**1. Introduction**

An RF transceiver integrated circuit operating in the MedRadio band is widely employed for biomedical devices and sensors, as the wireless communication is essentially needed between the implanted or body-worn medical devices and outside controllers. The wireless connectivity for the biomedical devices is used to exchange the diagnostic and therapeutic data. Its non-invasiveness significantly improves the patient's comfortability by avoiding unnecessary painful surgical operations. The MedRadio band was assigned in 2009 [1], in the frequency band of 401–406 MHz providing a total 5 MHz of contiguous spectrum on a secondary and non-interference basis. The MedRadio rule was amended later in 2011 to allow networking of the devices and controllers and referred to as a medical

Shin, H. A CMOS RF Receiver with Improved Resilience to OFDM-Induced Second-Order Intermodulation Distortion for MedRadio Biomedical Devices and Sensors. *Sensors* **2021**, *21*, 5303. https://doi.org/10.3390/s21165303

**Citation:** Lee, Y.; Chang, S.; Kim, J.;

Academic Editors: Jong-Ryul Yang and Seong-Tae Han

Received: 30 June 2021 Accepted: 3 August 2021 Published: 5 August 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

micropower network (MMN) [2]. Since then, numerous implanted and wearable medical devices equipped with the MedRadio RF transceiver have been reported in literature, such as a wireless bio-signal monitoring system [3], an implanted cardiac defibrillator [4], an implanted pacemaker [5], an intraocular pressure monitoring system [6], physiological state monitoring prosthetic teeth [7,8], wireless position sensing system in total hip replacement surgery [9], capsule endoscopy [10,11], and so on.

The RF communication channel of the MedRadio is accessed on a shared or secondary basis. Hence, they must be robust to interferers coming from nearby other authorized primary users [12]. For mitigating the interferences, system-level techniques, such as error detection and correction via proper channel-coding, listen-before-talk (LBT), and retransmission via a frequency monitoring and classification process, are widely employed [1]. Yet, even though the system-level interference mitigation techniques are employed, additional circuit-level techniques are still needed in the RF transceiver design to improve the overall interference resilience. Unfortunately, however, most previous MedRadio RF integrated circuits, either transceivers [4,5,12,13] or receivers [14–17], did not address those issues nor present proper circuit designs for its mitigation. Ba et al. [12] and Cha et al. [14] indeed mentioned the in-band interference issue and described the adjacent channel rejection (ACR) and the third-order intercept power (IIP3) performances. However, their studies were still limited only to the in-band interference situation and cannot be generalized to the out-of-band interference situation. It is also interesting to note that Cho et al. [18] addressed the very-high frequency (VHF) band interference issue in their dual-band RF receiver and demonstrated a blocker tolerance level of −45 dBm for the MedRadio receiver against the VHF body-channel communication interference. However, their result was also limited to the VHF-band single-tone interference issue and not applicable to the UHF-band multi-tone interference issue. It is also worth noting that non-conventional signal modulation techniques can be also effective for the interference resilience improvement. Novel approaches such as the two-tone modulation [19] and the spread-spectrum modulation [20] were proven effective in 900 MHz transceivers. Yet, they were only applicable to the on-off keying (OOK) modulation and not to the constant-envelope modulation that is more widely adopted by MedRadio devices.

The modern UHF and VHF bands are crowded with a variety of multi-tone signals. They always can be seen as unwanted strong interferers to the MedRadio biomedical devices and sensors. For example, the fifth-generation new radio (5G NR) band encompasses 600–800 MHz UHF band in its frequency range 1 (FR1) band. Additionally, digital broadcasting standards such as the advanced television systems committee (ATSC) of the United States and Korea [21], the digital video broadcasting (DVB) of Europe [22], and the intelligent service digital broadcasting (ISDB) of Japan [23] are serviced in the VHF band of 54–216 MHz and UHF band of 470–860 MHz. Moreover, these interferences are likely to adopt the orthogonal frequency division modulation (OFDM) signaling for high data rate and strong multi-path fading resilience. When an equally spaced multi-tone OFDM signal comes into the MedRadio device as an interferer, numerous intermodulation distortion components will be created by the multiple subcarrier tones, even though they are out of the band. Thus, in modern MedRadio receiver design, it is essential to analyze the effects of the out-of-band (OOB) interference on the receiver's signal-to-noise ratio (SNR) and to design circuits for mitigating its effects. Note that this issue usually cannot be neglected in typical MedRadio receivers even though the interference exists out of the band. We cannot expect sufficient filtering and attenuation for the OOB interference at the RF front end because typical MedRadio antennas show wideband characteristics [11], a complex of high-order matching and filtering at the RF front end may not be favored for low cost and small form factor realization [10], and the LNA in a receiver integrated circuit is not typically band-specific because resistive loads are frequently adopted rather than bulky inductors for the small silicon area.

