Analysis of RF Feedback Chain Isolation in Wireless Co-Time Co-Frequency Full Duplex

1.   Introduction

Co-time co-frequency full duplex (CCFD) operation has emerged as an attractive solution for increasing the spectrum efficiency of wireless communication systems^[1]-[6]. However, when a wireless terminal transmits and receives at the same time in a same frequency band, the self-interference problem arises and becomes one of the biggest practical impediments to CCFD operation^[7]-[11]. To suppress the self-interference efficiently, the RF feedback chain was employed in the CCFD architecture in [12] and [13]. However, the imperfect RF feedback chain isolation, as an important technical specification in practical project, is usually neglected for the analysis of the RF feedback chain.

For practical CCFD project, it has been experimentally demonstrated that the self-interference cancelation (SIC) performance is influenced by the RF chain isolation. The reason is that the RF signal leaks owing to the imperfect RF chain isolation. In this paper, we focus on the impact of the RF chain isolation on SIC performance. A mathematical analysis will be given first, and then a new scheme will be presented, aiming at reducing the adverse impact on SIC.

In the proposed scheme, firstly, the RF leakage signal is collected and analyzed by using the feedback RF chain. And then, the parameters for the reconstruction of the leakage signal are optimally estimated. With the optimal parameters, the CCFD receiver can subtract the real-time leaked RF signal from the required signal, so as to cancel the impact of the RF leakage signal on SIC performance.

The system model and the impact of the RF chain isolation on SIC are explained in Section 2. In Section 3, the proposed scheme for reducing the RF chain isolation impact is proposed. Numerical results are presented in Section 4. Conclusions are drawn in Section 5.

2.   System Model and RF Chain Isolation Impact

As depicted in Fig. 1, we consider a multiple-antenna CCFD architecture with RF feedback chain. For the analysis convenience, the architecture includes two transmit antennas (Tx), two receive antennas (Rx), and two corresponding feedback (Fb) chains. Certainly, similar analysis can be applied to more antennas.

Figure  1.  CCFD architecture with feedback chains. Tx, Fb, and Rx represent transmitting, feedback, and receiving, respectively.

DownLoad: Full-Size Img PowerPoint

As shown in Fig. 1, the expected signals are x₁ and x₂, respectively. Considering the RF leakage signal, the signals to be transmitted are x₁+γ₁x₂ and x₂+γ₂x₁, where γ₁ denotes the leakage factor from Tx₂ chain to Tx₁ chain, and γ₂ is the leakage factor from Tx₁ chain to Tx₂ chain. Similarly, the feedback signals are z₁=x₁+β₁x₂ and z₂=x₂+β₂x₁, where β₁ denotes the leakage factor from Tx₂ chain to Fb₁ chain, and β₂ is the leakage factor from Tx₁ chain to Fb₂ chain.

With h_{i, j} denoting the channel condition from the transmitting antenna Tx_i to the receiving antenna Rx_j, the signals at the receiving antennas can be represented as

and

For a better description of the RF leakage signal, the leakage signal power is measured with a spectrum analyzer, and the measured result is shown in Fig. 2. The transmitting antenna Tx₂ works while transmitting antenna Tx₁ is silent. The transmitted signal power is 30 dBm with a bandwidth of 20 MHz. The leakage signal in the feedback chain (Fb₂ chain) is measured as much as –7 dBm. The specific RF leakage signal impact on SIC performance is analyzed as follows.

Figure  2.  Power spectrum of the RF leakage signal.

DownLoad: Full-Size Img PowerPoint

For the SIC in CCFD, the channel information is usually determined as follows. At time t₁, the pilot signal x_{1, p} is transmitting at Tx₁ while Tx₂ is silent. The corresponding feedback signal and the received signal are z_{1, p}=x_{1, p} and y_{1, p}=h₁₁x_{1, p}+h₂₁γ₂x_{1, p}, respectively. Then the estimated channel condition ${\hat h_{11}}$ can be expressed as

At time t₂, the pilot signal x_{2, p} is transmitting at Tx₂ while Tx₁ is silent. The estimated channel condition ${\hat h_{21}}$ can be similarly analyzed as

With ${\hat h_{11}}$ and ${\hat h_{21}}$ , the estimated self-interference signal ${\hat s_{1}}$ at the Rx₁ chain can be obtained by

The practical self-interference signal is s₁=h₁₁z₁+h₂₁z₂. After SIC, the residual self-interference at the Rx₁ chain can be calculated by

The expected residual self-interference signal at the Rx₁ chain is ${{\hat e}_1} = 0$ , which is true only under the conditions β₁=0 and β₂=0. γ₁ and γ₂ do not affect the SIC performance. Similar analysis can be applied in the residual self-interference signal at the Rx₂ chain. However, these conditions are too critical to realize. To deal with this problem, a digital pre-processing scheme is provided in the following section.

