Realistic beamforming design using SRS-based channel estimate for ns-3 5G-LENA module

Beamforming (BF) is a key procedure to overcome propagation limits in millimeter-wave bands but also to extend network coverage in sub 6 GHz bands, as considered in recent 3GPP and IEEE communication standards. Up to date, ns-3 included various ideal BF methods, in which an ideal channel state acquisition is assumed and no BF overhead is considered. However, ns-3 lacks the implementation of realistic BF methods, in which the overhead needed to perform BF-related procedures and the errors due to a non-ideal channel state acquisition are taken into account. A way to perform realistic BF is to rely on Sounding Reference Signals (SRS) for channel estimation and then determine the best BF vectors based on the channel estimate. In this paper, we first present an abstraction model to perform BF using SRS-based channel estimation, and then we provide the implementation details of 5G New Radio (NR)-compliant SRSs and new realistic BF methods using SRS-based channel estimate, as included in the ns-3 5G-LENA simulator. Simulations are provided to compare realistic BF and ideal BF methods, for different propagation scenario conditions and SRS transmitted powers.


INTRODUCTION
The use of multiple antennas in communication systems (a.k.a. Multiple-Input Multiple-Output (MIMO) systems) has attracted a lot of attention in the recent decades. MIMO permits increasing the data rate by sending multiple data streams simultaneously (known as spatial multiplexing) or increasing the robustness of the data transmission by sending replicated data (known as transmit diversity) or providing array gain into specific spatial areas by properly Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. designing the antenna weights or beamforming vectors (known as beamforming) [7,18]. Beamforming (BF) is particularly essential at high carrier frequencies within the millimeter wave (mmWave) region to combat the high pathloss propagation losses and blocking effects [6,12,21]. In case of BF, a single spatial stream is sent per receiver and the multiple antennas are used to concentrate the radiated power towards the receiver's location, thus improving the received Signal to Interference plus Noise Ratio (SINR) and the probability of error at the target receiver, as well as reducing the generated interference towards other spatial locations. BF has been adopted in many recent communication standards, like IEEE 802.11 (Wi-Fi), IEEE 802.16 (WiMAX), 3GPP Long Term Evolution (LTE) (4G), and 3GPP New Radio (NR) (5G). IEEE 802.11ad/ay defines many mandatory and optional BF-related procedures [9,17,24]. 3GPP LTE covers BF in the so-called Transmission Mode 7 [22]. 3GPP NR standard has defined multiple beam management procedures [1,10], including beam measurement, beam sweeping, beam reporting, and beam determination, for both Time Division Duplexing (TDD) and Frequency Division Duplexing (FDD) systems, in sub 6 and mmWave bands.
3GPP NR has introduced Channel State Information Reference Signals (CSI RSs) and Synchronization Signal Blocks (SS blocks) for beam management in the Downlink (DL) and Sounding Reference Signals (SRSs) for beam management in the Uplink (UL) [1,10]. However, in TDD systems, SRS can be used for beam management in both DL and UL directions because, due to channel reciprocity 1 , beam reciprocity can be assumed (i.e., BF vectors for UL and DL are the same). This way, the SS blocks can be limited to the initial access and the use of CSI RSs for channel estimation at the user (UE in 3GPP) can be avoided.
The ns-3 mmWave module for 5G NR in mmWave bands [15], as well as the ns-3 5G-LENA module for 5G NR in sub 6 and mmWave bands [19,20], included various ideal BF methods. Those methods are ideal in the sense that no resources are employed to determine the best beams and an ideal channel estimation is assumed. However, as of today, both modules lack the implementation of realistic BF methods to correctly assess the additional overhead needed to perform beam management procedures and analyze the errors induced by a non-ideal channel estimation.
In this paper, we propose, implement, and evaluate a realistic beam management procedure for system-level simulation of 5G NR TDD systems in ns-3. First, we have implemented NR-compliant SRS signals transmissions and receptions in the ns-3 5G-LENA module. Based on SRS reception, we propose an abstraction model to estimate the channel matrix in a multi-antenna system. The abstraction model is used, as in typical network-level simulations, to avoid the related signal processing operations and reduce its computational complexity. Using the SRS-based channel estimation, the BF vectors for both DL and UL can be determined at the gNB side. For that, we have linked the SRS reception with the beam management classes at the gNB, enabling the realistic BF procedure. Finally, we have evaluated the proposed procedure and compared it with the ideal BF method.
The rest of the paper is organized as follows. Section 2 reviews different BF methods, the SRS defined in 3GPP NR specification, and its antecedents in ns-3. Also, we present an abstraction model to determine the BF weights using SRS-based channel estimation. Then, in Section 3, we describe the implementation of the NRcompliant SRS and the implementation of the realistic BF using SRS-based channel estimation. Examples and tests are described in Section 4. Simulation results are shown in Section 5. Finally, conclusions are drawn in Section 6.

