# Optimized DM-RS Configuration for Improved 5G New Radio Network Capacity and Performance.
## 4 Doppler Frequency Shift Analysis  
The main objective of this section is to analyze Doppler effects in detail to lay the foundation for the optimization of DM-RS configuration, with a focus on the minimization of additional DM-RS symbols, introduced to cope with challenges of channel estimation for high-speed users. As discussed earlier, 5G NR systems were designed to support various use cases with the flexibility to operate in different frequency bands. The focus of Doppler shift analysis is to determine minimal DM-RS density for most typical 5G/NR configurations in terms of operating frequency and subcarrier spacing (SCS), and for different types of user behavior in terms of mobility and related speeds. The channel time variations due to Doppler effects are closely related to the velocity (\(\
u\)) of the transmitter/receiver, where variation between OFDM symbols may become significant when speed is increased. The Doppler effect is mostly modeled by the Jakes model [11; 21], the autocorrelation function of which is the first-order Bessel function \(\int_{0}(2\pi\
u_{max}\Delta t)\) where \(\
u_{max}\) is the maximum Doppler shift (calculated as \(\
u_{max}=\text{Fc}\ast\text{v}/\text{c}\)), Fc is the carrier frequency, v is the velocity and \(\Delta t\) is the time separation. An autocorrelation channel function above 67% is considered good enough to secure smooth communication (marked in Figures 4 and 5 with a red dotted line). Owing to this model, the interval between two consecutive DM-RSs can be selected to ensure an arbitrary coherence time. Before modeling the impact and severity of the Doppler shift for moving UEs, it can be noticed that Doppler effects are driven by the operating frequency, as well as frame structure  
Figure 4: Impact of vehicle speed channel estimation, Doppler shift modeled with the first-order Bessel function: (a) midband (sub-6 GHz) deployment scenario: Fc = 3.5 GHz, SCS = 30 kHz; (b) millimeter-wave band deployment scenario: Fc = 26 GHz, SCS = 30 kHz. Figure 5: Impact of subcarrier spacing (SCS) on channel estimation, Doppler shift modeled with the first-order Bessel function: (a) midband (sub-6 GHz) deployment scenario: Fc = 3.5 GHz, v = 120 km/h; (b) millimeter–wave band deployment scenario: Fc = 26 GHz, v = 30 km/h. and length, which depends on subcarrier spacing (SCS). When it comes to frequencies allocated for 5G, various frequency bands are supported. At the same time, the radio interface in 5G NR systems is designed with high flexibility to address different use cases. One of the key functionalities is support for different numerologies, where SCS can be configured as 15 kHz, 30 kHz, 60 kHz, or 120 kHz. The first step was to analyze the impact of speed; the Doppler shift was modeled for standard widely adopted carrier frequencies of 3.5 GHz and 26 GHz, the most frequently used SCS of 30 kHz was selected, and speed was varied between values of 5 km/h, 30 km/h, 60 km/h, 120 km/h and 240 km/h (Figure 4). What can be observed in Figure 4 is that for most frequently mid-band deployment (use case: 3.5 GHz, SCS = 30 kHz) and users moving with speeds up to 120 Km/h, the autocorrelation function does not drop below the target value of 67% for all fourteen symbols in one time slot, and the configuration of second DM-RS symbol makes sense for speeds above 120 km/h. At the same time, for millimeter-wave deployment (26 GHz, SCS = 30 kHz) single DM-RS can support only very slow-moving UEs (up to 10-20 km/h). The next step was to analyze the impact of subcarrier spacing, which varied between values of 15 kHz, 30 kHz, 60 kHz and 120 kHz. The Doppler shift was modeled for midband deployment (Fc = 3.5 GHz) with the assumed speed of 120 km/h, while for millimeter-wave deployment (Fc = 26 GHz), a speed of 30 km/h was selected. What can be observed in Figure 5 is that for most common midband deployments (Fc = 3.5 GHz), even at 120 km/h speed, a single DMRS is enough for SCS greater than or equal to 30 kHz.