^{(k)}(t),$$ and then integrated to obtain

(23)
[TeX:] $$\begin{aligned} V_k= & \int_{t_{k-1}}^{t_k} f_{\mathrm{r}}^{(k)}(\tau) f_{\mathrm{d}}^{(k)}(\tau) d \tau \\ = & q_{\mathrm{r}} q_{\mathrm{d}} f_{\max } \int_{t_{k-1}}^{t_k}\left(\tau-t_{k-1}-\frac{t_k-t_{k-1}}{2}\right) \\ & \cos \left(\omega \tau+\alpha_1-\frac{2 m \pi}{N}-\beta\right) d \tau. \end{aligned}$$

The integrator outputs the results at the end of the switching cycle. [TeX:] $$V_k$$ is then fed into the VCO1 to adjust its output frequency [TeX:] $$f_{\mathrm{V} 1}^{(k+1)}.$$ The output of the frequency multiplier is transformed to a square wave signal by a waveform converter and then fed into a counter. The output of the counter, denoted by c(n), is increased by 1 if c(n − 1) < N − 1, and equals zero if c(n−1) = N. The multiplexer (MUX) 1, as shown in Fig. 1, selects the receive antenna with the index equal to the counter output.

Next, we will explain why the antenna switching module works. Firstly, according to the above-mentioned antenna switching criterion property (c), the Doppler frequency shift of the UL signal should be even symmetric during the switching period. Furthermore, as indicated by equation (22), the sawtooth signal displays odd symmetry during the switching period. Therefore, when the output of the frequency discriminator, [TeX:] $$f_{\mathrm{d}}^{(k)}(t),$$ presents different shapes during the switching period, [TeX:] $$V_k$$ has different values. The change of [TeX:] $$V_k$$ with [TeX:] $$f_{\mathrm{d}}^{(k)}(t),$$ is shown in Fig. 5. As shown in Fig. 5, when [TeX:] $$f_{\mathrm{d}}^{(k)}(t),$$ is not even symmetric during the switching period, [TeX:] $$V_k$$ is not equal to zero, such as Fig. 5 (a), (c) and (e), which is fed back to adjust the frequency of the VCO1 according to (20), and then adjusted during the switching period until the frequency discriminator output becomes an even symmetric function. When [TeX:] $$f_{\mathrm{d}}^{(k)}(t),$$ is even symmetric during the switching period, such as (b) and (d) in Fig. 5, [TeX:] $$V_k$$ is equal to zero. However, [TeX:] $$V_k$$ is unstable in the case of Fig. 5 (b) because [TeX:] $$V_k$$ would jump out of the point due to a bit of disturbance. Finally, [TeX:] $$V_k$$ converges to the situation in Fig. 5 (d), and the antenna switching control achieves the optimal.

Fig. 5.
The variation of [TeX:] $$V_k$$ with [TeX:] $$f_{\mathrm{d}}^{(k)}(t).$$

To show the procedure that [TeX:] $$f_{\mathrm{d}}^{(k)}(t)$$ converges to an even symmetric function, the following simulations were carried out for different values of the initial angle of antenna #1. In the simulation, the number of receive antennas is N = 4, the carrier frequency is at [TeX:] $$f_c=1.8 \mathrm{GHz},$$ the antenna array radius is r = 0.3 m, the antenna rotation angular velocity is ω = 314 rad/s, [TeX:] $$q_{\mathrm{r}}=1, q_{\mathrm{d}}=1,$$ and the free oscillation frequency of VCO1 is [TeX:] $$f_0=50 \mathrm{~Hz}.$$ The simulation results are shown in Fig. 6.

Fig. 6.
The control voltage [TeX:] $$V_k.$$

It can be seen from Fig. 6 that there are two zero points in the range [TeX:] $$(-\pi, \pi],$$ which is the same as we analyzed in Fig. 5. Let us look at the left zero point first. Near the left zero point, the slope of the curve is positive. Therefore, when [TeX:] $$V_k \lt 0,$$ the receive antenna switching period increases with the phase increase. When [TeX:] $$V_k \gt 0,$$ the receive antenna switching period decreases with the phase increase. Therefore, the left zero point is unstable. Moreover, the slope is negative near the zero point on the right. When [TeX:] $$V_k \gt 0,$$ the receive antenna switching period decreases as the phase increases. When [TeX:] $$V_k \lt 0,$$ the receive antenna switching period increases as the phase increases, so the zero point on the right side is stable, and [TeX:] $$V_k$$ will converge to this point.