SRS-BASED BEAMFORMING
This section reviews BF methods and SRS design in 3GPP NR, the two key components to implement a realistic BF algorithm using SRS-based channel estimate. We also describe the antecedents in ns-3. In brief, SRS are available in ns-3 LENA but used for link adaptation, not for beam management, while ideal BF methods are available in ns-3 mmWave and ns-3 5G-LENA modules, but both modules lack realistic BF models. After that, we present an abstraction model for channel estimation using SRS in TDD systems, which is the key part to link the two components.

Beamforming Methods
In general, there are three basic methods to find the BF weight vector: • Design the BF vector using direction of arrival (DoA). There are methods that allow estimating the DoA at the gNB from a UE transmitted signal, and so determine the UE position. Such DoA can then be used to steer the beam towards the UE location. • Design the BF vector using channel estimation. The optimal BF weight can be found from the channel matrix. The gNB can directly estimate the channel from an uplink signal transmission from the UE, and use such a channel estimation for nearly optimal BF design. Thanks to channel reciprocity in TDD systems, such BF vectors are valid for both DL and UL transmissions. In 3GPP LTE and NR, the SRS have been specifically designed to be used for that purpose. • Design the BF vectors by using beam training and receiver's feedback. In case that the gNB has a set of pre-defined beams, it can send training signals through all of them, so that the UE can measure the received signal quality and then report the index of the best beam. Such procedures are standardized in both IEEE 802.11ad/ay and 3GPP NR.

Sounding Reference Signal
SRS is a reference signal sent in the UL (from UE to gNB) in 3GPP NR to measure the channel quality. In particular, SRS receptions at the gNB provide information about the combined effect of multipath fading and power loss of the transmitted signal from the UE. Based on SRS reception, the gNB can take smart decisions for resource allocation and scheduling, link adaptation (e.g., modulation and coding scheme selection) [8], inter-cell interference management [11], and beam management [10]. According to 3GPP NR specification [4], SRS transmissions can be periodic, aperiodic, or semi-persistent. In time domain, the range for SRS transmission in a slot is from 8th to 13th OFDM symbol. NR leaves the 14th symbol in a slot for PUCCH. Within such a 6 OFDM symbol region, SRS transmissions can take maximum 4 OFDM symbols in time domain. In frequency domain, the bandwidth for SRS can be adjusted and interleaving is permitted. Interleaving is defined by the so-called transmission combination, which defines the frequency distance between two subcarriers used by SRS. Based on such pattern, multiple SRS signals (from different antenna ports or UEs) can be multiplexed in the same OFDM symbol.

