Estimation of Angle of Arrival for mmWave Channel Using Sub 6GHz Channel Information

Abstract
Data is the most valued commodity in the world, even more than oil. Some predictions indicate that data traffic will grow to surpass 130 exabytes by 2020. This influx of traffic will exacerbate the spectrum crunch that cellular providers are already experiencing. To address this issue, and to allow for the next generation of a smarter and faster world, it is envisioned that in 5G cellular systems certain portions of the mmWave band will be used, spanning the spectrum between 30 GHz to 300 GHz with the corresponding wavelengths between 1–10 mm.

Get Help With Your Essay
If you need assistance with writing your essay, our professional essay writing service is here to help!
Essay Writing Service

The proposed millimeter wave (mmWave) communication is a feasible solution for next gen high data-rate applications like V2X communication and next generation cellular communication. However, communications in the mmWave band faces significant challenges due to multipath fading, low penetration capability, variable channels, intermittent connectivity, and high energy usage. Moreover, the high frequency of operation forces the use of complex algorithms for tracking channel variations and adjusting resources which are impractical. In order to mitigate some of these challenges, we propose an architecture that integrates the sub-6 GHz and mmWave technologies. Our system exploits the spatial correlations between the sub-6 GHz and mmWave interfaces to estimate channel parameters required for channel selection, beamforming and data transfer in the latter through observing channels in the former.
Index Terms: Angle of Arrival, mmWave, Sub6 Channel, channel parameters, Beam Index, Codebook, Deep Neural Network Model.
I. INTRODUCTION
The annual data traffic generated by mobile devices is expected to surpass 130 exabytes by 2020 [1]. To address this alarming growth, there is a push to use certain portions of the mmWave band in the 5G cellular systems, spanning the spectrum between 30 GHz to 300 GHz with the corresponding wavelengths between 1–10 mm [2]. This will substantially increase the spectrum available to cellular providers, which is currently between 700 MHz and 2.6 GHz with only 780 MHz of bandwidth allocation for all current cellular technologies. MmWaves have applications in cellular systems [2], [3], [4], including fixed wireless access [5], backhaul [6], mobile access [2], [4], and even V2X communications [7], [8]. Vehicular communication nowadays employ multiple onboard sensors, and in the process are growing more bandwidth hungry [9], and the current vehicular communication systems are not able to keep up.
However, before mmWave communications can become a reality, there are significant challenges that need to be overcome. Firstly, juxtaposing with sub-6 GHz, the propagation loss in mmWave is much higher due to atmospheric absorption and low penetration. Although large antenna arrays have the potential to make up for the mmWave losses, they cause several other issues such as high energy consumption by components (e.g., analog-to-digital converters (ADC)). Moreover, in order to fully utilize the large directional antenna arrays, continuous beamforming and signal training at the receiver is needed [10]. Digital beamforming is highly efficient in reducing the delay, but there is a need for a separate ADC for each antenna, which may not be feasible for even a small to mid-sized antenna array due to high energy consumption. In contrast, analog beamforming requires only one ADC, but it can focus on one direction at a time, making the angular search costly in delay[11].
In order to remedy the high beamforming overhead of mmWave, we exploit its spatial correlations with sub-6 GHz. To this end, we first experimentally verify the correlation between the sub-6 GHz channel and mmWave channel path parameters, especially in the presence of line-of-sight (LOS), subsequently we also work towards a system to estimate the latter given the former.
A. Related Work
