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SCIENCE CHINA Information Sciences, Volume 60, Issue 10: 102302(2017) https://doi.org/10.1007/s11432-016-0291-9

Novel multi-tap analog self-interference cancellation architecture with shared phase-shifter for full-duplex communications

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  • ReceivedJun 14, 2016
  • AcceptedSep 30, 2016
  • PublishedMar 28, 2017

Abstract

Multi-tap analog self-interference (SI) cancellation structures adopt parallel taps to reconstruct and then cancel SI in full-duplex radios. Each tap is usually comprised of one fixed delay line, one variable attenuator, and one optional variable phase shifter. To balance the quantity of the variable phase shifters and the achievable SI cancellation (SIC) performance, this paper proposes a novel analog SIC cancellation structure, called shared-phase-shifter constrained multi-tap structure (SMTS). In the proposed architecture, all taps share one phase shifter to emulate the dominated phase offset of the SI channel, which reduces the complexity of the implementation of the multi-tap analog SIC structure and avoids the SIC performance degradation. Then, the proposed SMTS and the existing structures are compared in terms of SIC performance and power dissipation. Finally, extensive simulations show that SMTS provides the close-to-optimal SIC performance as well as the lowest power dissipation relative to the existing multi-tap structures.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61531009, 61501093, 61271164, 61471108) and Fundamental Research Funds for the Central Universities.


Supplement

Appendix

SIC performance provided by CMTS

Replacing $\boldsymbol{A}$ in (5) by $\boldsymbol{A}_\text{CMTS}=[a_1\exp(\text{j} \phi_1)a_2\exp(\text{j} \phi_2)\cdots$ $a_N\exp(\text{j} \phi_N)]^\text{T}$ yields the power of residual SI of CMTS $P_\text{e,CMTS}$, where $\phi_1,\phi_2,\dots,\phi_N$ are the phase offsets of the $N$ variable phase shifters in CMTS. The optimal $\boldsymbol{A}_\text{CMTS}$ to minimize $P_\text{e,CMTS}$ is an unconstrained minimization problem and can be solved by ordering $0=\nabla P_\text{e,CMTS}$[19], i.e., \begin{equation} \left\{\begin{aligned}&0={\partial P_\text{e,CMTS}}/{\partial\textrm{Re}\{\boldsymbol{A}_\text{CMTS}\}} =-2\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}\} +2\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}\textrm{Re}\{\boldsymbol{A}_\text{CMTS}\} -2\textrm{Im}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}\textrm{Im}\{\boldsymbol{A}_\text{CMTS}\}, \\ &0={\partial P_\text{e,CMTS}}/{\partial\textrm{Im}\{\boldsymbol{A}_\text{CMTS}\}} =-2\textrm{Im}\{\boldsymbol{O}^\text{H}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}\} +2\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}\textrm{Im}\{\boldsymbol{A}_\text{CMTS}\} +2\textrm{Im}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}\textrm{Re}\{\boldsymbol{A}_\text{CMTS}\}. \end{aligned}\right. \tag{18}\end{equation} The solution of (18) is derived as $\boldsymbol{A}_\text{CMTS}=\boldsymbol{O}^{-1}\boldsymbol{R}_{b}^{-1}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}$, which is the well-known Wiener solution 3). Then the SIC performance provided by CMTS is computed with (sect. 3.3) and given as \begin{equation} G_\text{CMTS}=I_{\text{t/r}}(I_{\text{t/r}}-\boldsymbol{H}^\text{H}\boldsymbol{Q}^\text{H}\boldsymbol{C}^\text{H}_b\boldsymbol{R}_{b}^{-1}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H})^{-1}. \tag{19}\end{equation}

Diniz P S R. Adaptive filtering—algorithms and practical implementation. 3rd ed. Spring Street, NY: Springer Science & Business Media, 2008. 25–47.