B. Proposed Doppler Frequency Shift Compensation Module

To compensate for the Doppler frequency shift of the UL signal, the Doppler frequency shift compensation module is designed, as shown in Fig. 7. The sine wave signal s(t) from VCO1 is fed into an N-stage phase shifter, each with a phase shift of [TeX:] $$2 \pi /N,$$ and then into comparators to control the multiplexer to select the smallest value. The smallest value of the N-stage phase shifter from the multiplexer MUX2 during the switching period is an even symmetric function to control the VCO2 generating complementary signal compared to the selected receive antenna UL signal. The output of VCO2 can be used for Doppler frequency shift compensation.

Fig. 7.
Block diagram of proposed Doppler frequency shift compensation module.

To validate the efficacy of the aforementioned design, we conducted the following simulations. In the simulation, the number of receive antennas is N = 4, carrier frequency is at [TeX:] $$f_c=1.8$$ GHz, antenna array radius is r = 0.3 m, antenna rotation angular velocity is ω = 314 rad/s, and the linear expression of VCO1 is [TeX:] $$f_{\mathrm{V} 1}^{(k)}=50+27.5 V_k, q_{\mathrm{r}}=1, q_{\mathrm{d}}=1, m_0=1.$$

Fig. 8 shows the relationship between [TeX:] $$V_k$$ and the number of antenna switch times k. After about 15 times of iteration, [TeX:] $$V_k$$ approaches almost zero.

Fig. 8.
Convergence curve of [TeX:] $$V_k$$.

IV. PERFORMANCE ANALYSIS

Let us begin with a brief review of our proposed duplex scheme. The UL and DL signals share the same frequency band over the wireless propagation channel and can be separated by rotating the receive antenna array. The DL signals no longer interfere with the UL signals, so the signal-tointerference plus noise ratio (SINR) of the UL signal increases, and the channel capacity increases. So, we use channel capacity for the scheme’s performance analysis.

Assuming that the received signal power of the UEa on each antenna is [TeX:] $$P_u$$, and the power of the received DL interference is [TeX:] $$P_d$$. The SINR of the UEa on the nth receive antenna can be expressed as

(24)
[TeX:] $$\gamma_n(t, f)=\frac{\frac{P_u}{B} Z\left(\frac{f-f_c}{B}\right)}{\frac{P_d}{B} Z\left(\frac{f-f_c-\frac{f_c \omega r}{\mathrm{C}} \cos \theta_n(t)}{B}\right)+N_0},$$

where [TeX:] $$N_0$$ is the power spectral density of the additive white Gaussian noise, and Z(f) is the normalized signal spectral function with [TeX:] $$\int_{-0.5}^{0.5} Z(f) d f=1.$$

The instantaneous channel capacity is

(25)
[TeX:] $$\tilde{C}(t)=\int_{f_c-B / 2}^{f_c+B / 2} \log _2\left(1+\gamma_n(t, f)\right) d f.$$

Due to the periodicity of the Doppler frequency shift, the channel capacity can be calculated and averaged in one cycle. Then, the channel capacity of the UEa can be expressed as

(26)
[TeX:] $$\tilde{C}(t)=\frac{1}{T} \int_0^T \int_{f_c-B / 2}^{f_c+B / 2} \log _2\left(1+\gamma_n(t, f)\right) d f d t.$$

We also provide the channel capacity of the half-duplex system. Generally, the channel capacity of a half-duplex system can be calculated as [20]

(27)
[TeX:] $$\tilde{C}^{\mathrm{HD}}=\frac{1}{2} E\left[\int_{f_c-B / 2}^{f_c+B / 2} \log _2\left(1+\gamma^{\mathrm{HD}}(f)\right) d f\right],$$

where [TeX:] $$E[\cdot]$$ represents the expectation operator, and [TeX:] $$\gamma^{\mathrm{HD}}(f)=\frac{P_u Z(f)}{B N_0}$$ denotes the signal-to-noise ratio (SNR) of the halfduplex system. The factor of 1/2 in the half-duplex channel capacity arises from the fact that resources are allocated between two communicating nodes.

