Digital Cancellation of Passive Intermodulation in FDD Transceivers

TL;DR

This paper introduces a digital cancellation method for passive intermodulation distortion in FDD transceivers, enhancing receiver sensitivity in LTE-Advanced and 5G networks by modeling PIM effects and demonstrating effective suppression through real RF measurements.

Contribution

It develops advanced baseband models for PIM distortion considering memory effects and proposes a digital cancellation technique validated with real RF data.

Findings

Digital cancellation significantly reduces PIM-induced interference.

The method improves receiver sensitivity in LTE-Advanced and 5G FDD systems.

Experimental results show excellent suppression of PIM in real measurements.

Abstract

Modern radio systems and transceivers utilize carrier aggregation (CA) to meet the demands for higher and higher data rates. However, the adoption of CA in the existing Long Term Evolution (LTE)-Advanced and emerging 5G New Radio (NR) mobile networks, in case of frequency division duplexing (FDD), may incur self-interference challenges with certain band combinations. More specifically, the nonlinear distortion products of the transmit signals or component carriers (CCs), stemming from the passive radio frequency (RF) front-end components of the transceiver, can appear in one or more of the configured receiver bands, potentially leading to the receiver desensitization. In this paper, we present advanced baseband equivalent signal models for such passive intermodulation (PIM) distortion viewed from the RX point of view, considering also potential memory effects in the PIM generation. Then, building on these signal models, a digital self-interference cancellation technique operating in the transceiver digital front-end is presented. The performance of the proposed solution is evaluated with real-life RF measurements for LTE-Advanced type user equipment (UE) with dual CC inter-band CA, demonstrating excellent suppression properties. The findings in this work indicate that digital cancellation is a feasible approach for improving the receiver sensitivity of mobile devices that may be prone to RF front-end induced PIM challenges.

