Enhancing 5G-NR mmWave : Phase Noise Models Evaluation with MMSE for CPE Compensation

The 5G-NR mmWave communication system [1, 11, 12] exploits the radio frequency spectrum with wavelengths ranging between 24 GHz and 100 GHz [3]. This specific frequency range is relatively underutilized. This offers a significant opportunity to enhance available bandwidth. Unlike lower frequencies which experience congestion due to existing TV and radio transmissions and 4G LTE networks, 5G-NR mmWave technology [1, 11, 12] enables faster data transmission, albeit with a reduced range. The high-frequency mmWave bands, especially those exceeding 24 GHz, have been selected for their ability to support substantial bandwidths and high data rates, making them pivotal for expanding wireless network capacity.

The mmWave bands between 24 GHz and 100 GHz, targeted for 5G deployment, can support bandwidths up to 2 GHz without requiring band combination, as illustrated in Figure 1. This vast bandwidth allows 5G-NR mmWave systems to support various high-bandwidth applications, including immersive virtual reality, augmented reality, high-definition video streaming and ultra-fast file downloads.

5G-NR mmWave propagation presents unique challenges due to increased path loss, susceptibility to atmospheric absorption and sensitivity to obstacles. To overcome these challenges, 5G-NR mmWave systems employ Phase Tracking Reference Signals (PT-RS) which play a crucial role in phase synchronization between the transmitter and receiver, ensuring reliable communication. PT-RS enables the estimation and compensation of phase errors induced by various sources, including oscillator imperfections, channel effects and hardware impairments, thereby enhancing the robustness and reliability of communication links.

In the realm of 5G-NR mmWave communication systems, accurate modeling of phase noise is pivotal for understanding and addressing signal degradation. Phase noise originates from various sources such as local oscillators, phase-locked loops (PLL) and hardware imperfections, posing significant challenges to reliable communication at millimeter-wave frequencies. In [13], a model considering three main noise sources—reference clock, PLL and VCO—is proposed.

We present three phase noise models: ’A’ [8], ’B’ [8] and ’C’ (TR 38.803 [14]) which are used to capture and represent the characteristics of phase noise in the context of 5G-NR mmWave. The phase noise characteristic is expressed as follows:

where ${\rm{PSD}}{{}_{\rm{0}}}$ is the power spectral density at zero frequency ($f=0$) in dBc/Hz, $f_{z,n}$ are zero frequencies and $f_{p,n}$ are pole frequencies. Table 2 shows three parameter sets obtained from practical oscillators operating at 30 GHz, 60 GHz and 29.55 GHz, respectively [8, 7].

Figure 2 shows the Phase Noise Power Spectral Density (dBc/Hz) based on the frequency (Hz) of the three phase noise models: ’A’ [8], ’B’ [8] and ’C’ (TR 38.803) [14].

Accurate estimation and compensation of Common Phase Error (CPE) in 5G-NR mmWave systems require sophisticated algorithms capable of mitigating the adverse effects of phase noise. In this section, we focus on the implementation of state-of-the-art algorithm, namely Minimum Mean Square Error (MMSE) [15, 16, 17] for CPE estimation and compensation.

Consider a 5G-NR communication system operating in the mmWave frequency range. Let $\mathbf{r}$ be the received signal corrupted by CPE and $\mathbf{s}$ be the transmitted signal. The received signal can be modeled as:

where $\mathbf{H}=\left[e^{j\phi_{l,n}}\right]_{(l,n)}$ represents the CPE matrix and $\mathbf{n}$ is the additive white Gaussian noise vector. The MMSE equalization for the CPE matrix $\mathbf{W}_{\text{MMSE}}$ is computed as follows:

where $\sigma^{2}$ is the noise variance, $\gamma$ is the signal-to-noise ratio (SNR) and $\mathbf{I}$ is the identity matrix.

Figure 3 shows the processing chain implemented for the phase noise models evaluation in 5G-NR mmWave systems. Accurate phase noise modeling enables the identification and mitigation of phase errors, ensuring the robustness of communication links and optimizing the overall precision of 5G-NR mmWave systems.

The different steps for NR-PDSCH transmission and reception (refer to Figure 3) are described as follows:

(a)

NR-PDSCH Encoding: In this step, the data intended for transmission over the downlink channel is encoded using error correction coding schemes such as LDPC (Low-Density Parity-Check) or Polar codes. Channel coding aims to introduce redundancy into the transmitted data to enhance error resilience and facilitate reliable communication.

(b)

CP-OFDM Modulation: After encoding, the modulated symbols are mapped onto resource elements (REs) within the allocated resource blocks. CP-OFDM (Cyclic Prefix Orthogonal Frequency Division Multiplexing) is employed for modulation. The modulated symbols are then transformed into the time domain using an inverse fast Fourier transform (IFFT), followed by the addition of a cyclic prefix to mitigate intersymbol interference (ISI) caused by multipath propagation.

