On Deep Learning-based Massive MIMO Indoor User Localization

On Deep Learning-based Massi v e MIMO Indoor User Localization Maximilian Arnold, Sebastian D ¨ orner , Sebastian Cammerer , Stephan ten Brink Institute of T elecommunications, Pfaf fenwaldring 47, Univ ersity of Stuttgart, 70659 Stuttgart, Germany { arnold,doerner ,cammerer,tenbrink } @inue.uni-stuttgart.de Abstract —W e examine the usability of deep neural networks for multiple-input multiple-output (MIMO) user positioning solely based on the orthogonal frequency di vision multiplex (OFDM) complex channel coefficients. In contrast to other indoor positioning systems (IPSs), the proposed method does not requir e any additional piloting overhead or any other changes in the communications system itself as it is deployed on top of an existing OFDM MIMO system. Supported by actual measurements, we are mainly interested in the more challenging non-line of sight (NLoS) scenario. However , gradient descent optimization is known to requir e a large amount of data-points for training, i.e., the requir ed database would be too large when compared to con ventional methods. Thus, we propose a two- step training procedure, with training on simulated line of sight (LoS) data in the first step, and finetuning on measured NLoS positions in the second step. This turns out to reduce the required measured training positions and thus, reduces the effort for data acquisition. I . I N T R O D U C T I O N Due to the huge success of mobile communication devices in almost any area of modern life, indoor positioning systems (IPSs) recei ve large attraction in both industry and academia. It can be seen as ke y enabler of a wide range of applications such as indoor navigation, smart factories, or could ev en provide a basic security functionality in distributed Internet of Things (IoT) sensor networks. Additionally , IPSs provide se veral promising benefits for existing technologies, e.g., for impro ved beamforming algorithms or motion prediction for channel estimation. On the other hand, multiple-input multiple-output (MIMO)-orthogonal frequency di vision multiplex (OFDM) systems are widely av ailable and are workhorses of many state-of-the-art communication standards. Thus, it appears attractiv e to focus on such OFDM multi-antenna systems in the following. While the line of sight (LoS) scenario is well-understood and multiple technologies are reported in the literature (e.g., angle- and time-of-arriv al based predictions and triangulation methods) suitable solutions for the non-line of sight (NLoS) scenario are still open for research. Therefore, this work tackles the more challenging NLoS case which cov ers a huge variety of different scenarios. Although there exists an under- lying channel transfer function which describes the behavior of the channel for any giv en position, this function is typically not known or can only be approximated as it is infeasible to fully capture the geometries of the room and its surrounding area. Thus, different approaches have been proposed (comp. [1], [2], [3], [4], [5], [6]) and in vestigated in the past, each optimized for different applications and system models (e.g., see [2] and [5] and references therein). Moreov er , geomagnetic sensors were tested in [3] as an indoor positioning system in combination with deep learning. Overall, these approaches can be split into two cate gories, where obviously mixtures between both categories exist: 1) Model-based: define how the channel is expected to behav e and estimate position accordingly (e.g., ray- tracing of a room). 2) Data-driven: collect a database with appropriate features (often called fingerprints) and corresponding positions (e.g., CSI [4], receiv ed signal strength indicator (RSSI) [7], [8] and recently time-reversal IPS (TRIPS) [9]) and, somehow , interpolate in-between. In this work, we follow the data-driven approach, i.e., we do not assume any specific underlying channel model (except a basic pathloss-model in Sec. III). In comparison to most approaches in the literature (e.g., see [5]), we formulate the problem as a regression task rather than a classification problem, i.e., we directly predict 3D positions. Thus, the neural network implicitly has to learn a channel model or more precisely , it has to appr oximate the dependency between the channel coefficients and the corresponding positions. The authors of [4] follow a similar approach (ho wever , for a con volutional neural network (CNN) structure) and report fractional-wa velength accuracy for a simulated channel model and thus, without considering the amount of training data. In many applications, machine learning and, in particular deep learning, is known to be very effecti ve whenev er the underlying model is hard to aproxmiate or unknown (see [10]). Therefore, deep learning methods appear to be a good match for IPSs where the fundamental problem boils down to the question How to appr oximate the channel behavior based only on a limited number of observations? Unfortunately , training such a deep neural network typically requires a huge amount of