Tables

Table 1. TABLE I : Example basis functions of the two considered PIM models

Signal model	Basis functions when $L_1=L_2=1$
Memoryless TX Chains	$s_1{\left[n+1\right]}^2{s}_2^{\ast }\left[n+1\right]$, $s_1{\left[n\right]}^2{s}_2^{\ast }\left[n\right]$, $s_1{\left[n-1\right]}^2{s}_2^{\ast }\left[n-1\right]$
TX Chains with Memory, $M_1=M_2=1$	$s_1{\left[n-2\right]}^2{s}_2^{\ast }\left[n-2\right]$, $s_1{\left[n-1\right]}^2{s}_2^{\ast }\left[n-1\right]$, $s_1{\left[n\right]}^2{s}_2^{\ast }\left[n\right]$, $s_1{\left[n-2\right]}^2{s}_2^{\ast }\left[n-1\right]$, $s_1{\left[n-1\right]}^2{s}_2^{\ast }\left[n\right]$, $s_1{\left[n\right]}^2{s}_2^{\ast }\left[n+1\right]$,
$s_1{\left[n-2\right]}^2{s}_2^{\ast }\left[n\right]$, $s_1{\left[n-1\right]}^2{s}_2^{\ast }\left[n+1\right]$,$s_1{\left[n\right]}^2{s}_2^{\ast }\left[n+2\right]$, $s_1\left[n-1\right]s_1\left[n-2\right]s_2^{\ast }\left[n-2\right]$, $s_1\left[n\right]s_1\left[n-1\right]s_2^{\ast }\left[n-1\right]$,
$s_1\left[n+1\right]s_1\left[n\right]s_2^{\ast }\left[n\right]$, $s_1\left[n-1\right]s_1\left[n-2\right]s_2^{\ast }\left[n-1\right]$, $s_1\left[n\right]s_1\left[n-1\right]s_2^{\ast }\left[n\right]$, $s_1\left[n+1\right]s_1\left[n\right]s_2^{\ast }\left[n+1\right]$,
$s_1\left[n-1\right]s_1\left[n-2\right]s_2^{\ast }\left[n\right]$, $s_1\left[n\right]s_1\left[n-1\right]s_2^{\ast }\left[n+1\right]$, $s_1\left[n+1\right]s_1\left[n\right]s_2^{\ast }\left[n+2\right]$, $s_1\left[n\right]s_1\left[n-2\right]s_2^{\ast }\left[n-2\right]$,
$s_1\left[n+1\right]s_1\left[n-1\right]s_2^{\ast }\left[n-1\right]$, $s_1\left[n+2\right]s_1\left[n\right]s_2^{\ast }\left[n\right]$, $s_1\left[n\right]s_1\left[n-2\right]s_2^{\ast }\left[n-1\right]$, $s_1\left[n+1\right]s_1\left[n-1\right]s_2^{\ast }\left[n\right]$,
$s_1\left[n+2\right]s_1\left[n\right]s_2^{\ast }\left[n+1\right]$, $s_1\left[n\right]s_1\left[n-2\right]s_2^{\ast }\left[n\right]$, $s_1\left[n+1\right]s_1\left[n-1\right]s_2^{\ast }\left[n+1\right]$, $s_1\left[n+2\right]s_1\left[n\right]s_2^{\ast }\left[n+2\right]$,
$s_1\left[n\right]s_1\left[n-1\right]s_2^{\ast }\left[n-2\right]$, $s_1\left[n+1\right]s_1\left[n\right]s_2^{\ast }\left[n-1\right]$, $s_1\left[n+2\right]s_1\left[n+1\right]s_2^{\ast }\left[n\right]$, $s_1\left[n+2\right]s_1\left[n+1\right]s_2^{\ast }\left[n+2\right]$,
$s_1{\left[n+2\right]}^2{s}_2^{\ast }\left[n+1\right]$, $s_1{\left[n+2\right]}^2{s}_2^{\ast }\left[n+2\right]$, $s_1{\left[n\right]}^2{s}_2^{\ast }\left[n-2\right]$, $s_1{\left[n+1\right]}^2{s}_2^{\ast }\left[n-1\right]$, $s_1{\left[n+2\right]}^2{s}_2^{\ast }\left[n\right]$,
$s_1{\left[n-1\right]}^2{s}_2^{\ast }\left[n-2\right]$, $s_1{\left[n\right]}^2{s}_2^{\ast }\left[n-1\right]$, $s_1{\left[n+1\right]}^2{s}_2^{\ast }\left[n\right]$, $s_1{\left[n+1\right]}^2{s}_2^{\ast }\left[n+1\right]$, $s_1{\left[n+1\right]}^2{s}_2^{\ast }\left[n+2\right]$,
$s_1\left[n+2\right]s_1\left[n+1\right]s_2^{\ast }\left[n+1\right]$

Table 2. TABLE II : Basic RF measurement parameters

Parameter	Value
Bandwidths of the TX CCs	5 MHz
Total transmit power	24 dBm
Post PA loss	4 dB
Duplexer insertion loss	3 dB
Switch insertion loss	1 dB
RX center frequency	2140 MHz
LS parameter learning sample size	90000
Number of PIM pre-cursor taps $\left(L_1\right)$	3
Number of PIM post-cursor taps $\left(L_2\right)$	4
Number of TX/PA pre-cursor taps $\left(M_1\right)$	0 or 1
Number of TX/PA post-cursor taps $\left(M_2\right)$	0 or 1

Equations

$$s_{\mathrm{RF}}[n]=\Re {\alpha }_1{s}_1[n]e^{j{\omega }_{1}n}+\Re {\alpha }_2{s}_2[n]e^{j{\omega }_{2}n},$$

$$s_{\mathrm{PIM}}[n]=\sum _{l=-L_1}^{L_2}{\gamma }_l{s}_1[n-l{]}^2{s}_2^{\ast }[n-l]$$

$$\begin{array}{r}{s}_{\mathrm{RF}}[n]=\Re e^{j{\omega }_{1}n}\sum _{m=-M_1}^{M_2}{\alpha }_{1,m}{s}_1[n-m]\\ +\Re e^{j{\omega }_{2}n}\sum _{m=-M_1}^{M_2}{\alpha }_{2,m}{s}_1[n-m],\end{array}$$