V. SIMULATION RESULTS

A. Performance Analysis

In this section, the channel capacity of the proposed scheme is analyzed by following simulations.

Assuming that the signal spectrum is raised cosine spectrum, the roll-off coefficients are α = 0, 0.1, 0.2, and 0.3, respectively. Fig. 9 depicts the relationship between the power spectral density and frequency for the uplink signal and the downlink interference signal with a bandwidth of 2 kHz and α = 0.2, where the power ratio between the downlink and uplink signals is 40 dB. Other simulation parameters are listed in Tab. II. The capacity is calculated according to (26), and the result is shown in Fig. 10. From Fig. 10, it can be observed that under different roll-off coefficients, the channel capacity initially increases and then decreases with the increase in bandwidth. Additionally, smaller roll-off coefficients result in higher channel capacity for the same bandwidth. This is because signals with smaller roll-off coefficients exhibit higher spectral efficiency, thereby enhancing the channel capacity.

TABLE II
SIMULATION PARAMETERS.
Fig. 9.
Power spectral density vs. frequency for uplink signal and downlink interference signals.

According to (9), the maximum interference-free bandwidth [TeX:] $$B_{\max }=555 \mathrm{~Hz}.$$ When [TeX:] $$B\lt B_{\max },$$ the system is interference-free, so the capacity will increase dramatically with the bandwidth increases. When [TeX:] $$B\gt B_{\max },\left(B-B_{\max }\right) / B \times 100 \%$$ spectrum is overlapped, which leads to severe interference and a capacity loss. For example, when α = 0.2, a good trade-off between bandwidth and interference is achieved when B = 0.6 kHz, that is, 7.5% of the spectrum is overlapped. When [TeX:] $$B\gt B_{\max },$$ due to the severe interference, the capacity decreases as the bandwidth increases, and the spectral efficiency decreases as the bandwidth increases.

To compare the performance of methods with and without antenna selection, we evaluated the channel capacity of both methods across different bandwidths. In the method without antenna selection (dashed line), antenna 1 was consistently chosen as the receiving antenna throughout the rotation period. As depicted in Fig. 10, the channel capacity without the antenna selection method is notably lower than that achieved with the antenna selection method. Without antenna selection, the Doppler frequency shift undergoes periodic variations, causing substantial interference from the downlink signal to the uplink signal. This interference may result in complete overlap, severely reducing the channel capacity.

Fig. 10.
Channel capacity for different roll-off coefficients.

Fig. 11 shows the capacity under different numbers of receive antennas, where the roll-off coefficient is α = 0.2. As shown in Fig. 11, the capacity increases as the number of receive antennas increases. For N = 16 receive antennas, the capacity is very close to the capacity for the infinite number of receive antennas.

Fig. 11.
Channel capacity for different numbers of receive antennas.

The influence of carrier frequency on capacity is shown in Fig. 12 for N = 16, and the roll-off coefficient is α = 0.2. It can be seen that the capacity increases as the carrier frequency increases. To further elucidate the relationship between the carrier frequency and channel capacity, Fig. 13 illustrates this relationship alongside the correlation between the carrier frequency and the maximum interference-free bandwidth, with N = 16 and a roll-off factor of α = 0.2. Fig. 13 shows that the maximum interference-free bandwidth demonstrates linear changes as the carrier frequency increases. Furthermore, we calculated the channel capacity under the corresponding carrier frequency’s maximum interference-free bandwidth, and the results indicate that the channel capacity is proportional to the carrier frequency. This relationship arises because the maximum interference-free bandwidth scales proportionally with the carrier frequency, and bandwidth is directly linked to channel capacity. Consequently, when computing channel capacity using the maximum interference-free bandwidth associated with the carrier frequency, the channel capacity scales proportionally with the carrier frequency.

Fig. 12.
Channel capacity for different carrier frequencies.
Fig. 13.
Relationship between carrier frequency and channel capacity, as well as maximum interference-free bandwidth.

In Fig. 14, the capacity performance is compared for different power ratios of the DL signal to UL signal equals 40 dB, 50 dB, and 60 dB, with roll-off coefficient of α = 0.2 and the number of receive antennas N = 16. In Fig. 14, the channel capacity achieves the maximum under B = 0.6 kHz bandwidth. Under different DL signal to UL signal power ratios, there is almost no difference in the capacity of the same bandwidth.