(c)

Phase Noise Modeling: Phase noise is inserted to accurately represent the impact of local oscillator imperfections on the transmitted signal.

(d)

Channel (CDL/TDL): The modulated signal traverses through the wireless channel which can be modeled using either a Clustered Delay Line (CDL) [18] or a Tap Delay Line (TDL) [18] model.

(e)

NR-PDSCH Receiver: At the receiver, the received signal undergoes timing synchronization and CP-OFDM demodulation to extract the NR-PDSCH transmitted information. Prior to NR-PDSCH decoding, phase noise estimation and correction based on MMSE estimation are applied to mitigate the impact of CPE on the received signal. The equations (3) is applied for that purpose.

The experimental setup was executed using MATLAB [19] which integrates the functionalities required for simulating the 5G-NR mmWave transmission chain. This tool enables the demonstration of phase noise impact in a 5G-NR mmWave system and the role of Phase Tracking Reference Signal (PT-RS) in compensating for Common Phase Error (CPE). Table 3, Table 4, Table 5 and Table 6 list the parameters used during the simulation process.

The carrier frequency for the simulation is set at 29.55 GHz, 30 GHz and 60 GHz, allowing for the exploration of different carrier frequencies’ impact on the system’s behavior, aligned with the mmWave spectrum characteristics.

Table 4 defines the cell parameters used in the simulation for evaluating phase noise models and the Zero-Forcing/MMSE algorithms within the 5G-NR mmWave context.

Table 5 provides the configuration parameters specific to the Physical Downlink Shared Channel (PDSCH) within the simulation setup, with PTRS enabled to ensure accurate phase noise tracking.

The evaluation of phase noise models ’A’ [8], ’B’ [8] and ’C’ (TR 38.803 [14]) is based on the parameter sets defined in Table 2. These models are implemented within MATLAB’s 5G Toolbox [19] using the hPhaseNoiseModel() function which simulates the phase noise characteristic PSD for specific frequency offsets and carrier frequencies.

Error Vector Magnitude (EVM) in both dB and percentage is the key metric for comparison, used to assess phase error variance introduced by each model. The models’ accuracy is tested across diverse channel conditions, including scenarios with high path loss, multipath fading and varying SNR, ensuring comprehensive evaluation under realistic mmWave conditions.

In this subsection, we detail the implementation of the MMSE algorithms for CPE estimation and compensation in the context of 5G-NR mmWave. These algorithms are crucial for mitigating phase errors introduced by various factors, thereby enhancing the reliability and performance of mmWave communication systems.

The MMSE algorithms for CPE estimation and compensation are derived from equations (3) and (LABEL:Equ:04). The implementation of these algorithms within the NR-PDSCH receiver is executed using MATLAB’s nrEqualizeMMSE() function, designed to handle the complexities of CPE estimation and compensation in 5G-NR mmWave systems.

Performance metrics such as Block Error Rate (BLER), Signal-to-Noise Ratio (SNR) and throughput are employed to assess the effectiveness of the MMSE algorithms. These metrics serve as key indicators of the robustness and reliability of the algorithms for CPE estimation and compensation in the 5G-NR mmWave context.

The NR-PDSCH receiver implementation utilizes the capabilities of MATLAB’s 5G Toolbox [19], leveraging a suite of essential functions tailored for 5G communication systems. A selection of these functions, along with their descriptions, is provided in Table 7.

By leveraging these functions within the 5G Toolbox, the NR-PDSCH receiver implementation achieves accurate and efficient processing of received signals by facilitating the recovery of transmitted data in 5G-NR mmWave communication systems.

Figures 4, 5 and 6 demonstrate the impact of Common Phase Error (CPE) compensation on the performance of 64QAM and 256QAM modulation schemes. For 64QAM, CPE compensation reduces the Error Vector Magnitude (EVM) from 7.4% to 4.6% and improves the EVM in dB from -22.6 dB to -26.8 dB, indicating a significant enhancement in signal quality. The Bit Error Rate (BER) for 64QAM also drops dramatically from $5.5\times 10^{-3}$ to $5.2\times 10^{-5}$, highlighting a substantial reduction in transmission errors.

Similarly, for 256QAM, CPE compensation decreases the EVM from 5.4% to 4.3% and improves the EVM in dB from -25.3 dB to -27.4 dB. The BER for 256QAM also shows improvement, although less pronounced, decreasing from $3.5\times 10^{-2}$ to $6.1\times 10^{-3}$. These results demonstrate that CPE compensation significantly enhances signal integrity and reduces errors, making it a valuable technique in communication systems utilizing these modulation schemes.