Antecedent Implementations in ns-3
The mmWave module [15] introduced various BF methods for mmWave bands in ns-3. Namely, the long-term covariance matrix method, the beam search method and the line-of-sight (LOS) path method. In the long-term covariance matrix method, BF vectors are computed from the maximal eigenvectors of the channel covariance matrix. In the beam search method, it is assumed that there is a discrete number of beams from a pre-designed codebook, from which the beam that provides the largest SINR (considering the beam and the channel matrix) is selected for each gNB-UE link. In the LOS path method the DoA is assumed to be perfectly known and used to calculate the BF vectors to steer the beam towards such direction. In the 5G-LENA module [19] (and in its extension for unlicensed spectrum operation [20]), we have available the beam search method and the LOS path method. Also, we introduced the representation for a quasi-omnidirectional BF, and multiple combinations with the previous methods (e.g., the gNB using beam search method and the UE using quasi-omni reception). However, all the methods available in ns-3 NR modules [15,19,20] up to date, were ideal BF methods in the sense that they assume perfect knowledge of the channel matrix and do not consume any time/frequency overhead to design the BF vectors.
SRS are implemented in ns-3 LENA module [8]. The implemented model uses periodic SRS. SRS are sent by the UE with a pre-configured periodicity (SrsPeriodicity attribute in LteEnbRrc that defaults to 40 ms), spanning over the whole bandwidth (not interleaved) and sent over the last symbol of the slot (14th OFDM symbol). The RRC model includes an algorithm to dynamically assign a periodicity as a function of the number of UEs attached to an eNB, which outputs the SRS subframe offset and the SRS periodicity for each UE. In ns-3 LENA module, SRS are used by the eNB for link adaptation, i.e., to determine the UL MCS, through the computation of an UL CQI that uses the SINR received during the SRS transmission.
Realistic Beamforming Design using SRS-based Channel Estimate for ns-3 5G-LENA Module B. Bojović, S. Lagén, L. Giupponi Both mmWave and 5G-LENA modules were missing SRS implementation. In addition, in 5G-LENA our objective by including SRS is different as compared to that of LENA. We want to use SRS for beam management purposes, in addition to link adaptation. For beam management, we can use the SRS to estimate the channel in multi-antenna TDD systems, assuming channel reciprocity (DL channel matrix equals to the transpose of the UL channel matrix) and use the channel estimate for BF design. For that, we cannot rely on the received signal from an SRS transmission, since this is not modeled in ns-3 spectrum. Instead, we need an abstraction model for SRS-based channel estimation.

Abstraction Model for SRS-based Channel Estimation
Assume a single-antenna system. Let ℎ denote the (complex-valued) small-scale fading channel between a UE and a gNB. Then, the estimation of the small-scale fading channel at the gNB can be modeled as [14]: where is a scaling factor to maintain normalization of the estimated channel, and is the white complex Gaussian channel estimation error. The estimation error ( ) is assumed to be characterized by zeromean and variance 2 . The variance of the error is given by where SINR is the received SINR of SRS at the gNB and Δ is the gain obtained from time-domain filtering during the channel estimation. According to 3GPP analysis of SRS transmission, Δ is set to 9 dB [14]. The scaling factor ( ) is given by . ( In case of multi-antenna systems, assuming independent smallscale fading among antenna elements, the model in (1) can be used to estimate each fading component of the 3GPP spatial channel matrix [25]. Then, the channel matrix estimate can be used to compute transmit/receive BF vectors, as part of the beam management.
In particular, the model in (1) can be applied to each channel matrix coefficient separately, if an independent and orthogonal reference signal is transmitted on each UE antenna, for whatever number of gNB antennas. Otherwise, we need as many OFDM symbols as the number of UE antennas, to properly estimate all the channel matrix coefficients. Therefore, depending on the MIMO configuration and BF architecture of the UE, the SRS configuration needs to be adjusted to enable the estimation of the multi-antenna system appropriately.

