The demand for high-precision location information in indoor positioning systems such as logistics, security, emergency etc., has increased the use of 5G systems as an alternative technology solution to the satellite-based positioning technologies. The 5G mobile networks provide more accurate and reliable positioning location in conditions of obstacles and changes. In this paper, the direction of arrival has been used for these localization approach. A description of In-Situ calibration of linear array antennas to enable direction of arrival estimation with 5G signals is provided. Despite the widely employed antenna arrays in 5G to facilitate the measurement of the direction of arrival (DOA), its performance is often degraded by array errors. Therefore, having coherent phases, accurate array manifold response, and delay and frequency ofset OFDM waveform correction is a mandatory requirement to perform direction of arrival estimation. We provide an experimental validation of the calibration process and evaluate the DoA estimation performance using measurement data. In addition, we present a comparison among the performance of DoA estimation without calibration, when only the calibration of RF channel error is performed and when the full calibration including the antenna error calibration is done. It is then demonstrated via real test with commercial hardware equipment that an average reduction of 40% for DOA estimation error can be achieved by the proposed In-Situ calibration.
In the recent years, with the rapid development of smart devices and technologies, there has been
a strong demand on indoor Location-Based Services (LBS) [
The radio direction finding is closely related with the use of multiple antennas enabling high
accuracy of position and orientation estimation, a strict requirement in the level of accuracy
in 5G systems. An important prerequisite for antenna array base DoA estimation is phase
coherence [
The calibration of antennas means that their antenna response is determined. The antenna
calibration is mostly carried out in a controlled environment, i.e., without multipath propagation
and interference, e.g., a dedicated measurement chamber. However, the antenna response is
also afected by the surroundings. Therefore, it is important to measure the entire system, e.g.,
in a near-field measurements chamber, to obtain a better antenna response. This method can be
costly. A more practical and less costly form to calibrate the antennas, is the In-Situ calibration
method [
In this paper, we show the process of the In-Situ calibration of a linear array antenna of 4 elements to achieve high accuracy DoA estimation for the purpose of indoor positioning in conditions of multipath and interference efects. The sounding reference signal (SRS) for positioning in the uplink has been used for the estimation of angle of arrival, where an analytical model of time, frequency, and phase error of the array multichannel receiver has been done. The preliminary results of the 5G direction of arrival using the In-Situ calibration corrections has been presented followed by a discussion on the antenna response observability as well as DoA estimation performance and to showcase the advantage of using calibration error corrections.
In this work, an indoor DoA estimation scenario, where the uplink 5G signal is transmitted
using an Universal Software Radio Peripheral (USRP) hardware N310 [
We consider a 5G uplink reference signal (SRS) signal composed by 4 SRS symbols, each
occupying subcarriers, with being the total number of subcarriers available for modulation.
The subcarriers are symmetrically arranged around the central frequency. Note that, according
to 3GPP standard [
The subcarrier spacing is defined as Δ = 1/, with being the duration of the OFDM symbol without cyclic prefix (CP). CP is a repetition sequence of the last samples of the OFDM symbol that is placed at the beginning of the same symbol in order to prevent the inter-symbol interference from the previous OFDM symbol. The resource allocation pattern of the SRS signal used for transmission starts from the 11-th symbol until the 14-th symbol. Table 2 gives the configuration parameters to generate the uplink SRS signal.
Finally, the digital base-band of the i-th OFDM symbol in time-domain: [] =
1 fft 2fft − 1 ∑︁ =− fft 2
[] · 2fft (− ), with = 0, 1, . . . , + − 1 being the sample index of an OFDM symbol, and m-th the OFDM subcarrier index, is generated using the IFFT. The digital signal s is transmitted by one source, periodically at a fixed repetition of time (with 4 SRS symbols per slot), at a predefined DoA and impinges on an antenna array of elements. The received time-domain multichannel SRS signals are transformed to the frequency domain using FFT and removing the CP from each OFDM symbol. The stream at the -th radio channel of the receiver is denoted as x = [1,, 2,, ..., ,] ∈ C,1, where , represents the received complex data SRS symbol at n-th receiving channel and m-th sub-carrier. The received signal at each received channel can be written also as: , = ()( + ) · · ΔΦ′ · ^ + ,, (1) (2) where () = √︀()Φ() is the antenna response at n-th front-end channel composed by the gain pattern () and phase pattern Φ(), ( + ) is the delayed transmitted signal () received at n-th front-end channel, is the carrier frequency ofset of the received signal at n-th front-end channel, Φ() is the phase ofset introduced by the front-end hardware, and ^ represent the rest of phase ofset afecting in the error of antenna response such as antenna non-idealities including mutual coupling, manufacturing, as well imperfections and surrounding structure of the installation, multipath and/or interference. Lastly, represents the noise at n-th receiving channel and m-th subcarrier. Each radio channel of the receiver represents a separated baseband received signal provided by the hardware front end. They are arranged into a single matrix X = [x1; x1; ...; xN] ∈ C, .