SIC performance provided by DMTS

In DMTS, the power of residual SI $P_\text{e,DMTS}$ is obtained by replacing $\boldsymbol{A}$ by $\boldsymbol{\tilde{A}}$ in (5). Finding the optimal tap coefficients in DMTS to minimize $P_\text{e,DMTS}$ is expressed as \begin{equation} \begin{aligned}\min &P_\text{e,DMTS} \\ \textrm{subject to} &\boldsymbol{\tilde{A}}\ge0\end{aligned} \Leftrightarrow \ \begin{aligned}\min \Bigg\|&\left[ \begin{matrix} \operatorname{Re}( {{\boldsymbol{\Lambda }}^{1/2}}{{\boldsymbol{U}}^{-1}}\boldsymbol{O} ) \\ \operatorname{Im}( {{\boldsymbol{\Lambda }}^{1/2}}{{\boldsymbol{U}}^{-1}}\boldsymbol{O} ) \\ \end{matrix} \right]\boldsymbol{\tilde{A}}-\left[ \begin{matrix} \operatorname{Re}( {{\boldsymbol{\Lambda }}^{-1/2}}{{\boldsymbol{U}}^{-1}}{{\boldsymbol{C}}_{b}}\boldsymbol{QH} ) \\ \operatorname{Im}( {{\boldsymbol{\Lambda }}^{-1/2}}{{\boldsymbol{U}}^{-1}}{{\boldsymbol{C}}_{b}}\boldsymbol{QH} ) \\ \end{matrix} \right] \Bigg\|_{2}^{2} \\ &\textrm{subject to} \boldsymbol{\tilde{A}}\ge0\end{aligned}, \\ \tag{20}\end{equation} where $\boldsymbol{R}_{b}=\boldsymbol{U}\boldsymbol{\Lambda}\boldsymbol{U}^\text{H}$$^{2)}$, $\boldsymbol{\Lambda}$ is the diagonal matrix consisting of the eigenvalues of $\boldsymbol{R}_{b}$, $\boldsymbol{U}$ is the unitary matrix consisting of the normalized eigenvectors of $\boldsymbol{R}_{b}$, and $\|\cdot\|_2$ is the Euclidean norm of a vector[20]. Eq. (20) is an nonnegative least squares optimization problem and can be solved with various well-developed numerical approaches 4), and then the SIC performance provided by DMTS is computed with (sect. 3.3) and given as \begin{equation} G_\text{DMTS}=I_{\text{t/r}}({{I}_\text{t/r}} -2\textrm{Re}\{\boldsymbol{H}^\text{H}\boldsymbol{Q}^\text{H}\boldsymbol{C}^\text{H}_b\boldsymbol{O}\}\boldsymbol{A}_\text{DMTS}+ \boldsymbol{A}_\text{DMTS}^\text{T}\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}\boldsymbol{A}_\text{DMTS})^{-1}, \tag{21}\end{equation} where $\boldsymbol{A}_\text{DMTS}$ is the numerical result of (20).

The upper bound of ${G}_\text{DMTS}$ is derived as follows. Relaxing the constraint $\boldsymbol{\tilde{A}}\ge0$, the optimal $\boldsymbol{\tilde{A}}$ for (20) is derived as $\boldsymbol{\hat{A}}_\text{DMTS}=\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}^{-1} \textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}\}$ by ordering $0=\nabla P_\text{e,DMTS}$[19], and then the corresponding SIC performance is computed with (5) and (sect. 3.3) as $\hat{G}_\text{DMTS}=I_{\text{t/r}}({{I}_\text{t/r}} - \textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}\}^\text{T} \textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}^{-1} \textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}\})^{-1}$. To compare $\hat{G}_\text{DMTS}$ with ${G}_\text{DMTS}$, $1/{G}_\text{DMTS}-1/\hat{G}_\text{DMTS}=\|\boldsymbol{\Sigma}^{-1/2}\boldsymbol{V}^\text{H}\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}\} -\boldsymbol{\Sigma}^{1/2}\boldsymbol{V}^\text{H}\boldsymbol{A}_\text{DMTS}\|_2^2/I_{\text{t/r}}\ge0$ is computed, and then $\hat{G}_\text{DMTS}\ge {G}_\text{DMTS}$ is derived, i.e., $\hat{G}_\text{DMTS}$ is the upper bound of ${G}_\text{DMTS}$, where $\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}=\boldsymbol{V}\boldsymbol{\Sigma}\boldsymbol{V}^\text{H}$, $\boldsymbol{\Sigma}$ is the diagonal matrix consisting of the eigenvalues of $\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}$, $\boldsymbol{V}$ is the unitary matrix consisting of the normalized eigenvectors of $\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}$.

