# Guard Band Protection Scheme to Facilitate Coexistence of 5G Base Stations and Radar Altimeters
## 2 Modelling for Guard Band Protection and Analysis
### Aclr  
ACLR indicates the ratio of the mean power centred on the assigned channel frequency to the mean power centred on an adjacent channel frequency:  
\[\mathrm{ACLR}=\overline{\mathrm{P_{input}}-\mathrm{P_{channel}}}, \tag{14}\]  
where \(P_{\mathrm{input}}\) is the input signal power, and \(P_{\mathrm{channel}}\) is the channel power in dBm, defined as [24]  
\[\mathrm{P_{channel}}=10\log_{10}\biggl{[}\frac{\mathrm{BW_{channel}}}{\mathrm{ BW_{re}}\cdot\mathrm{k_{n}}}\cdot\frac{1}{\mathrm{N}}\cdot\sum_{i=1}^{\mathrm{N}}10^{ \frac{\mathrm{P_{i}}-\mathrm{i_{r}}(\mathrm{RRC})}{10}}\biggr{]}, \tag{15}\]  
where \(BW_{\mathrm{channel}}\) is the channel bandwidth (in kHz), \(BW_{\mathrm{re}}\) is the resolution bandwidth, \(k_{n}\) is the correction factor for noise bandwidth of a specific resolution, \(N\) is the number of pixels within the channel, \(P_{i}\) is the level represented by pixel \(i\) of the trace (in dBm), and \(a_{\mathrm{i}(\mathrm{RRC})}\) represents the attenuation of the 3 GPP root-raised cosine (RRC) filter at pixel \(i\) (in dB). We assume that 5G downlinks are allocated to the 3.7-4.0 GHz band with a bandwidth of 100 MHz. The subcarrier spacing is set as 30 kHz, and the duplexing mode is time division duplexing (TDD). To generate the 5G NR test model (TM) waveforms, we use the MATLAB R2024a class hNRReferenceWaveformGenerator, with the parameters outlined in Table 1.  
Subsequently, we use the helper function hACLRParametersNR to acquire the necessary parameters for measuring ACLR from the generated waveform. Finally, the helper function hACLRMeasurementNR is adopted to calculate the input signal power in the main channel and ACLR using a square window on adjacent channels [25]. Through these calculations, the ACLR is determined to be 64.166 dB. Notably, the orthogonal frequency division multiplexing (OFDM) signal is derived through the inverse continuous-time Fouriertransform, which can be challenging for many hardware implementations. Therefore, the modulation process of OFDM is accomplished using the inverse discrete Fourier transform. As depicted in Figure 4a, excessive out-of-band powers, attributable to extreme side lobes, results from implicit windowing in the OFDM time domain. To mitigate interference in adjacent channels, we design a filter to enhance the ACLR [26]. Figure 5 illustrates the process flow for ACLR measurement with filter design. The design process is initiated by generating 5G NR-TM waveforms, specifying parameters as outlined in Table 1. Subsequently, a low-pass filter is devised with its stopband centred at 3.95 GHz and a bandwidth of 50 MHz. The transition band starts at the edge of the occupied bandwidth and stops at the edge of the channel bandwidth. Moreover, the stopband bandwidth is set as 49.14 MHz, accompanied by an attenuation of 80 dB. To ensure perfect reconstruction of the signal, oversampling of the filtered 5G NR-TM waveforms is performed at a sampling frequency twice the highest frequency of the input signal. Following the oversampling, a high-power amplifier model is applied to introduce out-of-band distortion, thereby generating adjacent channel carrier signals. This filter design aims to shape the spectrum within the original bandwidth of the waveform. The transition band begins at the edge of the occupied transmission bandwidth and ends at the edge of the overall channel bandwidth. Unlike other advanced filter technologies that rely on narrowband high-Q filters made with specialized materials [27], our approach focuses on efficiently managing spectral leakage within the existing transmission system without altering the sampling rate or requiring additional complex hardware. Figure 4b illustrates the ACLR performance following waveform filtering. Power leakage in the first adjacent channel is significantly reduced. This improvement is attributable to the implementation of a low-pass filter in the frequency domain, effectively cancelling out a specific amplitude of the OFDM reference signal and achieving peak cancellation.