As previously stated, the array modeling errors that greatly depends on DoA estimation performance can be divided into two main error sources: one part induced by the antenna elements and the other part induced by the the synchronization of channels in phase and time at the receiver side. The phase and amplitude imbalances between channels are needed to be corrected. Therefore, the multichannel receiver should be configured to enable the LO sharing between channels across multiple daughter-boards and eventually enabling the phase-aligned operation. There are several possible LO configurations that can be performed in NI-2955: • Independent, where each channel will use its own LO and the LO input ports will be disabled. • Import, where channels will use the LO provided at the corresponding import ports. • Shared and Export, where channels will use the same LO from first channel, whose LO will be exported to their LO output ports. • Re-import, where the LO from first channel is exported and both channels will use the LO provided at the corresponding import ports. • Shared, where both channels of the same daughter-board will use the same LO from first channel of the channel couple.
In order to achieve coherent phases among the four channels, LO-sharing ability is enabled. One pair of channels is configured with Shared and Export and the other pair is set to Import. Then, the LO signal from the first pair is injected to the other pair with external cables through the corresponding LO ports. Another error source that efects in the phase alignment is the sampling rate. The received signals at all front ends should be sampled at the same time instant. NI-2955 provides a re-sampling process that allows to use a wide range of sampling rates. The USRPs include options for using an internal or external clock reference with the added ability to export the clock reference and time base. In this work, the receiver NI-2955 uses its internal clock giving a frequency accuracy of 2.5pmm.
The main focus in this work is to investigate the accuracy of DoA estimation in a realistic
indoor environment, whose performance is influenced to a large extent by the calibration
phase. The calibration procedure consists of three steps: RF channel error calibration; delay and
carrier phase ofset estimation and compensation of the received signal at each of n-th received
channels; and antenna error calibration. All the calibration procedures involve placing the
transmitter and the receiver hardware at a known distance and DoA, and performing repeated
DoA measurements distributed over all possible directions limited to the sector coverage area
of the environment, i.e., in the present case, − 90∘ to 90∘ with an angular separation of 5∘ .
All the measurements are conducted in a indoor working environment with line-of-sight
(LOS) propagation conditions. The transmitted waveform has been generated following the
configuration parameters and conditions set by the 5G standard as explained in [
The wideband 5G signal is conducted to the RF channels of the receiver by connecting all antenna ports of USRP-Rx NI-2955 via coaxial cables with a power splitter. The transmission of the 5G SRS signal is done through a single antenna port of USRP N310, at predefined system parameters: carrier frequency, sampling rate and transmission gain. The transmit power for this experiment is − 15 dBm. On the receiver’s side, each radio channel acquire the baseband stream provided by the hardware front-end at carrier frequency and sampling rate set in the transmission part and predefined reception gain; and store them in a custom binary data format with inphase/quadrature (I&Q) samples of 16 bits each. Both in transmission and reception, the transmission gain is set so that it avoids the distortion of the signal. The acquisition of the data stream of each radio channel is done in a sustained way for a predefined duration. The start and the end of the received OFDM signals define the phase of the waveform in the time domain. The phase diference between channels corresponds to the angle of the maximum peak of the cross correlation between one of the channels taken as reference with the rest of the channels. Because of the LO configuration explained in 2.2, all phases should be aligned.
The RF coeficients are measured by directly conducting the 5G uplink signal to the received RF channels. Since the LO configurations ensure the phase coherence during all time (even after a new power-cycle of the receiver maintaining the same system parameters), the diferential phaseshift between the channel taken as reference and the rest of RF channels at the receiver’s side is pre-measured before undergoing the calibration process of the antennas. These coeficients will be then compensated in both calibration and DoA estimation procedure. These coeficients are measured as the strongest correlation peak between the received waveform at the reference channel with the received waveform at the rest of the receiver RF channels. The calibration ofsets are computed for every snapshot of the received data stream with duration of one slot and the average value of the computed coeficients is taken as a final calibration reference.