In this work, we analyze the intermodulation distortion effects induced by the OOB OFDM interferer on the MedRadio receiver and, then, present a design of a CMOS RF receiver by focusing on the second-order intermodulation (IM2) distortion tolerance improvement. This work is carried out based on our prior work [17], which is expanded by adding a complex bandpass filter to realize a low-IF receiver and an IM2 calibration circuit to minimize the OOB OFDM-induced IM2 distortions.

#### **2. Analysis of OFDM-Induced IM2 Distortion Effects**

Let us assume that a desired MedRadio RF signal comes into the receiver along with an OOB OFDM blocker. Since the OFDM signal comprises multiple subcarrier tones that are independently modulated and equally spaced in the frequency domain, any combination of two subcarrier tones within the entire OFDM signal will create multiple intermodulation distortion components. Figure 1a shows the first situation such that two subcarrier tones at *fk* and *fm* create the third-order intermodulation (IM3) distortion at 2*fk* − *fm*. The resulting IM3 falls inside the desired RF channel at *fRF*, directly leading to SNR degradation at *fRF*. Considering that the typical subcarrier spacing is in the range of a few 100 Hz to a few kHz for the communication and broadcasting signals, this effect is only possible when the two subcarrier tones are very close to *fRF*. Such a close blocker signal will be likely to exist inside the desired band. Then, the in-band interference mitigation techniques such as the channel-scan-and-search-based LBT will be effective enough for its mitigation.

**Figure 1.** Two-tone blocker effects. (**a**) Third-order intermodulation effect for the close-in blocker, (**b**) second-order intermodulation effects for the far-out blocker.

On the other hand, when the OFDM blocker signal is far away from *fRF* as shown in Figure 1b and is, thus, likely to be out of the MedRadio band, then its IM3 tone cannot directly affect the desired band at *fRF*. Yet, the IM2 distortion at *fm* − *fk* will fall in the down-converted IF or baseband channel at *fIF* and lead to the SNR degradation. The LBT technique that works for the close blocker signal will not work for this situation because the blocker signal is located far away out of the band and is, thus, likely out of the channel scan range.

It should be noted that a variety of communication and broadcasting services that are being offered worldwide in the UHF and VHF bands employs the OFDM signaling. Hence, the IM2 distortions induced by the OOB OFDM blocker signal need to be analyzed rigorously to accurately assess the SNR degradation in the MedRadio receiver. Figure 2 illustrates that the OOB OFDM blocker signal at *fBL* appears beside the desired MedRadio RF signal at *fRF*. Let the number of subcarriers and subcarrier spacing of the OFDM blocker are *Nsub* and *fsub*, respectively. For example, in the ATSC 3.0 standard [21], given the channel bandwidth of 6 MHz, *fsub* is 843.7, 421.8, and 210.9 Hz depending on the OFDM FFT modes of 8K (*Nsub* = 6913), 16K (*Nsub* = 13,826), and 32K (*Nsub* = 27,649), respectively. Similarly, we can find that *fsub* is 279–8929 Hz for DVB-T2 [22], and 992–3968 Hz for ISDB-T [23].

**Figure 2.** IM2 distortions induced by the multi-tone OFDM blocker.

As shown in Figure 2, any combination of two subcarrier tones out of the total *Nsub* subcarrier tones will create ( *Nsub* − 1) of IM2 tones at the baseband, starting from the first at *fsub* to the last at ( *Nsub* − 1)·*fsub*. If the desired IF signal band overlaps with the IM2 tones, the total IM2 distortion power can be computed by integrating its power spectral density (PSD) over the IF channel bandwidth. Then, the SNR degradation caused by the OFDM-induced IM2 distortions can be accurately evaluated. For example, the IF signal bandwidth of Figure 2 encompasses the 3rd IM2 tone at 3·*fsub* through the 10th IM2 tone at 10·*fsub*. Thus, the total IM2 distortion power should be computed by integrating from the 3rd through the 10th IM2 distortion power.

The well-known input-referred second-order intercept point power (*IIP2*) of an RF receiver is expressed as

$$IIP\_2 = P\_{\rm in} + (P\_{\rm out} - P\_{\rm OIM2}) \tag{1}$$

where *Pin* is the input power, *Pout* is the output power, and *POIM2* is the output-referred IM2 distortion power, all expressed in dB or dBm. When a OFDM blocker signal that has the total power of *Pin.total* is fed to a receiver having *IIP2* and a power gain of *GP*, the input-referred IM2 distortion power *PIIM2* (= *POIM2* − *GP*) can be expressed by

$$P\_{IIM2} = 2P\_{\text{in.total}} - IIP\_2 \tag{2}$$

If the total number of subcarriers is *Nsub*, the power of each subcarrier *Pin.sub* is given by