training samples, hindering practical usability . As a result, besides the achiev able accuracy , we belie ve the more fundamental question is how much information (datapoints) about a new en vironment does the system need in order to provides sufficient accuracy . In the follo wing, we propose a two-step training strategy , where the neural network (NN) is pre-trained on a simulated LoS channel in the first step, and later , in a second step finetuned, with only a small number of measured training samples. W e then consider the performance of the NN for different reference case scenarios to answer basic questions on generalization and training strategies. W e believ e that the major contribution of this paper is to show that a NN, pre- trained on a simulated LoS channel, can learn the NLoS scenario faster (i.e., with less training data) than a randomly initialized NN. The intuition behind this approach is that both tasks are closely related. Thus, the weights from the previous task are a good starting point for learning the second task, leading to a reduction in overall training complexity . In machine learning terminology this means that we found a better way of initializing the weights of the NN, rather than a random initialization. For the presented LoS and NLoS results all data was mea- sured with a spider-antenna setup [11] which inherently pro- vides ground truth (i.e., 3D position labels) at sub-centimeter precision. I I . B AC K G RO U N D A. Deep learning for user positioning W e refer the interested reader to [10] for a comprehensive introduction to machine learning. Howe ver for the sake of completeness and to clarify the notation we provide a short introduction. In its basic form, a feed-forward NN is a directed compu- tation graph consisting of multiple neurons with connections only to neurons of the subsequent layer . Each neuron sums up all weighted inputs and optionally applies a non-linear acti- vation function, e.g., the rectified linear unit (ReLU) function g ReLU ( x ) = max { 0 , x } , before forwarding the output to all connected neurons. Let layer i have n i inputs and m i outputs, then it performs the mapping f ( i ) : R n i → R m i defined by the weights and biases as parameters θ i . Consecutiv ely applying this mapping from input v of the first layer to the output w of the last layer, leads to the function w = f ( v ; θ ) = f ( L − 1)  f ( L − 2)  . . .  f (0) ( v )  (1) where θ is the set of parameters and L defines the depth of the net, i.e., the total number of layers. T raining of the NN describes the task of finding suitable weights θ for a given dataset and its corresponding labels (desired output of the NN) such that a given loss function is minimized. This can be efficiently done with the stochastic gradient descent algorithm [10] as implemented in many state- of-the-art software libraries. W e use the T ensorflo w library [12]. In principle, the universal approximation theorem found in [13] states that such a multi-layer NN can approximate any continuous function on a bounded region arbitrarily closely for L ≥ 2 , giv en non-linear activ ation functions and a sufficiently large amount of neurons. − 10 − 5 5 10 2 4 6 initial training area testing area antennas user position channel coeff. h i x [m] y [m] Fig. 1: System model under in vestigation. B. System Model Fig. 1 shows the basic system model, where a linear antenna array (i.e 8 antennas on a line) is used. As indicated by the model, each antenna sees a slightly different single-tap complex channel coef ficient h i for any user position and the NN needs to learn to estimate the user’ s position based on these inter-antenna channel differences. During the first training step the NN is initially trained on random user positions within the blue area in front of the antenna array . Since the 3D-spatial channel coefficients for any user position can be calculated by a LoS channel model, this training phase can be done with an unlimited amount of training data and with an arbitrarily large initial training area. The only limitation is that the initial training area should include that area which the NN is later tested and finetuned on. The initial training step is completed once the NN reaches a sufficient accuracy . An ev aluation on the pre-trained NNs performance for different numbers of antennas and additive noise samples is shown in Section III. The second training step uses measured datapoints taken from the green area (Fig. 1) to finetune the pre-trained NN for the actual testing area. In Section IV, we ev aluate the required amount of finetuning datapoints and their respective positions. Note that this system model is only described for a 2-dimensional area, but can be extended to a 3D system straightforwardly . W e use this system setup since all of our measurements are done in a 2D area with a 16-antenna linear array . Due to the antenna positions’ symmetry , such a linear antenna array cannot distinguish between frontside and backside of the array . Therefore, a system that cov ers all positions of a 2D-plane also needs a 2-dimensional antenna array; accordingly for a 3D-area a 3-dimensional antenna array would be required. 