The USRP N310 has been deployed on a PC with an Intel i5-9500 CPU @ 3GHz and 32GB of RAM memory. The NI-2955 has been deployed on a PC with an Intel i7-10700 CPU @ 2.9GHz and 32GB of RAM memory. The latter has Windows 10 OS installed, while the other system has Ubuntu 22.04 LTS OS installed. The hard drives employed are Solid Stated Drives (SSD) NVMe-based of Category 3, enabling a sustained writing rate.
The baseband I&Q samples are checked to estimate and establish the time and frequency synchronization to the uplink received signal with a local replica signal as a reference. Firstly, a coarse estimate of time and frequency ofset is done in the time domain. No demodulation of the received waveform is performed to estimate the errors. Then a fine estimation and correction process is undertaken to refine the initial estimates and increase precision. This process synchronize the received data streams at each of the RF channels to the beginning of radio frame.
The initial carrier frequency ofset (CFO) estimation is performed by the strongest correlation peak between the received waveform with the local replica of the signal. The CFO is estimated by making a search over a frequency range of residual carrier frequency to estimate, i.e. from where is the discrete time delay in samples. The process is repeated for each set of frequencies in the search range. The coarse time ofset is chosen to be the one that gives the strongest correlation values and the corresponding correction frequency being the coarse frequency ofset. Then, a data interpolation is performed in order to make a fine estimation of time and frequency ofset around the coarse estimation value. The accuracy of the carrier frequency ofset estimation is limited to the subcarrier spacing.
Apart from the RF channel errors induced by the multichannel receiver, the efect of the mutual coupling between antenna elements, the location perturbations and beam-pattern errors of antenna elements, as well as other radio conditions, the antenna errors are direction-dependent. The estimation of DoA is done evaluating the phase ofsets across receiving antennas. The receiving array elements (an uniform linear array (ULA) with a half-wavelength spacing) are swiveled within a specified sector coverage and a predefined angular step. For each of the known DoA to estimate, after RF channel error, and time and frequency ofset correction, the phase ofsets caused by free-space propagation are evaluated and compensated to the received data stream. The channel response of array antenna at the receiver side is used to estimate the actual array manifold and compared with the true manifold a(). The mismatch between manifolds (i.e., deviation of the actual manifold from the ideal one) will serve as a reference metric for correcting the array response during the DoA estimation. The calibrated array manifold a^() aims to delineate the true array response with the array error computed and corrected in the searching-based DoA estimation algorithms. The searching-based DoA estimation algorithm, in concrete the multiple signal classification method (MUSIC), can directly employ this calibrated array manifold. The calibrated array manifold can be expressed as ( ) = ∑︁ [] · * [ + ], ^ = arg max{|( )|2}, (3) (4) (5) − Δ to Δ with a step of one tenth of Δ that represents the value of the subcarrier spacing. For each of the frequencies in the search range, a compensation on the received signal is applied and a correlation of the corrected received signal [] with a shifted and conjugated version of the reference signal [] is computed. The resulting correlation is defined by where [] is a circular shifted of the local replica waveform resulting in a matched filter of the OFDM signal. The estimated delay can be expressed as
a^() = ( ()) · a(), with () = [1, ^2 , ..., ^ ] being the mismatch array error correction obtained from the InSitu calibration process and a() = [1, − 2 () , ..., − 2 (− 1)() ] being the theoretical antenna response where is the antenna element distance. Then, dominant spectral peaks are used to find the DoAs.
The calibration process has been conducted in an 56 m2 empty laboratory room of the ofice building, where a single transmitter and receiver are placed within a distance of 5 m (see 1(a) and 1(b)). A sector of 180∘ , i.e., − 90∘ to 90∘ with an angular step of 5∘ corresponding to 37 4.5 5 4 5m
Rx pilot angles of arrival evenly distributed is considered. Note that the sector coverage is limited by the scenario where the experiments are performed. The receiver is placed near the wall, at one side of the room and the transmitter is placed 3 m away from the other side as in 1(b). To obtain diferent DoA, the array manifold at the receiver side is swiveled. The SRS signal is transmitted periodically every 1 millisecond during 2 sec from the single antenna port of USRP-Tx N310. The system parameters used are a carrier frequency of 2.4875 GHz, transmission gain of 65 dB, and sampling rate of 30.72 Msps, corresponding to 25 MHz bandwidth with Fast Fourier Transform (FFT) length 2048. Both the transmitter and receiver utilize the same antenna modules, omnidirectional monopole antennas. The single transmitter antenna is mounted directly on one of the transmission channels of USRP-Tx N310, while on the receiver’s side the antennas are mounted in a platform with a separation of / 2 between elements of the antenna. Two sets of measurements for each of the pilot angles of arrival are taken. The first set of data stream will serve to perform calibration of the antenna errors and the other set will be used to evaluate the performance of DoA estimation under the conditions of calibration and non calibration. The phase ofsets between antennas are computed by averaging over phases of subcarriers with the same carrier frequency. All experiments are carried out under LOS condition.