$$P\_{in\,sub} = P\_{in\,total} - 10\log(N\_{sub})\tag{3}$$

Now, let us compute the total input-referred IM2 distortion power by integrating the IM2 PSD over the band of interest. Ranjan et al. in their OFDM distortion analysis [24] derived an analytic expression of the IM2 PSD by assuming that IM2 tones at the baseband are uncorrelated with the original causative OFDM data. Although the exact PSD expression (Equation (12) of [24]) is not repeated here, we can find that the numerical integration of PSD can be simply carried out by collecting and adding the subcarrier PSD components at their center frequencies without a significant loss in generality and accuracy. Let us take an example of the 3rd *PIIM2* illustrated in Figure 2, which is the first IM2 tone that exists in the IF band. We can find that the 3rd *PIIM2* is created by ( *Nsub* − 3) of two subcarrier tones that are apart by 3·*fsub* in the original OFDM blocker signal. This observation can be generalized such that the *k*-th IM2 power *PIIM2.kth* can be obtained by *k*-th *PIIM2* multiplied by the total number of the subcarrier pairs responsible for creating the *k*-th IM2 tone. It is expressed by

$$10^{\frac{P\_{IM2\text{-}hth}}{10}} = (N\_{sub} - k) \cdot 10^{\frac{2P\_{in\text{-}wh} - 1IP2}{10}}\tag{4}$$

If the band of interest covers from the *ki*-th IM2 tone through the *kf*-th IM2 tone, then, the total input-referred IM2 power *PIIM2.total* that exists within the band of interest can be calculated by summing ( *Nsub* − *k*) of *PIIM2.kth* of (4) from the first *ki*-th through the last *kf*-th. It is expressed as follows

$$10^{\frac{P\_{IIIM\text{Delta}}}{10}} = \sum\_{k=k\_i}^{k\_f} \left( (N\_{sub} - k) \cdot 10^{\frac{2P\_{\text{ins,ub}} - 1IP2}{10}} \right) \tag{5}$$

Equation (5) can be written again in dB as follows

$$P\_{IIM2.total} = \left(2P\_{\text{in.sub}} - IIP\_2\right) + 10\log\left(\sum\_{k=k\_i}^{k\_f} (N\_{\text{sub}} - k)\right) \tag{6}$$

By substituting *Pin.sub* of (6) with (3), Equation (6) can be arranged as 

$$P\_{IIM2.total} = 2\left(P\_{in.total} - P\_{offset}\right) - IIP2\tag{7}$$

where *Poffset* is given by

$$P\_{offset} = 10 \log \frac{N\_{sub}}{\sqrt{\sum\_{k=k\_i}^{k\_f} (N\_{sub} - k)}} \tag{8}$$

Equations (7) and (8) imply that the IM2 distortion power induced by the OFDM signal can be equivalently evaluated by the IM2 distortion power induced by the two-tone blocker signal as long as the two-tone blocker signal power is set to be lower than the original OFDM blocker signal power *Pin.total* by *Poffset*.

This finding greatly simplifies the simulation and characterization of the OFDMinduced IM2 distortion in an RF receiver. Involvement of a multi-carrier OFDM signal in RF circuit simulations will typically require a sophisticated OFDM signal modeling, a very complex numerical analysis method, and a long simulation time. Thus, it is very timeconsuming and impractical to examine the OFDM-induced IM2 effects in RF circuit design. However, if the OFDM blocker signal can be replaced simply by an equivalent two-tone blocker signal by considering an offset parameter *Poffset*, the whole simulation process will become much simpler and more convenient because we can use the conventional timeand frequency-domain circuit simulation methods. Thus, these analytic results enable us to evaluate the OFDM-induced IM2 effects very efficiently when only examining an equivalent two-tone blocker induced IM2 effects.

Let us take an example of 16K FFT mode of ATSC 3.0 [21], which has *Nsub* = 13,825 and *fsub* = 421.875 Hz. When the IF band of a low-IF MedRadio receiver resides in 150–450 kHz, the IM2 tones appearing within the band are from *ki* = 356th to *kf* = 1066th components. Then, *Poffset* is computed to +6.56 dB by (8). It implies that if an ATSC blocker of −10 dBm is injected to a receiver and induces IM2 distortion at the baseband, the same amount of IM2 distortion power is also induced by a simple two-tone blocker of −16.56 dBm. Moreover, assuming the input signal power of the receiver is −50 dBm, and the receiver *IIP2* is +30 dBm, *PIIM2.total* will be −63.1 dBm (=2 × (−10 − 6.56) − 30) according to Equation (7), and the resulting SNR will be +13.1 dB as the input signal power is −50 dBm and the input-referred distortion power *PIIM2.total* is −63.1 dBm