There is a ton of research material, where the existence of a spatial congruence between Sub-6 and mmWave band is both stated and explored through experimental measurements [12]–[15]. Prior work on using out-of-band information in communication systems primarily targets beamforming reciprocity in frequency division duplex (FDD) systems. Based on the observation that the spatial information in the uplink (UL) and downlink (DL) is congruent [16]-[18], several strategies were proposed to estimate DL correlation from UL measurements (see [19], [20] and references therein). The estimated correlation was in turn used for DL beamforming. Along similar lines, in [21] the multi-paths in the UL channel were estimated and subsequently the DL channel was constructed using the estimated multi-paths. In [22], the UL measurements were used as partial support information in compressed sensing based DL channel estimation. The frequency separation between UL and DL is typically small. As an example, there is 9.82 frequency separation between 1935 MHz UL and 2125 MHz DL [18]. In essence, the aforementioned strategies were tailored for the case when the separation the channels under consideration is small and spatial information is congruent.
In [23], the directional information from legacy WiFi was used to reduce the beam-steering overhead of 60 GHz WiFi. The measurement results presented in [23] confirm the value of out-of-band information for mmWave link establishment. In [24], the coarse angle estimation at sub-6 GHz followed by refinement at mmWave was pitched. The implementation details and results, however, were not provided. In [25], the mmWave spatial correlation was estimated using sub-6 GHz spatial correlation. This channel parameter estimation process, however, is fundamentally limited by the system and hardware capability in resolving these channel parameters, which highly affects the quality of the extrapolated channels
II. PROBLEM DEFINITION
Problem 1 In this project we are interested in exploiting the spatial congruence that exists between the mmWave and Sub6 Ghz channels, and to use the relationship to estimate channel path parameters such as Azimuth and Elevation of Angle of Arrivals for mmWave channel with knowledge of Sub6 channel at either a collocated or distributed base station and user setup.
Problem 2 We have explored earlier works which try approaching this channel estimation problem with traditional computing algorithms while most did not specify the implementation details. Keeping in mind this channel parameter estimation process is fundamentally limited by the system and hardware capability, which highly affects the quality of the extrapolated channel parameters. Through the course of this research, we strive towards deploying new age technologies such as machine learning and deep learning to exploit the spatial congruence of the two channels and and to estimate the channel parameters in one given suitable information from the other.
Problem 3 Deploying the proposed solution in wide range of test scenarios to test system performance and verify its validity and increase system robustness.
III. SYSTEM MODEL
Consider the scenario in Fig. 1 where a base station (BS) is communicating with a mobile user equipment. The BS is assumed to employ two transceivers; one transceiver operating in the sub-6GHz and employs Msub−6 antennas, and the other one is operating at a mmWave frequency band and adopts an MmmW-element antenna array. We assume that the two uniform linear array of antennas, belonging to both the mmWave and sub-6GHz transceivers are co-located (for simplicity’s sake). However, the proposed concepts in this paper can be extended to other setups with separated and distributed array setups. The mobile user is assumed to employ a single antenna capable of operating in both mmWave and sub-6GHz bands[12]. Thus, we summarize the system operation and the adopted channel model.
System Operation: In this paper, we consider two modes of system operation, one where signaling happens at the sub6GHz band while another occurs at the mmWave band. If hsub−6[k] ∈ CMsub−6×1 denotes one channel vector from the mobile user to the sub-6 GHz BS array at the kth subcarrier, k = 1,…,K, then one received signal at the BS sub-6GHz array can be written as
ysub−6[k] = hsub−6[k]sp[k] + nsub−6[k], (1)
Similarly, we can depict another received signal in mmWave band as, ymmWave[k] = hmmWave[k]sp[k] + nmmWave[k], (2)