1) Simulated Channels: The channel model can generate a complex channel coefficient h i for each spatial user position and antenna in a 3D area, as the (baseband) phase and amplitude of an LoS-channel can be computed using h i, LoS =  λ 4 π d  e j 2 π d λ , (2) where d is the distance between the transmitter antenna (TX) and the receiver antenna (RX), and λ is the free-space wa velength. In this case a carrier frequency of f c = 2 . 35 GHz is used. W ith this LoS channel model an infinite number of -0.8 -0.4 0 0.4 1.5 2 2.5 3 x [m] y [m] Sim. LOS -0.8 -0.4 0 0.4 x [m] LOS -0.8 -0.4 0 0.4 x [m] NLOS − 10 − 5 0 [dB] Fig. 2: Spatial energy map o ver testing area, sim. LoS vs meas. LoS vs meas. NLoS for MR precoding with a tar get user (black circle) at x = 0 . 31 m, y = 2 . 96 m, 16-antenna linear array . training points can be generated to pre-train the NN for the LoS scenario. 2) Measur ed Channels: The spatial consistent channel measurements conducted in [11] will be briefly explained. A spider antenna is used to move a software-defined radio as a transmitter in the x , y -plane to measure a spatially consistent channel in two spatial dimensions, and to study linear transmit precoding. In Fig. 2, the spatial energy ov er the area is shown for the simulated LoS and the measured LoS and NLoS case for a spatial precoding: 16 antennas in a line with a distance of λ/ 2 are precoded with respect to the user position at x = 0 . 31 m and y = 2 . 96 m using a maximum ratio (MR) precoder . The single purpose of Fig. 2 is to show that there are only slight differences between the simulated and the measured LoS case, whereas there are huge differences to the NLoS case. Remark: For this work, we only consider a single sub- carrier of the OFDM system per antenna. W e hav e additionally trained NNs for all sub-carriers as input, but did not observe a significant gain besides the expected gain due to an improved SNR through av eraging of the sub-carriers. Howe ver , the training complexity (and the required net dimension) increases drastically . The intuition behind is that the indoor channel (room size) does not show a significant frequency selectiv e behavior for the measurement bandwidth of 40 MHz in our scenario (also not for the indoor NLoS case). Thus, the NN does not benefit from the increased amount of observations as there is only little additional information contained in sub- carrier interrelation and we conclude that one sub-carrier per antenna is sufficient. C. P erformance metric Due to the antennas’ beam pattern, a user position with a large distance to the base station is more difficult to estimate than a user close to the base station. Therefore, we propose a performance metric to compare different measurement setups, algorithms, reference scenarios etc. which is independent of the user position. This metric is defined over the normalized mean squared error (NMSE) as a “relativ e” accuracy metric NMSE = E " k p − ˆ p k 2 k p k 2 # , (3) where the mean squared error (MSE) of the estimated position ˆ p to the actual position p is normalized with respect to the distance d = k p k 2 (assuming the antenna array to be at the origin and p is the user position in x - y - z coordinates). For example, this metric returns a NMSE of 1% for a user position with a distance of 1m and an error distance of 1 cm. W ith increasing distance to the antenna array the difficulty of estimating the channel increases, which is compensated by this normalization. I I I . I N I T I A L T R A I N I N G O N S I M U L AT E D L O S C H A N N E L S T ABLE I: Layout of the neural net Layers: Parameters Output dimensions Input 0 16 (antennas) x 2 (Re/Im) Dense (relu) 33 , 792 1024 Dense (relu) 1 , 049 , 600 1024 Dense (relu) 1 , 049 , 600 1024 Dense (linear) 3075 3 In this section, we show a basic proof-of-concept, where the NN is able to approximate the user position, by e valuating the performance after the initial training step. Thus, the NN is tested on noisy , simulated LoS channel coef ficients of random positions out of the blue area shown in Fig. 1. All results presented in the follo wing have been achiev ed with a simple, non-hyperparameter-tuned NN, which has a total of 2 , 136 , 067 trainable weights and is defined in detail in T able I. Although the structure of the NN is quite simple as it only consists of dense layers, it contains a large amount of trainable parameters. 