$$\begin{array}{rl}{s}_{\mathrm{PIM}}[n]=& \sum _{k_{11}=0}^2\sum _{k_{12}=0}^{2-k_{11}}\cdots \sum _{k_{1M}=0}^{2-{\sum }_{i=1}^{M-1}{k}_{1i}}\sum _{k_{21}=0}^1\sum _{k_{22}=0}^{1-k_{21}}\cdots \sum _{k_{2M}=0}^{1-{\sum }_{i=1}^{M-1}{k}_{2i}}\sum _{l=-L_1}^{L_2}{\gamma }_{l,k_{11},\cdots ,k_{1M},k_{21},\cdots ,k_{2M}}\times \\ & s_1[n-l+M_1{]}^{k_{11}}{s}_1[n-l+M_1-1{]}^{k_{12}}\cdots s_1[n-l-M_2{]}^{2-{\sum }_{i=1}^M{k}_{1i}}\times \\ & s_2^{\ast }[n-l+M_1{]}^{k_{21}}{s}_2^{\ast }[n-l+M_1-1{]}^{k_{22}}\cdots s_2^{\ast }[n-l-M_2{]}^{1-{\sum }_{i=1}^M{k}_{2i}}.\end{array}$$

$${\mathbf{s}}_{\mathrm{PIM}}=\mathbf{A}\mathbf{\theta },$$

$$\hat{\mathbf{\theta }}={\left({\mathbf{A}}^H\mathbf{A}\right)}^{-1}{\mathbf{A}}^H{\mathbf{y}}_{\mathrm{RX}},$$

$$y_{\mathrm{RX},\mathrm{canc}}[n]=y_{\mathrm{RX}}[n]-{\mathbf{a}}^T[n]\hat{\mathbf{\theta }},$$

Full text

I Introduction

The increasing amounts of data usage by mobile network subscribers imply the need for higher throughputs and higher network capacities. The existing and emerging mobile communication networks, such as 4G long term evolution (LTE)-Advanced and 5G New Radio (NR), are designed to meet these needs and requirements [1]. Carrier aggregation (CA) is one of the key techniques that was introduced in LTE-Advanced to support higher throughput requirements, where multiple component carriers (CCs) at one or multiple LTE bands are aggregated together to form larger transmission bandwidth, and also to facilitate efficient utilization of the available radio spectrum [2, 3, 4]. In this work, we particularly focus on the case where the aggregated CCs are at different bands, commonly referred to as inter-band CA.

In general, modern radio systems employing wideband multicarrier waveforms are vulnerable to practical analog circuit implementation related challenges and imperfections. One of these challenges is the so called passive intermodulation (PIM) that can severely limit the performance of frequency division duplexing (FDD) based systems. Such PIM is typically generated in the passive components of the radio frequency (RF) transceiver front-end, such as duplexer, diplexer, multiplexer or antenna selection switches. Moreover, the nonlinear junctions typically caused by poor RF connection or the presence of dirt over the metal surfaces in the radio components can also generate PIM. As a consequence, unwanted nonlinear distortion products are created due to the intermodulation of the transmit CCs that generally appear at the specific intermodulation (IM) sub-bands. Depending on the used bands and adopted CC center-frequencies, some of these nonlinear PIM products may appear in one or more of the receiver operating bands as illustrated in Fig. 1. Furthermore, since the PIM is generated in the radio transceiver front-end at or after the duplexer filter, it leaks directly into the receiver and may lead to receiver desensitization.

A concrete example case, in terms of exact LTE bands and frequencies, is given in Fig. 1 illustrating uplink inter-band CA transmission at Band 1 (1920-1980 MHz) and Band 3 (1710-1780 MHz). As shown in the figure, the upper third-order IM sub-band (IM3) falls within the Band 1 downlink, reflecting thus the self-interference problem due to PIM. Other LTE bands that can experience similar problems are, e.g., B3+B8, B2+B4, B5+B7, as discussed and acknowledged also in many inter-band CA related 3GPP technical documents, such as [5], [6]. In general, the problem of PIM-induced self-interference is not only limited to UE devices but can actually be even more pronounced in the base station (BS) transceiver systems [7], [8] where, in addition to internal PIM sources, external sources such as metal objects in the antenna near field and reflections from nearby buildings can cause self-interference. Therefore, PIM can be a big concern also for network vendors and operators.