Fig. 14.
Channel capacity for different power ratio of the DL signal to UL signal.

Fig. 15 compares the capacity for the roll-off coefficient α = 0.2, bandwidth B = 0.6 kHz, and the number of receive antennas N = 16. In Fig. 15, for different power ratios of DL signal to UL signal, the capacity increases as the SNR increases. Due to the signal bandwidth being greater than the maximum interference-free bandwidth, i.e., [TeX:] $$B\gt B_{\max }=$$ 555 Hz, the signal with a frequency exceeding the maximum interference-free bandwidth would suffer from a significant capacity loss due to the serious interference from DL to UL. Under different ratios of DL signal power to UL signal power, channel capacity is mainly contributed from the bandwidth interference-free, so the channel capacity of UEa does not change.

Fig. 15.
Channel capacity changes with SNR under different DL and UL signal power ratios.

Fig. 16 illustrates the channel capacity under varying SNRs. The number of receive antennas is N = 8 or 16, the rolloff coefficient is α = 0.2, the [TeX:] $$P_d / P_u=60 \mathrm{~dB}$$ and the signal bandwidth is B = 0.6 kHz. As shown in Fig. 16, since there is no DL UE interference in the single UL UE system, it has the highest capacity. Under all SNR conditions, the proposed full-duplex methods (N = 8 and N = 16) demonstrate markedly higher channel capacities compared to both the half-duplex system and the capacities achieved by SI cancellation method [14] and the adaptive least mean squares (LMS) algorithm [15]. This suggests that the proposed fullduplex methods effectively enhance channel capacity across diverse SNR conditions. While the channel capacity reaches its maximum value under conditions of no SI, the proposed fullduplex methods demonstrate performance very close to this ideal scenario across all SNR ranges (for example: for N = 16 and C = 5 kbps, the capacity loss is only 0.2 dB). This is because in the proposed method, [TeX:] $$B\gt B_{\max }=555 \mathrm{~Hz},$$ so interference leads to a smaller capacity loss. This suggests that our method effectively suppresses SI, achieving performance close to the ideal scenario.

Fig. 16.
Channel capacity for different SNRs.
B. Complexity Analysis

We conducted a complexity comparison between our proposed method and baseline methods, covering hardware and signal processing costs, as shown in Tab. III.

From Tab. III, it is evident that while our method may entail higher hardware costs due to the utilization of a rotating circular antenna array and potential additional hardware components, our hardware cost performance is relatively acceptable compared to the SI cancellation circuit of the SI cancellation method. More importantly, our method incurs relatively lower costs in terms of signal processing, primarily relying on the measurement and processing of Doppler effects, thus avoiding the need for complex algorithms or expensive equipment. While the adaptive LMS algorithm may have lower hardware costs, it faces relatively higher costs in digital signal processing. Therefore, considering both cost and performance comprehensively, the proposed approach exhibits significant advantages, particularly in terms of the simplicity and efficiency of signal processing.

TABLE III
COMPLEXITY COMPARISON BETWEEN THE PROPOSED METHOD AND BASELINE METHODS.

VI. CONCLUSION

In this paper, we introduced an innovative full-duplex scheme that leverages the Doppler effect and incorporates an antenna switching criterion to maximize interference-free bandwidth. Moreover, an antenna switching module based on the criterion and a Doppler frequency shift compensation module were designed. By theoretical analysis, the antenna optimum switching time and the maximum interference-free bandwidth of the duplex communication system are derived, and the performance is analyzed in terms of channel capacity. Simulation results corroborated our theoretical analysis, demonstrating that the proposed scheme can effectively suppress DL interference and yield significant capacity gains compared to traditional half-duplex systems and benchmark methods. This full-duplex scheme holds promise in numerous application scenarios, including NB-IoT (Narrowband Internet of Things). We intend to conduct an in-depth study of the aforementioned scenario in the future.

Biography

Hao Feng

Hao Feng received the B.S. degree in Communication Engineering from the Zhengzhou University, Zhengzhou, China, in 2018 and received the M.S. degree from the Peking University, Beijing, China, in 2021. He is currently pursuing the Ph.D. degree in Peking University, Beijing. His research interests include wireless communication systems and signal processing techniques.