IMPLEMENTATION IN NS-3
In this section we provide the implementation details of SRS allocation, transmission, and reception, as implemented in ns-3 5G-LENA simulator. Also, we describe the developed extension of the BF framework and the implementation of the new realistic BF procedure, which uses the abstraction model presented in Section 2.4 to estimate the channel based on SRS report. In the frequency domain, in order to allow frequency multiplexing, SRS is typically transmitted over only a subset of subcarriers, defined by the configuration, e.g., each 2nd or each 4th subcarrier is used for SRS transmission. However, since the minimum transmission granularity in 5G-LENA module is a RB in frequency domain, all subcarriers are used for SRS transmission. Figure 1 shows example of SRS transmissions of 2 different UEs, considering SRS periodicity equal to 20 slots. Numerology considered is = 0. F in the figure stands for frame and SF for subframe. As per 5G-LENA design there is at most 1 UE SRS transmission per slot. The figure illustrates the slot structure and the symbols over which the SRS transmission spans, assuming a repeated TDD pattern structure of [DL F UL UL UL] (i.e., one DL slot, followed by one flexible slot and three UL slots 2 ) and that SRS transmissions occur in F slots (i.e., slots number 1 and 6 in the figure).
In 5G NR, SRS parameters, such as periodicity and offset, are typically configured by RRC and notified to UE [2]. Another option is to have gNB MAC scheduler to determine the SRS periodicity/offset and then to notify UE through DCI format 2_3 on which resources SRS should be transmitted [5]. The latter option, scheduling-based SRS, is a more dynamic approach and allows more flexible SRS parameter and periodicity assignment, e.g., when there are less UEs, a lower periodicity value can be used, while when there are more UEs, the gNB MAC scheduler can dynamically increase the periodicity and then update the offsets accordingly. We have implemented scheduling-based SRS.
To allow dynamic SRS scheduling and adjustment of SRS periodicity/offset of all UEs, we introduced NrMacSchedulerSrs and NrMacSchedulerSrsDefault into 5G-LENA model. NrMacSched-ulerSrs is an interface that is used by the NR gNB MAC scheduler to obtain the SRS offset/periodicity for a UE. There can be various implementations of this interface that would simulate different algorithms for SRS offset/periodicity generation. In NrMacScheduler-SrsDefault, we provide one of possible implementations. Each time a new UE is attached it is called the function AddUe that returns the offset/periodicity configuration. When scheduler detects that the SRS periodicity is too small for the number of UEs it calls function IncreasePeriodicity, which picks up the next periodicity value from the list of standard values, i.e., 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320, 640, 1280, 2560 slots [2]. Scheduling-based SRS is more flexible approach than SRS configuration through RRC. E.g., in 4G-LENA SRS configuration is through RRC and static, which requires that a user needs to configure SRS periodicity based on the maximum expected number of UEs in the simulation scenario. To allow dynamic SRS periodicity adaptation in 5G-LENA, it was necessary to set a constraint which is that at most 1 UE can send the SRS in a single slot.
Configuration parameters related to SRS transmissions are specified in NrMacSchedulerNs3 class. The user can configure the number of SRS symbols that will be allocated for SRS transmission through the attribute SrsSymbols. Additionally, the user can configure whether SRS will be transmitted only in flexible slots, or in both flexible and UL slots by setting the attribute EnableSrsInUl-Slots.