Fig. 1: The system model adopted here has a base station and mobile user communicating over both the mmWave and the Sub-6 GHz.The assumption here is that the base station and mobile user employ co-located sub-6GHz and mmWave arrays.
After having established the above setting, we work towards estimating the channel path parameters especially Azimuth- Angle of Arrival (φ) and Elevation-Angle of Arrival (θ) in the mmWave band by utilizing channel information extracted in the Sub6 band.
IV. CHANNEL MODEL
In this research paper, we consider a geometric channel model for both the sub-6GHz and mmWave channels [26]. Thus, the mmWave channel (and similarly the sub-6GHz channel) can be written as

where L is number of channel paths, αl,τl,θl,φl are the path gains (including the path-loss), the delay, the azimuth AoA (φ), and elevation AoA (θ), respectively, of the l’th channel path. TS represents the sampling time while D denotes the cyclic prex length (assuming that the maximum delay is less than DTS).We focus on the physical channel model due to its ability to capture the physical characteristics of the signal propagation including the dependence on the environment geometry, materials, frequency band, etc., which serves as the crux around which our machine learning based channel parameter estimation approach is built upon. The parameters of the geometric channel models, such as the angles of arrival and path gains, will be obtained using accurate 3D raytracing simulations [12], which are cardinal in training the deep learning models later in this paper.
V. EXPERIMENTAL SETUP
Ray-tracing based channel generation: For our experiments, we consider a frequency selective geometric channel model as described in Section 4. For this model, the important question is how to generate the mmWave and Sub-6 channel parameters, such as the Azimuthal AoAs (φ), Elevation (θ), path gains and delays of each ray. We normally resort to stochastic models in generating these parameters [26], [27], [28]. It is a crucial factor in our experiment, to generate realistic channel parameters that correspond to real environment geometry. This is the main motivation for using ray-tracing in generating the channel parameters. In the Wireless InSite ray-tracing [29], we use the X3D model with Shooting and Bouncing Ray (SBR) tracing mode. In this mode, the simulator shoots hundreds of rays from the transmitters and select the ones that nd paths to the receiver for which it generates the key parameters (azimuthal and elevation AoAs etc.). Considering the ray-tracing channel parameters for the strongest path between antennas of chosen BS and set of mobile users using MATLAB [30]. The considered setup adopts an OFDM system of size K = 32. Note that for every candidate user location in the x-y grid, we generate 4 channel vectors which correspond to the sub-6 and mmWave channels between this user and the 4 antennas of an arbitrary base station.

Fig. 2: Outdoor situation being considered for dataset generation. From the DeepMIMO generator we focus on the O1_3p5 and O1_28 scenarios.
VI. DATASET
In evolving fields like mmWave communication, it is difficult to find relevant dataset to use in experiments. There is a need for datasets that can be used to evaluate the developed algorithms, reproduce the results, set benchmarks, and compare the different solutions especially while applying machine learning methodology. In our research, we primarily make use of the DeepMIMO dataset [30], which is a generic dataset for mmWave/massive MIMO channels. Since the DeepMIMO dataset is generic/parameterized it is

Fig. 3: Antenna Placement for the scenario. We consider a ULA setup (consisting of 4 antennas) along the y-axis for the BS.
very intuitive for us to adjust a set of system and channel parameters to tailor the generated DeepMIMO dataset for the target machine learning application. The DeepMIMO dataset can then be completely dened by the (i) the adopted raytracing scenario and (ii) the set of parameters,which enables the accurate denition and reproduction of the dataset.
The parameter setting used for our experiments is as mentioned below:

DeepMIMO Dataset Parameters

Parameters

Settings

params.scenario

O1_3p5,O1_28

params.active_BS

2

params.active_user_first

1

params.active_user_last

502

params.num_ant_x

1

params.num_ant_y

4

params.num_ant_z

1

params.ant_spacing

1λ

params.bandwidth

0.5GHz

params.num_OFDM

32

params.OFDM_sampling_fac

1

params.OFDM_limit

32

params.num_paths

1

Datasets are generated independently of both the scenarios. The scenarios considered are O1_3p5 which is in sub6GHz frequency band and O1_28 which is in mmWave frequency band. We consider 502 rows of users (181 users in each row) to be served by Base Station (BS) 2 for dataset generation. The BS in focus is assumed to posses a uniform linear array of antennas, in this case having four antennas along the y axis. The above mentioned setting will produce about 100000 data samples. The dimension of the dataset for a 4 antenna case with the above setting will be 100000×256. Each data sample has 128 complex number values associated with the channels in the dataset. The channel parameters (Elevation and Azimuthal Angle of Arrival (θ,φ) of O1_28 scenario are predicted using the channel values of O1_3p5 scenario. In the next section we will be discussing about the Neural network architecture we used for this experiment.
VII. DEEP NEURAL NETWORK MODEL
This section describes the model architecture, necessary data pre-processing and training method.
We have chosen a feedforward neural network or multi-layer perceptron with W hidden layers. The channel values of O1_3p5 scenario generated from the settings mentioned in the above section is fed as input to the neural network. The channel values are for the 4 different antennas being considered. The channel values are complex numbers in nature. The model is not capable of handling the complex values directly as input to it. Therefore, we start off by separating the real and imaginary part of the complex number. Considering the 4 antenna scenario, originally the dataset dimension will be 10000 × 128. Separating the complex number values as real and imaginary will make the dataset dimension to be 100000 × 256. Further, the dataset is divided into train and test datasets. The train dataset (75% of the dataset) is used to train the model and the remaining part of it is used to test the model. The train and test data samples are selected randomly.
The goal of the neural network is to learn the relationship between the sub-6 channel values provided as the input, and estimate the Angle of Arrivals (Azimuthal and Elevation) of the mmWave channel, i.e the output, where both the channels are deployed in the exact same setting.