Obvious solutions to avoid or reduce the PIM-induced self-interference are to either reduce the transmit signal power or to allow for a degradation in the receiver reference sensitivity level. At the UE side, these approaches are referred to as the maximum power reduction (MPR) and maximum sensitivity degradation (MSD), respectively. However, these approaches impact negatively the UL link budget and throughputs [9] and are thus not the most appealing solutions. Alternatively, one could argue to utilize higher quality RF components with good linearity characteristics, however, this may considerably raise the overall radio implementation costs and size.

Some recent works have addressed digital cancellation of PIM. Specifically, Dabag et al. [10] considered third-order PIM cancellation caused by the antenna switch by devising a multiple input single output (MISO) canceller to suppress the frequency-selective PIM with time delay differences between different transmit signals. While showing promising results, the associated parameter estimation complexity is very high. Then, in [11], digital cancellation of second-order PIM due to a diplexer is pursued. In general, these reference techniques do not take into account the nonlinear behavior of the individual PAs in the transmitter chains and the memory effects of the PAs. Since the transmit CCs are distorted in a nonlinear fashion by each of the individual PAs before entering a PIM nonlinearity, this implies that the self-interference is in fact a combination of two nonlinearities. This has been identified recently in [12] and [13], where different digital cancellers for joint mitigation of PA and PIM nonlinerities are proposed and experimented.

In this paper, we develop advanced digital cancellation solutions for suppressing the PIM with memory effects while exclude the PA nonlinearities for simplicity. In addition to PA memory, the proposed method can also account for different mutual time delays of the transmit signals before entering the PIM source, while can also account for memory along and after the PIM generation stage. For presentation simplicity, we focus primarily on modeling and digital cancellation of third-order PIM. The performance of the developed method is evaluated through practical RF measurements, adopting commercial LTE/LTE-Advanced UE transceiver modules and RF components. Moreover, we also address in the performance evaluations and RF measurements an additional practical case where the UE is equipped with a diversity RX chain. Specifically, we show that PIM coupled over-the-air from main transceiver to the diversity RX can also be a real problem. Although such PIM coupling over the air can basically be avoided by improving the isolation between the antennas, the isolation is in practice limited by the compact size of the mobile devices. The proposed digital cancellation solution is shown to be able to efficiently suppress the PIM appearing in the main RX branch as well as in the diversity RX branch. Thus, in general, the proposed solution can relax the RF components’ linearity requirements and improve the receiver sensitivity by effectively suppressing the PIM, and is applicable in both main RX and diversity RX branches.

The rest of the paper is organized as follows. In Section II, we address baseband equivalent modeling of third-order PIM at RX band under various sources of memory. The corresponding digital cancellation solution and the necessary parameter estimation procedures are presented in Section III. Then, the RF measurement results are reported and analyzed in Section IV. Finally, Section V concludes the paper.

II Baseband Equivalent Models for Passive Intermodulation at RX Band

In this section, we present the relevant signal models for describing the PIM observed in the RX chain, particularly at digital baseband. A block diagram describing the considered FDD radio transceiver system supporting inter-band CA is shown in Fig. 2. It is assumed that the adopted bands have dedicated TX-RX chains, each, while on the transmit direction the CCs are combined together in a duplexer or a multiplexer [14]. The PIM then occurs in the passive RF components due to cross-modulation between the aggregated transmit signals, and may appear in one or more of the configured receiver bands causing nonlinear self-interference.

Generally speaking, as shown in [12] and [13], the TX PAs can also cause nonlinear distortion to the individual transmit carriers, leading to spectral regrowth around the main transmit carriers. Such nonlinear distortion in the transmit CCs can then affect the overall characteristics of the PIM-induced self-interference and its cancellation. However, in this paper, we restrict our attention to linear transmit chains and PAs, thus basically assuming that the PAs are properly linearized, e.g., through digital pre-distortion (DPD). It can, however, be argued that the transmit carriers experience some filtering or linear distortion effects before they are combined and thus experience the PIM nonlinearity. Additionally, there can also potentially be multiple PIM sources in the transceiver. As a result, the overall TX-RX PIM coupling path can be viewed as a system of nonlinearities with memory effects. Keeping this in view, we consider two cases for PIM modeling. In the first case, we consider linear and memoryless PAs and pursue frequency-selective behavioral modeling of the nonlinear passive components. In the second case, we also adopt the memory or linear distortion modeling of the individual transmit CCs, prior to the actual PIM stage. As we later demonstrate with practical RF measurements, the latter model can facilitate more accurate PIM modeling and enhanced cancellation.