3.   Digital Pre-Processing Scheme for Reducing RF Chain Isolation Impact

The proposed digital pre-processing scheme is shown in Fig. 3, which is implemented before the CCFD transceiver starts to work. The procedure of the proposed scheme is briefly depicted as follows:

Figure  3.  Proposed digital pre-process scheme.

DownLoad: Full-Size Img PowerPoint

a) The parameters of RF leakage signal owing to imperfect RF chain isolation are tuned and determined, including time, amplitude, and phase.

b) Based on the determined parameters, the RF leakage signal is estimated and subtracted from the required signal for reducing the RF chain isolation impact.

c) The residual signal power after subtraction is calculated to determine whether the estimated RF leakage signal is well approximated with the practical RF leakage signal.

d) If not, go on with step a). Others, the proposed scheme is complemented, and the CCFD transceiver starts to work with the determined RF leakage parameters.

As shown in Fig. 3, the signal g₁ is transmitted in the Tx₂ chain, and the RF signal is leaked to the Tx₁ chain as g₄. To eliminate the RF leakage signal impact, the estimated RF leakage signal g₂ is subtracted from g₄ to obtain the feedback signal g₀.

Based on the baseband transmitting signal g₁(k) and the estimated parameters, the RF leakage signal estimated in the digital processing unit is ${g_2}\left( k \right) = \displaystyle\sum \limits_{n = 1}^N {g_1}\left( {k - {{\hat {\text{τ}} }_n}} \right){{\hat {\text{α}} }_n}{e^{{\rm{j}}{{\hat {\text{θ}} }_n}}}$ , which can be further written in the RF domain as

where ${{{\hat {\text{τ}} }_n}}$ , ${{\hat {\text{α}} }_n}$ , and ${{{\hat {\text{θ}} }_n}}$ denote the estimated time delay, amplitude, and phase offsets, respectively. After RF processing, we get the estimated RF leakage signal

Similarly, the practical RF leakage signal g₄(t) is expressed as

Suppose ${\hat{\text{A}}} = {[{{\hat {\text{α}} }_1}{e^{{\rm{j}}{{\hat {\text{θ}} }_1}}},\;\;{{\hat {\text{α}} }_2}{e^{{\rm{j}}{{\hat {\text{θ}} }_2}}},\cdots, {{\hat {\text{α}} }_N}{e^{{\rm{j}}{{\hat {\text{θ}} }_N}}}]^{\rm T}}$ and ${\hat{\text{B}}} = {{\text{β}} _0}{e^{{\rm{j}}{{\text{ϕ}} _0}}}{\left[ {{g_1}\left( {t - {{\hat {\text{τ}} }_1}} \right),{g_1}\left( {t - {{\hat {\text{τ}} }_2}} \right),\cdots ,\;{g_1}\left( {t - {{\hat {\text{τ}} }_N}} \right)} \right]^{\rm T}}$ , then g₃(t) can be rewritten as

Similarly, the real RF leakage signal g₄(t) can be given by

where ${\text{B}} = {{\text{β}} _1}{e^{{\rm{j}}{{\text{ϕ}} _1}}}{\left[ {{g_1}\left( {t - {{\text{τ}} _1}} \right),\;{g_1}\left( {t - {{\text{τ}} _2}} \right),\cdots ,\;{g_1}\left( {t - {{\text{τ}} _M}} \right)} \right]^{\rm T}}$ and ${\text{A}} = {[{{\text{α}} _1}{e^{{\rm{j}}{{\text{θ}} _1}}},\;\;{{\text{α}} _2}{e^{{\rm{j}}{{\text{θ}} _2}}},\cdots ,\;{{\text{α}} _M}{e^{{\rm{j}}{{\text{θ}} _M}}}]^{\rm T}}$ .

As described in the proposed scheme, the estimation of the time delay, amplitude, and phase offsets on each path is the key problem to be solved. Firstly, ${{{\hat {\text{τ}} }_N}}$ is determined by the time difference between the signals g₃ and g₄. Then the time delay of each path can be calculated by ${{\hat {\text{τ}} }_i} = i·{{\hat {\text{τ}} }_N}/N$ . Later in the paper, we will focus on the estimation of amplitude and phase offsets.