Realistic Beamforming
5G-LENA BF framework is extended to provide support for realistic BF algorithms. While ideal BF algorithms decide the beams based on either the assumptions of perfect knowledge of the channel (e.g., cell scan method) or the exact positions of the devices (e.g., DoA method), the realistic BF algorithms are expected to select the best beam based on some measurements, and this is the main difference between these two types of algorithm implementations in 5G-LENA. Various ideal BF algorithms can be implemented by inheriting IdealBeamformingAlgorithm class. To implement a new realistic BF algorithm, we have created a separate class called Re-alisticBeamformingAlgorithm. Both classes, implement Beam-formingAlgorithm interface and thus both must have the function GetBeamformingVectors which determines BF vectors to be used on a pair of devices, i.e., gNB and UE. For example, CellScanBeamforming implements a type of ideal BF algorithm that searches for the best pair of BF vectors from the set of pre-defined BF vectors assuming the perfect knowledge of the channel. On the other hand, RealisticBeamformingAlgorithm uses SRS SINR measurements. Similarly to previously mentioned CellScanBeamforming there is a set of pre-defined BF vectors, but the knowledge of the channel is not perfect, and depends on the quality of reported SRS measurement. Another difference between ideal BF algorithm implementations and the realistic one, is that ideal BF vectors of all devices are updated at the same time based on the configured periodicity through BeamformingPeriodicity attribute of Ideal-BeamformingHelper. On the other hand, when RealisticBeam-formingAlgorithm is used, the BF vectors are updated when the configured trigger event occurs, and only the BF vectors of the pair of devices for which SRS measurement has been reported (pair of gNB and UE) are updated. The BF vector trigger update event can be either SRS count event (e.g., after every N SRSs are received, the BF vectors are updated), or based on the delay event after SRS reception (e.g., time after each SRS reception). The type of event and its parameters can be configured through RealisticBfManager class. Hence, in order to use realistic BF functionality it is necessary to install RealisticBfManager at gNBs PHY instead of the default BeamManager class. The configuration of trigger event and its parameters can be done per gNB instance granularity, but can be easily extended to be done per UE.
When UE is attached to gNB, a BF task is created. The BF task is composed of a pair of connected devices for which the realistic BF helper will manage the update of the BF vectors by calling Get-BeamformingVectors of configured realistic BF algorithm. Also, for each task is created an instance of realistic BF algorithm, which is then connected to NrSpectrumPhy SRS SINR trace to receive SRS reports. Realistic BF algorithm is also connected to its helper through callback to notify it when BF vectors of device pair needs to be updated (based on configuration and SRS reports). When BF vectors need to be updated, the function GetBeamformingVector or realistic BF algorithm is called, which calls GetEstimat-edLongTermComponent for each pair of pre-defined beams of the receiver and transmitter in order to estimate the channel quality of each of them based on the SRS reports. The estimation of the channel is done based on the abstraction model explained in Section 2.4. Finally, CalculateTheEstimatedLongTermMetric calculates the metric that is used to select the best BF pair.
In Figure 2, we show the diagram of the classes that are used for realistic BF based on SRS measurements, the dependencies among classes, and the most important methods. E.g., we can see that RealisticBeamformingAlgorithm needs to access to ThreeGp-pChannelModel to obtain the channel matrix in order to perform the estimation of the channel based on SRS report.

EXAMPLES AND TESTS
The example cttc-realistic-beamforming.cc included in the nr module demonstrates the usage of the proposed realistic BF framework. This simulation script can be used for the realistic BF evaluation. The topology consists of a single gNB and single UE, placed at a certain distance from each other and communicating over a wireless channel. Simulation allows to configure various parameters out of which the most important are: the distance (by configuring deltaX and deltaY parameters, which determine the position of the UE), the type of the BF method (ideal or real), the random run number (which allows to run many simulations and to average the results), the UE power, 3GPP scenario (Urban Macro, Urban Micro, Indoor Hotspot, etc). The output is saved in the database (simulation configuration parameters and measured average SINR). The database is created in the root project directory if not configured differently.
The test nr-realistic-beamforming-test.cc included in the nr module tests the realistic BF implementation. It involves two devices, a transmitter and a receiver, placed at a certain distance from each other and communicating over a wireless channel at 28 GHz carrier frequency. The test compares the performance of two different BF methods: 1) the proposed realistic BF algorithm, which uses SRS reception to estimate the channel and computes BF weights based on such channel estimate, and 2) an ideal BF algorithm, which selects the BF weights assuming perfect knowledge of the channel matrix coefficients. The test checks that with low SINR from SRS, realistic BF algorithm makes more mistakes in channel estimation than ideal BF algorithm. Also, the test checks that with high SINR from SRS, realistic BF algorithm generates almost always the same decision as that of the ideal BF method, and so, the same pair of beams are selected for the two communicating devices.