For presentation purposes and notational simplicity, we focus on third-order PIM effects, while more elaborate higher-order cases as well as coexisting cascaded nonlinearities are addressed in [13].

II-A Baseband Equivalent PIM Model: Memoryless TX Chains

Let us denote the complex baseband waveforms of the two transmit CCs by $s_{1}[n]$ and $s_{2}[n]$, respectively. The signals are up-converted to their respective RF frequencies and amplified by the PAs. The corresponding aggregated RF signal at the multiplexer/duplexer output, after combining the carriers, can then be expressed as

[TABLE]

where $\alpha_{1}$ and $\alpha_{2}$ denote the complex voltage gains of the two PAs, and $\omega_{1}$ and $\omega_{2}<\omega_{1}$ are the angular center frequencies of the individual CCs after up-conversion. This signal then travels towards the antenna, however, due to nonlinear passive components, unwanted PIM products of the transmit signal are created. Assuming that the upper third-order IM sub-band, i.e. $2\omega_{1}-\omega_{2}$, lies in the downlink frequency band, similar to Fig. 1, the baseband equivalent complex PIM waveform appearing in the RX band reads then

[TABLE]

where $\gamma_{l}$ denote the impulse response coefficients of the third-order nonlinear term modeling the memory of the PIM generation mechanism, while $L_{1}$ and $L_{2}$ are the numbers of pre-cursor and post-cursor memory taps in the PIM model, respectively. The total memory length of the PIM generation stage is then $L_{1}+L_{2}+1$.

II-B Baseband Equivalent PIM Model: TX Chains with Memory

We next generalize the PIM modeling to the case where the individual TX component carrier signals are subject to memory or linear distortion prior to the PIM stage. When complemented with a memory polynomial model for the actual PIM generation stage, this allows for versatile memory modeling, for example in cases where there are mutually different delays along the TX paths, or more generally the frequency responses of the two TX chain are different and both contain memory.

To this end, the two transmit carriers travel through their independent TX chains before arriving at the PIM source, and are subject to linear filtering effects described by the impulse responses $\alpha_{1,m}$ and $\alpha_{2,m}$, respectively. The corresponding RF signal model for the combined signal, prior to the PIM stage, then reads

[TABLE]

where $M_{1},M_{2}$ are the numbers of the input pre- and post-cursor memory taps for the TX carriers, with the total input memory length being $M_{1}+M_{2}+1$. When the above combined signal with memory is subject to a third-order PIM nonlinearity with additional memory, the baseband equivalent PIM waveform at own RX band can be written as shown in (4), next page, where $\gamma_{k_{11},\cdots,k_{1M},k_{21},\cdots,k_{2M}}$ are the effective total memory coefficients for the term defined by the parameters $k_{1M},k_{21},\cdots,k_{2M}$, and $M=M_{1}+M_{2}$. Note that in this model, the memory lengths of the transmit CCs and the PIM nonlinearity can be independently chosen, resulting in an overall flexible model from the modeling and cancellation perspective.

To give a concrete example, Table II-B shows the basis function samples stemming from the two signal models presented in this section, with short memory orders of $L_{1}=L_{2}=1$ and $M_{1}=M_{2}=1$ for presentation simplicity. As can be observed, the signal model under TX chains with memory has altogether $42$ basis functions, opposed to $3$ basis functions obtained in the memoryless TX chain case. As a consequence of the different sample delays between the CCs in the basis functions, the more complicated signal model has the potential of better estimating and cancelling also the impacts of any potential timing mismatch errors as well as overall frequency responses in the TX chains. This is achieved, however, at the cost of an increased computational complexity.