Fig. 4: Neural Network architecture used for the experiment
Figure.4 is the architecture of the deployed neural network with W hidden layers. Each layer has Nw neurons in it. The model is designed such that it learns the non-linear relationship between the input channel values (Sub-6 band) and the Angle of Arrival (Elevation and Azimuthal) parameters, in mmWave band). The model follows a “supervised learning” approach. For every set of input channel values, we have a specified output of AoA (Elevation or Azimuthal). Furthermore, a loss function is added to the training process in-order to keep track of and evaluate the model performance during training.
VIII. INITIAL CHALLENGES
During the process of accomplishing the objectives set in Section 2, a number of challenges were met, which are worth mentioning here. Knowledge of the above, might serve useful for readers working on similar applications, by providing insight on the numerous pre-processing steps which are to be followed to obtain the desired outcome.
i The dataset from the DeepMIMO dataset generator formulti antenna scenario is obtained as a structure of complex values as expected. Hence, it is required by the user to access channel values for every antenna from this single complex structure. The channel values of the individual antennas can later be stitched by joining them adjacently.
ii Fundamentally, neural networks are not capable ofhandling complex numbers as samples in the dataset. However, the channel values obtained from DeepMIMO simulator are complex numbers. To overcome this issue , we resolved to pre-processing the dataset by splitting the real and imaginary parts. This is a necessary step in feature engineering before feeding to the neural network.
iii Tweaking the design of the neural network was anotherchallenge faced. The dataset varies with the increase in number of antennas considered. The model needed redesign from 2 antenna scenario to 4 antenna scenario. Every scenario required careful reconfiguration of the neural network.
iv Since the dataset being considered is massive in size,system requirement plays another important role in conducting experiments. We recommend usage of GPU (due to its higher capability to parallel process which is a deciding factor in such experiments) rather than CPU, purely considering model running time as a primary factor.
IX. EXPERIMENTAL RESULTS
In this section we present the results obtained for the scenario setting as mention in section VI. Further, we would also like to mention here that the results shown are for model which was trained for a higher number of epochs (1000 epochs). We also trained the model for a lesser number of epochs and compared the results with the former setting. As expected, the 1000 epochs model gave us the best trade off between over-fitting the curve and a good out of sample prediction accuracy. We have presented the model performance in prediction of mmWave Azimuthal AoA(φ) and Elevation AoA (θ) given the sub-6 channel values deployed in same environment setting, in the below section. As seen, the predicted values are very close to (if not same) the real values obtained from the mmWave dataset.
A. Test Settings- Four Antenna Scenario
Here we focus on the 4 antenna setup. Two tests were carried out in this setting. Both the tests were conducted by increasing the training epochs. The figure shown below is for 1000 epochs. The rmse model performance, is evident as the predicted angle has an error range of (-1,1) degrees which is already much better than the findings explored in the prior work section.

Fig. 5: Root Mean Square Error of the model after optimal epochs of training plotted against the size of the dataset considered in training, for predicting Elevation Angle of Arrival (θ)

Fig. 6: Root Mean Square Error of the model after optimal epochs of training plotted against the size of the dataset considered in training, for predicting Azimuthal Angle of Arrival (φ)
Figures.5&6 depict the proposed model’s performance. The Root Mean Square Error evaluation of the model predictions for both the elevation and azimuthal AoAs (θ,φ)is gradually decreasing with the increase in size of input dataset, as expected. Care was taken to avoid over fitting the neural network.
B. Test Settings- Two Antenna Scenario
Further, to test our model for other settings of the DeepMIMO dataset generator, we collected the data samples for a 2 antenna setup. We achieve this by constructing the DeepMIMO dataset by taking 2 antennas as part of the uniform linear array (antennas taken along y axis).
As seen for the two-antenna scenario, once again the proposed model is able to predict values close to the real values. The configurations had been kept the same as that of the 4 antenna scenario. The values predicted by the model has an error range similar to the earlier setting and this is evident through observing model rmse performance.
The figures.7&8 below depict the proposed model’s performance. The Root Mean Square Error evaluation of the model predictions for both the elevation and azimuthal AoAs (θ,φ)is gradually decreasing with the increase in size of input dataset, as expected. Care was taken to avoid over fitting the neural network.