SIMULATION RESULTS
For the performance assessment, we use ns-3 5G-LENA [19] with the 3GPP spatial channel model developed in [25], compliant with TR 38.901, and the NR-based PHY abstraction model in [13]. The script used for the performance evaluation is cttc-realisticbeamforming.cc explained in Section 4. We focus on three propagation scenarios: Urban Macro (UMa), Urban Micro (UMi), and Indoor Hostpot (InH), which define the channel and propagation models, as per TR 38.901 [3]. Also The duplexing mode is TDD, with dynamic downlink-uplink slot structure. The SRS is configured to use 1 OFDM symbol. The simulations are performed by varying the 3D distance among the gNB and the UE. For UMa and UMi scenarios, we test up to 1 Km distances, and for InH scenario, distances up to 200 m are considered. We compare ideal BF method using cell scan and the proposed realistic BF method using SRS-based channel estimate. Also, we test different UE transmit powers: 0 dBm, 10 dBm, and 20 dBm, to assess the impact of the UE power on the SRS report, and so on the beam selection. For each configuration of 3D distance and UE transmit power, we compute the average SINR received at the UE, in DL, to analyze the impact of the BF vector selection. Simulation results are averaged over 40 random channel realizations. Figure 3 shows the DL SINR as a function of the 3D gNB-UE distance for UMa, UMi, and InH scenarios. For each scenario, we evaluated the Line-Of-Sight (LOS) channel condition (Figures 3a,  3c, and 3e) and the Non-Line-Of-Sight (NLOS) channel condition (Figures 3b, 3d, and 3f), to determine under which conditions the non-ideal channel estimation impacts the most. Results show that with LOS conditions, in any of the considered scenarios (UMa, UMi, and InH), there is no impact on the DL SINR when using realistic BF and a variety of UE transmit powers and gNB-UE distances (see Figures 3a, 3c, and 3e), meaning that the channel can be properly estimated and the same BF vectors are selected with both ideal and realistic BF methods. This is due to the good propagation channel under LOS conditions, which allows a good estimate of the channel matrices based on SRS measurements and, therefore, a proper BF vector selection. However, in NLOS conditions, in all of the considered scenarios (UMa, UMi, and InH), we can see a degradation of the DL SINR due to the use of realistic BF (see Figures 3b, 3d, and 3f). The DL SINR loss is more evident as the 3D distance increases, because the SRS SINR reduces with the distance, which negatively affects the BF selection. Such a DL SINR degradation is further increased in the case of using a lower UE transmit power for SRS transmissions (e.g., 0 dBm), as expected. This is because, at low SRS transmit power, the Realistic Beamforming Design using SRS-based Channel Estimate for ns-3 5G-LENA Module B. Bojović, S. Lagén, L. Giupponi SRS SINR report value is reduced, and so the channel estimation has more errors and the BF vector selection differs more from the optimal one, which ultimately affects the DL SINR negatively. With a lower UE transmit power, the DL SINR degradation appears at shorter distances, as compared to scenarios in which the UE uses a higher UL transmit power. Thus, with high UE transmit powers, the realistic BF procedure can maintain the performance of the ideal BF over a wider range of distances. In fact, in UMi NLOS and UMa NLOS scenarios, UE transmit powers of 20 dBm (and higher) do not exhibit performance degradation up to 200 m distance. With 10 dBm UE transmit power, the DL SINR degradation starts after 100 m distance in NLOS. Under InH NLOS scenario, transmit powers of 20 dBm (and higher) do not exhibit performance degradation up to 60 m distance, while with 10 dBm and 0 dBm UE transmit powers, the DL SINR degradation starts after 40 m and 20 m, respectively.

CONCLUSIONS
In this paper, we presented the extension of 5G-LENA module to support simulations with realistic BF procedures in TDD systems. First, we have presented an abstraction model to perform BF vector selection using SRS-based channel estimates.