Chen D, Plemmons R. Nonnegativity constraints in numerical analysis. In: Bultheel A, Cools R, eds. The Birth of Numerical Analysis. Hackensack: World Scientific, 2010. 109–139.

Reconstruction power efficiencies of CMTS and DMTS

After $G_\text{CMTS}$ and $G_\text{DMTS}$ are maximized, the reconstruction power efficiencies of CMTS and DMTS are computed by substituting $\boldsymbol{A}_\text{CMTS}$ and $\boldsymbol{A}_\text{DMTS}$ into (14) and given as \begin{equation} \left\{\begin{array}{l} \eta_\text{CMTS}= ({(\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H})^\text{H}\boldsymbol{R}_{b}^{-1}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}})/({(\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H})^\text{H} \boldsymbol{R}_{b}^{-2}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}})/2^{\lceil\log_2(N)\rceil}, \\ \eta_\text{DMTS}=({\boldsymbol{A}_\text{DMTS}^\text{T}\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}\boldsymbol{A}_\text{DMTS}})/({\boldsymbol{A}^\text{T}_\text{DMTS}\boldsymbol{A}_\text{DMTS}})/2^{\lceil\log_2(N)\rceil}, \end{array}\right. \tag{22}\end{equation} respectively, where the fixed power combiner arrays in CMTS and DMTS are assumed to also have the tree structure, and thus likewise have an insertion loss $2^{\lceil\log_2(N)\rceil}$. With the property of the Rayleigh quotient[20], $\eta_\text{DMTS}\in[\lambda_\text{min}\{\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}\}/2^{\lceil\log_2(N)\rceil}, \lambda_\text{max}\{\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}\}/2^{\lceil\log_2(N)\rceil}]$ and $\eta_\text{CMTS}\in[\lambda_\text{min}\{\boldsymbol{R}_b\}/2^{\lceil\log_2(N)\rceil}, \lambda_\text{max}\{\boldsymbol{R}_b\}$$/2^{\lceil\log_2(N)\rceil}]$ can be derived from (22). Combining with (15), the variation ranges of $\eta_\text{CMTS}$ and $\eta_\text{DMTS}$ are summarized as \begin{equation}\left\{\begin{array}{l} \eta_\text{CMTS}\in[\lambda_\text{min}\{\boldsymbol{R}_{b}\}/2^{\lceil\log_2(N)\rceil}, \lambda_\text{max}\{\boldsymbol{R}_{b}\}/2^{\lceil\log_2(N)\rceil}], \\ \eta_\text{DMTS}\in[\max(\lambda_\text{min}\{\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}\}, \lambda_\text{min}\{\boldsymbol{R}_b\})/2^{\lceil\log_2(N)\rceil}, \min(\lambda_\text{max}\{\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}\}, \lambda_\text{max}\{\boldsymbol{R}_b\})/2^{\lceil\log_2(N)\rceil}], \end{array}\right. \tag{23}\end{equation} respectively.


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  • Figure 1

    Multi-tap analog SIC schemes. (a) CMTS; (b) DMTS.

  • Figure 2

    The proposed SMTS.

  • Figure 3

    Design of the reconfigurable power combiner array. (a) Structure of a SuDiC; (b) structure of the proposed reconfigurable power combiner array, where $x_i$ represents the signal from the $i$th tap.

  • Figure 4

    (a) Considered FD transceiver frontend; (b) power delay profile of SI channel.

  • Figure 5

    (Color online) Convergence of the developed numerical algorithm with 7 taps, i.e., $N=7$. (a) $G_\text{SMTS}$ vs. iteration time for 20-MHz SI; (b) $G_\text{SMTS}$ vs. iteration time for 100-MHz SI; (c) $\phi$ vs. iteration time for 20-MHz SI; (d) $\phi$ vs. iteration time for 100-MHz SI.

  • Figure 6

    (Color online) SIC performance vs. tap number. (a) 20-MHz SI; (b) 100-MHz SI.

  • Figure 7

    (Color online) CDF of SIC performance. (a) 20-MHz SI and $N=3$; (b) 20-MHz SI and $N=5$; (c) 20-MHz SI and $N=7$; (d) 100-MHz SI and $N=3$; (e) 100-MHz SI and $N=5$; (f) 100-MHz SI and $N=7$. Simulations are performed by 3000 times.