Fig. 7: Root Mean Square Error of the model after optimal epochs of training plotted against the size of the dataset considered in training, for predicting Elevation Angle of Arrival (θ)

Fig. 8: Root Mean Square Error of the model after optimal epochs of training plotted against the size of the dataset considered in training, for predicting Azimuthal Angle of
Arrival (φ)
X. CONCLUSIONS
In this paper, we proposed to develop an integrated machine learning and Sub-6 channel information coordinated mmWave channel parameter estimation (Azimuth and Elevation AoA) strategy that enables highly-mobile applications in large antenna array mmWave systems by easing the high beam selection overhead experienced from prior approaches. The prediction of the mmWave Angle of Arrivals (AoA’s) is done via a deep neural network learning model, with a very minimal error range. The results obtained through our proposed approach is found to be more efficient than the findings in the Grid-of-Beam, Grid-of-Beam based Auxiliary Beam Pair techniques for AoA estimation (primarily using wide beams). The findings in our research i.e prediction of AoA can be leveraged in directing the mmWave beams towards the user without much overhead, provided prior knowledge of Sub-6 channel in similar setting. Also, using the predicted channel parameters of mmWave, selecting the beam index for beamforming becomes simpler. This can potentially circumvent the problems discussed in Section I in mmWave implementation. Future applications of the information obtained through our research could potentially include indoor localization, as indoor localization has no definitive approach apart from fingerprinting, at present.
REFERENCES
[1] Cisco Mobile VNI, 2019,”Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update”, 2017–2022 White Paper.
[2] Morteza Hashemi et al,”Out-of-Band Millimeter Wave Beamforming and Communications to Achieve Low Latency and High Energy Efficiency in 5G Systems”IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 66, NO. 2, FEBRUARY 2018.
[3] S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter-wave cellular wireless networks: Potentials and challenges,” Proc. IEEE, vol. 102, no. 3, pp. 366–385, Mar. 2014.
[4] T. S. Rappaport, R. W. Heath, Jr., R. C. Daniels, and J. N. Murdock,Millimeter Wave Wireless Communications. London, U.K.: Pearson Education, 2014.
[5] V. Nurmela et al., METIS Channel Models, document ICT317669,Seventh Framework Programme, 2015.
[6] S. Collonge, G. Zaharia, and G. E. Zein, “Influence of the human activity on wide-band characteristics of the 60 GHz indoor radio channel,” IEEE Trans. Wireless Commun., vol. 3, no. 6, pp. 2396–2406, Nov. 2004.
[7] A. Adhikary et al., “Joint spatial division and multiplexing for mmwave channels,” IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp. 1239–1255, Jun. 2014.
[8] A. Ali, N. González-Prelcic, and R. W. Heath, Jr. (2017). “Millimeter wave beam-selection using out-of-band spatial information.” [Online]. Available: https://arxiv.org/abs/1702.08574.
[9] Y. Kim, K. Lee, and N. B. Shroff, “An analytical framework to characterize the efficiency and delay in a mobile data offloading system,” in Proc. 15th ACM Int. Symp. Mobile Ad Hoc Netw. Comput., 2014, pp. 267–276.
[10] W. Roh et al., “Millimeter-wave beamforming as an enabling technology for 5G cellular communications: Theoretical feasibility and prototype results,” IEEE Commun. Mag., vol. 52, no. 2, pp. 106–113, Feb. 2014.