This section analyzes CPE Compensation performance across different SNR levels, Phase Noise models and antenna configurations. Figures 7 and 8 show the Error Vector Magnitude (EVM) values in decibels (dB) for 64QAM and 256QAM modulation schemes under various Phase Noise (PN) models, both with and without CPE compensation. EVM measures the accuracy of the modulation and demodulation processes, with lower values indicating better performance. The results consistently show that CPE compensation improves EVM across all modulation schemes and PN models. For instance, in the case of 64QAM with PN Model ’A’, the EVM improves from -22.6 dB without compensation to -26.8 dB with compensation. This trend is consistent across most scenarios, indicating the effectiveness of CPE compensation techniques in mitigating phase errors and enhancing communication performance in mmWave systems.

Variations in performance among different PN models and modulation schemes are also observed. PN Model ’B’ generally exhibits lower EVM values compared to PN Model ’C’, suggesting that the choice of PN model significantly impacts system performance. 64QAM and 256QAM also exhibit differences in EVM, with 256QAM typically showing higher EVM values due to its increased complexity and higher data rate.

When analyzing the performance of Phase Noise (PN) Models ’A’, ’B’ and ’C’ under the same modulation scheme, PN Model ’B’ generally performs better than PN Models ’A’ and ’C’ in terms of EVM values, both with and without CPE compensation. This indicates that PN Model ’B’ is more effective at reducing phase errors and maintaining signal accuracy, leading to improved communication performance.

Figures 9 and 10 illustrate the BLER performance of NR-PDSCH under different antenna configurations (NTx = 1 and 2, NRx = 2) and phase noise models. The results consistently show that CPE compensation enhances system performance by significantly lowering the BLER across various SNR values, particularly at higher SNR levels where the gap between compensated and non-compensated curves widens. This indicates that CPE compensation is highly effective in mitigating the adverse effects of phase noise, leading to more reliable data transmission.

Figures 11 and 12 present BLER performance for NR-PDSCH at SNR values of -2.5 dB and 10 dB, respectively, under different antenna configurations. At lower SNR (-2.5 dB), BLER remains relatively high across all configurations, with marginal differences observed between cases with and without CPE compensation. At this low SNR, the impact of CPE compensation on BLER is limited due to the dominant noise floor. However, at higher SNR (10 dB), a pronounced reduction in BLER with CPE compensation is observed across all configurations. The most significant improvements are noted in scenarios with more antennas (NRx = 4), indicating that CPE compensation becomes increasingly effective as the number of antennas increases, due to improved channel estimation and spatial diversity.

The BLER results depicted in Figure 13 indicate that CPE compensation consistently improves performance across all phase noise models. The reductions in BLER are as follows: from $8.5\times 10^{-2}$ to $7.8\times 10^{-2}$ for PN Model ’A’, from $9.7\times 10^{-2}$ to $8.4\times 10^{-2}$ for PN Model ’B’ and from $8.4\times 10^{-2}$ to $7.6\times 10^{-2}$ for PN Model ’C’. Among these, PN Model ’B’ shows the highest BLER, both with and without CPE compensation, indicating that it introduces more severe phase noise compared to PN Models ’A’ and ’C’. Conversely, PN Model ’C’, when CPE compensation is applied, exhibits the lowest BLER, showcasing the most significant improvement.

The variations in BLER performance among the PN models highlight the differing severity and predictability of the phase noise inherent in each model. PN Model ’B’ presents a greater challenge for compensation algorithms, leading to higher BLER. On the other hand, PN Model ’C’, with its less severe and more predictable phase noise, allows compensation algorithms to perform more effectively, resulting in the most significant improvement and the lowest BLER.

The results of this study underscore the critical role of CPE compensation in enhancing the performance of 5G-NR mmWave communication systems. Across various modulation schemes, antenna configurations and phase noise models, the implementation of CPE compensation consistently leads to improvements in signal quality, as evidenced by reductions in EVM and BLER. The effectiveness of CPE compensation becomes particularly evident at higher SNR levels, where it significantly reduces error rates, thereby enhancing the reliability and robustness of communication systems.

Moreover, the comparison of different PN models reveals that the severity and predictability of phase noise have a substantial impact on the performance of CPE compensation techniques. Models with more predictable phase noise, such as PN Model ’C’, allow for more effective compensation, resulting in lower BLER and improved system performance.

The practical implications of these findings are significant for the design and optimization of 5G-NR mmWave communication systems. The choice of phase noise model and the implementation of effective CPE compensation strategies are critical for achieving optimal system performance, particularly in environments characterized by high SNR and complex antenna configurations. Future research should continue to explore the characteristics and limitations of various phase noise models and compensation techniques to further enhance the reliability and efficiency of mmWave communication systems.