Because an ISM radio band is used for transmission, the presence of interference is inevitable. During the experimentation process, the presence of a signal at center frequency of 2.479 GHz of 2 MHz bandwidth has been detected. To improve the resolution ability, interference correction is undertaken by choosing only the subcarriers that does not contain the interference after the demodulation of the waveform.
The experiments have been conducted twice: one to compute the mismatching between ideal array manifold response, and the other to investigate the impact of calibration in DoA estimation, as well as the impact of the multipath condition in the estimation accuracy. Figure 2 shows the theoretical array response for each of the incident direction; the corresponding experimental array response and the estimated array phase error from the expected value. The latter will serve as a mismatch parameter to correct the phase error coming from the antennas. These results are computed after correcting the phase ofset between channels coming from the RF channels. Results show that, even in conditions of multipath and interference, the computed steering vector follows the behavior of the theoretical one that considers an ideal antenna response. Note that the interference is eliminated by excluding the subcarriers that contain the interference signal.
The presence of multipath efects in the propagation delay of a reference signal at each =1 · − 2 Δ , with being the m-th subcarrier of the signal has a phase shift of ∑︀ propagation delay of k-path, K being the total number of paths of the propagation channel and being the absolute amplitude of the k-th signal. In severe multipath conditions, the efect of propagation delay for each of the subcarriers is 5.3∘ within successive subcarriers. For the incident angles in between the angles, at which the tests are performed, an interpolation within the range of array modeling errors set of data (computed during antenna error calibration process) is done. All these inaccuracies depend on the performance of the DoA estimation, reflected in the results shown in Figure 3. Results show a significant improvement in DoA estimation accuracy with a maximum of 46.74% when applying only the RF channel error corrections. The large improvement in the accuracy of DoA estimation show the high phase ofset that the received RF channels apply and therefore a severe degradation on the angle of arrival is faced. Moreover, an additional reduction of error estimation of maximum 25.9% is noted when the antenna error correction is applied, especially in cases close to the end-fire array where unsatisfactory performance is expected. The maximum error estimation deviation reaches ± 17.32 degrees and it reduces up to less than one degree (± 0.58) when applying the full calibration corrections estimated during In-Situ calibration. These results show the importance of the calibration process enabling the stability and accuracy of the DoA estimation since the measured antenna array manifold severely deviates from the nominal manifold. Therefore, the In-Situ measurements cause improvement of the incident angles as it captures the real array responses more precisely by using the post-established in-field measurements.
All in all, the preliminary results show that with only calibrating the received RF channels, a significant improvement is achieved. A precise estimation is achieved when the antenna errors are also considered in the DoA estimation process.
Array manifold Ch0-Ch1
− 20 0 20 Direction of arrival (degree) Array manifold Ch0-Ch2 − 20 0 20 Direction of arrival (degree) Array manifold Ch0-Ch3 200
− 20 0 20 Direction of arrival (degree) 40 60 80 100
In this work we presented the preliminary results of 5G DoA estimation using In-Situ calibration metric for the purpose of accurate indoor positioning solution even in conditions of multipath and interference in signal propagation. Moreover, the required steps to achieve coherent phases between RF channel of a universal radio receiver are presented. The obtained results show a significant improvement of DoA estimation accuracy because of calibration. The calibration process fully exploits the bandwidth resources provided by 5G signal to resolve the presence of interference in the measurement data. We believe this is an important step to provide high precision DoA estimation and therefore an accurate positioning location. Moreover, it is shown a scalable solution to calibrate universal hardware and antenna arrays.
RF-channel calibration RF-channel &Antenna-error calibration 80 ) e reg 60 e d l(a 40 v i r r fa 20 o e lgn 0 a d ta − 20 e m i se − 40 t e g re − 60 a v A
80
80 − 50 0 50 Direction of arrival (degree)
− 50 0 50 Direction of arrival (degree)
− 50 0 50 Direction of arrival (degree)
This work was supported in part by the Spanish Agency of Research (AEI) under the Research and Development projects PID2020-118984GB-I00/AEI/10.13039/501100011033 and PDC2021-121362I00/AEI/10.13039/501100011033; and mobility grant SEBAP (Societat Económica Barcelonesa d’Amics del País).