The residual RF leakage signal power can be expressed as

For analysis convenience, let

where ${\rm{C}} = \left[ {{\rm{Re}}\left\{ {{{\widehat {\rm{B}}}^{\rm{T}}}} \right\} + {\rm{jIm}}\left\{ {{{\widehat {\rm{B}}}^{\rm{T}}}} \right\} - {\rm{Im}}\left\{ {{{\widehat {\rm{B}}}^{\rm{T}}}} \right\} + {\rm{jRe}}\left\{ {{{\widehat {\rm{B}}}^{\rm{T}}}} \right\}} \right]$ and ${\rm{D}} = {\left[ {{\rm{Re}}\left\{ {\widehat {\rm{A}}} \right\}\;\;{\rm{Im}}\left\{ {\widehat {\rm{A}}} \right\}} \right]^{\rm{T}}}$ . Here Re(x) and Im(x) denote the real part and the imaginary part of x, respectively. Then we get

With ${P_4} = E\left\{ {{{\left( {{{\text{A}}^{\rm T}}{\text{B}}} \right)}^{\rm H}}\left( {{{\text{A}}^{\rm T}}{\text{B}}} \right)} \right\}$ as the power of the RF leakage signal g₄, ${\text{R}} = E\left\{ {{{\text{C}}^{\rm H}}{\text{C}}} \right\}$ , and ${\text{Z}} = {{\text{B}}^{\rm H}}E\left\{ {{{\text{A}}^*}{\text{C}}} \right\}$ , we get

which is shown to be convex on D. (Refer to AppendixA.)

Here $\widehat {\rm{A}}$ denotes the amplitude and phase offsets. It means that P₀(D) is convex on the amplitude and phase offsets needed in the proposed scheme.

The above analysis focuses on the case where Tx₂ is transmitting while Tx₁ is silent. Then the same process is applied in the other case where Tx₁ is transmitting while Tx₂ is silent. Finally, with all the parameters achieved, the digital pre-processing scheme is completed for the CCFD framework as shown in Fig. 3.

By employing the proposed scheme, the leakage signal shown in Fig. 2 can be effectively reduced from –37.00 dBm to –56.05 dBm, which is shown in Fig. 4.

Figure  4.  Power spectrum of the RF leakage signal.

DownLoad: Full-Size Img PowerPoint

4.   Numerical Results

To confirm the theoretical analysis, the simulation platform is developed as follows 3rd generation partnership project long term evolution (3GPP LTE) protocol with 20 MHz bandwidth is applied in the CCFD system and the recursive least square (RLS) algorithm is employed as the digital self-interference cancelation method^[14],[15]. The interference to noise ratio (INR) is set to be 60 dB, and correspondingly the expected SIC performance is 60 dB with the residual RF leakage signal canceled perfectly.

The practical RF leakage signal is assumed to be comprised of three paths. The amplitudes, phases, time delays for these paths are respectively defined as follows, the amplitudes are α₁=1, α₂=0.9, and α₃=1.1, the phases are ϕ₁=0, ϕ₂=0.5, and ϕ₃=1, and the time delays are τ₁=0, τ₂=3Δ, τ₃=6Δ. Here Δ=1/30.72×10⁶ is the chip time based on LTE protocol.

Fig. 5 depicts the SIC performance in different RF signal leakage ratios. RF signal leakage ratio is the ratio between the signal power to be transmitted and the signal power leaked. From Fig. 5, it is found that the SIC performance with the proposed scheme is close to the expected value 60 dB, which means that the RF chain isolation impact can be canceled with the proposed scheme. However, without the proposed scheme, the SIC performance is apparently damaged with increasing RF signal leakage ratio. This is because the residual RF leakage signal is the main part of the residual interference signal.

Figure  5.  CCFD SIC performance comparison in different RF signal leakage ratios.

DownLoad: Full-Size Img PowerPoint

5.   Conclusions

In this paper, it is analyzed that the imperfect RF chain isolation damages the SIC performance in CCFD. Then a digital preprocessing scheme is proposed for eliminating the RF chain isolation impact. With both theoretical analysis and simulation demonstration, it is shown that the proposed scheme achieves a better performance in the CCFD with the RF feedback chain.

Appendix

Based on [17], the residual RF leakage signal power can be expressed as

With ${P_4} = E\left\{ {{{\left( {{{\text{A}}^{\rm T}}{\text{B}}} \right)}^{\rm H}}\left( {{{\text{A}}^{\rm T}}{\text{B}}} \right)} \right\}$ as the power of the RF leakage signal g₄, ${\text{R}} = E\left\{ {{{\text{C}}^{\rm H}}{\text{C}}} \right\}$ , and ${\text{Z}} = {{\text{B}}^{\rm H}}E\left\{ {{{\text{A}}^*}{\text{C}}} \right\}$ we get

Since R is an autocorrelation and positive semidefinite matrix, ${P_0}\left( \text{D} \right)$ is convex on $\text{D}$ ^[17]. Here ${\rm{D}} = {\left[ {{\rm{Re}}\left\{ {\widehat {\rm{A}}} \right\}\;\;{\rm{Im}}\left\{ {\widehat {\rm{A}}} \right\}} \right]^{\rm{T}}}$ and $\widehat {\rm{A}}$ denotes the amplitude and phase parameters depending on [9], which means that ${P_0}\left( \text{D} \right)$ is convex on the amplitude and phase parameters needed in the proposed scheme.

Disclosures

The authors declare no conflicts of interest.