  • Figure 8

    (Color online) Coupling channel. The tap number is 7, i.e., $N=7$. (a) Magnitude response with 20-MHz SI; (b) magnitude response with 100-MHz SI; (c) time domain response with 20-MHz SI; (d) time domain response with 100-MHz SI.

  • Figure 9

    (Color online) CDF of reconstruction power efficiency. The delay interval of the delay lines is $\Delta\tau=4$ ns. (a) 20-MHz SI and $N=3$; (b) 20-MHz SI and $N=5$; (c) 20-MHz SI and $N=7$; (d) 100-MHz SI and $N=3$; (e) 100-MHz SI and $N=5$; (f) 100-MHz SI and $N=7$. Simulations are performed by 3000 times.

  •   

    Algorithm 1 The numerical algorithm to solve (10)

    Require:Given threshold $P_\text{th}$, one temporary variable $k$;

    $\boldsymbol{\tilde{A}}_0\Leftarrow0$, $P_\text{e}(0)\Leftarrow {{{P}_{\text{tx}}}}I_{\text{t/r}}$, $\phi_0\Leftarrow0$, $k\Leftarrow0$;

    repeat

    $k\Leftarrow k+1$;

    $\boldsymbol{\tilde{A}}_k\Leftarrow\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\}^{-1}\textrm{Re}\{\boldsymbol{O}^\text{H}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}\exp(-\text{j} \phi_{k-1})\}$;

    $\phi_k\Leftarrow\text{Ang}\{{\boldsymbol{O}^\text{H}\boldsymbol{C}_b\boldsymbol{Q}\boldsymbol{H}^\text{T}\boldsymbol{\tilde{A}}_k}\}$;

    $P_\text{e}(k)\Leftarrow{{{P}_{\text{tx}}}}(I_{\text{t/r}}-\textrm{Re}\{\boldsymbol{H}^\text{H}\boldsymbol{Q}^\text{H}\boldsymbol{C}^\text{H}_b\boldsymbol{O}\boldsymbol{\tilde{A}}_k\exp(\text{j} \phi_k)\}+\boldsymbol{\tilde{A}}_k^\text{T}\boldsymbol{O}^\text{H}\boldsymbol{R}_b\boldsymbol{O}\boldsymbol{\tilde{A}}_k)$;

    until $\|P_\text{e}(k)-P_\text{e}(k-1)\|\le P_\text{th}$

  • Table 1   Various multi-tap analog SIC prototypes
    Paper Type Number of taps BW (MHz) SI reduction$^\text{a)}$ (dB) Tuning time$^\text{b)}$ (ms)
    Ref. [5] CMTS 4 20 43 10
    Ref. [6] CMTS 4 30 31
    Ref. [7] CMTS 10 20 57
    Ref. [8] CMTS 4 20 35
    Ref. [9] DMTS 2 20 13
    Ref. [10] DMTS 2 10 20 0.13
    Ref. [11] DMTS 16 20 57 1
    Ref. [12] DMTS 12 20 53
  • Table 2   Comparisons of CMTS, DMTS, and SMTS with $N$ taps
    Item CMTS DMTS SMTS
    1. Number of fixed delay lines $N$ $N$ $N$
    2. Number of variable scalars $N$ $N$ $N$
    3. Number of variable phase shifters $N$ 0 1
    4. $N$-way power combiner array 1 1 1
    5. Dimensions of control algorithm $2N$ $N$ $N+1$
  • Table 3   Comparisons of CMTS, DMTS, and SMTS with $N$ taps
    Item CMTS DMTS SMTS
    1. SIC performance Highest Lowest Medium
    2. Quantity of variable phase shifters $N$ 0 $1$
    3. Quantity of power combiners$^\text{a)}$ $2^{\lceil\log_2(N)\rceil}-1$ $2^{\lceil\log_2(N)\rceil}-1$ $2^{\lceil\log_2(N)\rceil}-1$
    4. Quantity of selectors 0 0 $2^{\lceil\log_2(N)\rceil}-1$
    5. Reconstruction power efficiency Lowest Medium Highest
    6. Dimensions of control algorithm $2N$ $N$ $N+1$

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