[11] J. Mo, A. Alkhateeb, S. Abu-Surra, and R. W. Heath, Jr. (2016). “Hybrid architectures with few-bit ADC receivers: Achievable rates and energyrate tradeoffs.” [Online]. Available: https://arxiv.org/abs/1605.00668.
[12] Alrabeiah, Muhammad, and Ahmed Alkhateeb. “Deep learning for mmwave beam and blockage prediction using Sub-6GHz channels.” arXiv:1910.02900 (2019).
[13] ] M. Hashemi, C. E. Koksal, and N. B. Shroff, “Out-of-band millimeter wave beamforming and communications to achieve low latency and high energy efficiency in 5g systems,” IEEE Transactions on Communications, vol. 66, no. 2, pp. 875–888,Feb 2018.
[14] M. Peter, K. Sakaguchi, S. Jaeckel, S. Wu, M. Nekovee, J. Medbo, K. Haneda, S. Nguyen, R. Naderpour, J. Vehmas et al., “Measurement campaigns and initial channel models for preferred suitable frequency ranges,” Deliverable D2, vol. 1, p. 160, 2016.
[15] T. Nitsche, A. B. Flores, E. W. Knightly, and J. Widmer, “Steering with eyes closed: Mm-wave beam steering without in-band measurement,” in 2015 IEEE Conference on Computer Communications (INFOCOM), April 2015, pp. 2416–2424.
[16] Anum Ali et al, “Millimeter Wave Beam-Selection Using Out-of-Band Spatial Information” arXiv:1702.08574v1 [cs.IT] 27 Feb 2017.
[17] ] S. Singh et al., “Tractable model for rate in self-backhauled millimeter wave cellular networks,” IEEE J. Sel. Areas Commun., vol. 33, no. 10, pp. 2196–2211, Oct. 2015.
[18] “Federal communications commission. Spectrum frontiers R0 and FNPRM: FCC16-89.” Jul. 2016.
[19] J. Scarlett, J. S. Evans, and S. Dey, “Compressed sensing with prior information: Information-theoretic limits and practical decoders,” IEEE Trans. Signal Process., vol. 61, no. 2, pp. 427–439, Jan 2013.
[20] J. A. Tropp, A. C. Gilbert, and M. J. Strauss, “Simultaneous sparse approximation via greedy pursuit,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), vol. 5, Mar. 2005, pp. 721–724.
[21] T. Aste et al., “Downlink beamforming avoiding DOA estimation for cellular mobile communications,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), May 1998, pp. 3313–3316.
[22] K. Hugl, K. Kalliola, and J. Laurila, “Spatial reciprocity of uplink and downlink radio channels in FDD systems,” May, COST 273 Technical Document TD(02) 066, 2002.
[23] Thomas Nitsche et al,”IEEE 802.11ad: Directional 60 GHz Communication for Multi-Gigabit-per-Second Wi-Fi” IEEE Communications Magazine,December 2014
[24] Emil Björnson et al,”Massive MIMO in Sub-6 GHz and mmWave: Physical, Practical, and Use-Case Differences” arXiv:1803.11023v2 [cs.IT] 14 Jan 2019
[25] Luca Sanguinetti et al,”Towards Massive MIMO 2.0: Understanding spatial correlation, interference suppression, and pilot contamination” arXiv:1904.03406v3 [eess.SP] 5 Oct 2019
[26] R. W. Heath, N. Gonzlez-Prelcic, S. Rangan, W. Roh, and A. M. Sayeed, “An overview of signal processing techniques for millimeter wave MIMO systems,” IEEE Journal of Selected Topics in Signal Processing, vol. 10, no. 3, pp. 436–453, April 2016.
[27] A. Alkhateeb and R. W. Heath, “Frequency selective hybrid precoding for limited feedback millimeter wave systems,” IEEE Transactions on Communications, vol. 64, no. 5, pp. 1801–1818, May 2016.
[28] F. Sohrabi and W. Yu, “Hybrid digital and analog beamforming design for large-scale MIMO systems,” in Proc. of the IEEE International Conf. on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, Australia, Apr. 2015.
[29] Remcom, “Wireless insite.” [Online]. Available: http://www.remcom.com/wireless-insite.
[30] Alkhateeb, Ahmed. “DeepMIMO: A generic deep learning dataset for millimeter wave and massive MIMO applications.” arXiv preprint arXiv:1902.06435 (2019).