Biography

Meng Ma

Meng Ma received the B.S. and Ph.D. degrees in Electrical Engineering from Peking University, Beijing, China, in 2001 and 2007, respectively. From 2007 to 2011, he was an Assistant Professor with the School of Electronics Engineering and Computer Science, Peking University, where he has been an Associate Professor, since 2011. From 2009 to 2010, he was a Visiting Scholar with the Commonwealth Scientific and Industrial Research Organization, Sydney, Australia. His research interests include signal processing in wireless communication systems, interference cancellation technique, and information theory.

Biography

Yuping Zhao

Yuping Zhao received the B.S. and M.S. degrees in Electrical Engineering from Northern Jiaotong University, Beijing, China, in 1983 and 1986, respectively, and the Ph.D. and Doctor of Science degrees in wireless communications from Aalto University, Espoo, Finland, in 1997 and 1999, respectively. She was a System Engineer for telecommunication companies in China and Japan. She was a Research Engineer with the Nokia Research Center, Helsinki, Finland, in radio resource management for wireless mobile communication networks. She is currently a Professor with the State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronics Engineering and Computer Science, Peking University, Beijing. Her current research interests include wireless communications and corresponding signal processing, especially for orthogonal frequency division multiplexing, ultra wideband, multiple-input multiple-output systems, cooperative networks, cognitive radio, and wireless sensor networks.

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TABLE I

SIMULATION PARAMETERS.
Parameters Values
The number of receive antennas N 4
Angular velocity ω 314 rad/s
The radius of the antenna array r 0.3 m
The central frequency of bandwidth [TeX:] $$f_c$$ 1.8 GHz

TABLE II

SIMULATION PARAMETERS.
Parameters Values
The number of receive antennas N 4
Angular velocity ω 314 rad/s
The radius of the antenna array r 0.3 m
The central frequency of bandwidth [TeX:] $$f_c$$ 1.8 GHz
[TeX:] $$P / N_0\left(P_u=P\right)$$ [TeX:] $$3.6 \times 10^6$$
[TeX:] $$P_d / P_u$$ 40 dB

TABLE III

COMPLEXITY COMPARISON BETWEEN THE PROPOSED METHOD AND BASELINE METHODS.
Methods Hardware cost Signal processing cost
Proposed scheme The hardware cost is relatively high. It necessitates the implementation of a rotating circular antenna array to induce a Doppler frequency shift, potentiallyincreasing the complexity and expense of the hardware. Lower digital signal processing cost. This method separates signals from uplink and downlink users in the RF domain. Only demodulation and decoding are performed in the digital domain, eliminating the need for complex algorithms or expensive equipment.
SI cancellation method [14] The hardware cost is relatively high. The authors utilized a self-interference cancellation circuit, which necessitates additional hardware components and circuits, consequently increasing the hardware cost of the full-duplex system. High digital signal processing cost. The selfinterference cancellation algorithm involves intricate computations, demanding powerful processing capabilities. Consequently, this increases the signal processing cost and overall system complexity.
Adaptive LMS method [15] The hardware cost is relatively low. As the LMS algorithm is employed to estimate the self-interference channel and subtract it from the received signal prior to analog-to-digital conversion, fewer hardware devices are required. High digital signal processing cost. It heavily relies on the adaptive LMS algorithm for estimating and eliminating self-interference signals, necessitating substantial computational resources and real-time adaptation capabilities.
Diagram of the proposed duplex system.
The instantaneous frequency of the UL and DL signal from the active receive antenna.
The frequency of the UL and DL signal after Doppler frequency shift compensation.
Block diagram of proposed antenna switching module.
The variation of [TeX:] $$V_k$$ with [TeX:] $$f_{\mathrm{d}}^{(k)}(t).$$
The control voltage [TeX:] $$V_k.$$
Block diagram of proposed Doppler frequency shift compensation module.
Convergence curve of [TeX:] $$V_k$$.
Power spectral density vs. frequency for uplink signal and downlink interference signals.
Channel capacity for different roll-off coefficients.
Channel capacity for different numbers of receive antennas.
Channel capacity for different carrier frequencies.
Relationship between carrier frequency and channel capacity, as well as maximum interference-free bandwidth.
Channel capacity for different power ratio of the DL signal to UL signal.
Channel capacity changes with SNR under different DL and UL signal power ratios.
Channel capacity for different SNRs.