1 Thus, its capacity already exceeds our entire measured training data set (only 16 × 2 values per sample of about 60 , 000 measured positions), which is why we focused on preventing ov erfitting effects during finetuning. Note that the capacity of the NN is no problem during the pre-training stage, because we can train the NN with an infinite amount of different samples and thereby outnumber the NN’ s memory capabilities. This can be considered as another benefit of a pre-training stage, since it can obviate overfitting during the finetuning stage. W e introduce a signal-to-noise-ratio (SNR) definition SNR = P N ant n =1 | h LoS ( n ) | 2 σ 2 (4) which is independent on the distance for all possible user positions. The notation, σ 2 is the power of the complex ad- ditiv e white Gaussian noise (A WGN), and N ant is the number of antennas at the base station, i.e., the linear array . Fig. 3 1 Remark: for the LoS scenario less weights are sufficient, howe ver , the idea of pre-training requires the same dimensions for the LoS and NLoS scenario. W ithout considering complexity such a large structure turned out to reach higher accuracy for the NLoS case than smaller NNs. Howe ver , we cannot claim this observation to hold in general. Using CNNs may reduce the number of trainable parameters if required (cf. [4]), but also requires further hyper-parameter optimization. 0 5 10 15 20 25 30 10 − 3 10 − 2 10 − 1 10 0 SNR [dB] NMSE N ant = 4 N ant = 8 N ant = 16 N ant = 32 N ant = 64 N ant = 128 Fig. 3: Sweep over SNR and varying number of antennas for the simulated LoS scenario. shows that a system with only 4 antennas can estimate the user position with an accuracy of 1% NMSE at an SNR of 30dB. Moreov er, if the number of antennas is doubled, the expected gain of 3dB due to gains in noise av eraging sho ws up. Note that, not the channel model function is learned by the NN but the triangulation task as a whole, which may ev en be more challenging. These results show that the NN is able to estimate the user position within the training area suf ficiently well. But we also noticed that, if we test the NN on user positions outside of the initial training area, the estimations become rather bad. Apparently , the NN seems to learn an interpolation between fingerprints rather than it finds a global solution of the triangulation task itself. While this is not a problem for the simulated LoS channel scenario, since we can always generate the coefficients and train on all positions, it is a problem for real-world applications, as it implies that the NN needs to be trained on the whole area it is later used for and generalization to “external areas” is limited. This raises two key questions: How many labeled samples ar e needed, and wher e do they have to be located? For this, we define three reference scenarios for the second training step of finetuning on actual measured data , described in the following section. I V . F I N E T U N I N G O N M E A S U R E D L O S / N L O S D AT A Next, we consider the green area outlined in Fig. 1 and examine the required amount of datapoints and their spatial distribution for achieving a specific accuracy . A. Datapoint distribution Fig. 4 schematically shows the three reference cases: 1) For the “random”-scenario, random datapoints taken from the whole testing area are used for finetuning training and, also, validation data to verify that the NNs accuracy is pick ed randomly from the whole testing area. 2) The “left-right” scenario is based on the idea of having trained a room (right side), but estimating on another room (left side), and splits the testing area into two areas where random datapoints from the left area are used for Random Left-Right Border T esting Finetuning V alidation Fig. 4: Reference scenarios; different colors mark the different datasets. 200 400 600 800 1 , 0001 , 200 1 , 400 1 , 6001 , 800 10 − 3 10 − 2 10 − 1 λ Number of Points used for training NMSE Left-Right (LoS) Border (LoS) Rand. (LoS) Left-Right (NLoS) Border (NLoS) Rand. (NLoS) Fig. 5: NNs NMSE performance after finetuning on measured LoS (solid) and NLoS (dashed) area for dif ferent reference scenarios over the amount of used finetuning samples. 100 epochs are used for training. finetuning training and datapoints from the right area are used for validation. 3) In the “border”-scenario, which is motiv ated by the idea of only measuring the edges of a room, the finetuning datapoints are taken from a border area (here 30% of the area), and the validation datapoints are from the remaining (and unknown to the NN) center area. Next, we use the NN, that has been pre-trained on the simulated LoS channel, (see previous section) and finetune it with actually measured LoS data according to the three different scenarios of Fig. 4. . Fig. 5 compares the NMSE performance of the NN for the different scenarios in the LoS and NLoS case. Note that the random case is always used as the (best-case) reference. Apparently , for the “left-right” case, the NN does not con ver ge at all, which matches with our observ ations for the simulated LoS channel. For the “border” case, the NN con verges to a reasonably good estimation accuracy . It appears that the pre- trained NN only needs to see a few samples (about 400) from the border area during finetuning training to con ver ge and estimate the positions reasonably well. As expected, generally , the NLoS scenarios shows higher prediction errors caused by the more complex channel be- havior . Similar to the LoS measurements, the NN does not con verge in the “left-right” case, where the NMSE perfor- mance remains at about 10.8%. Interestingly , the performance of the “border” case performs similar to the random case up to 0 50 100 150 200 10 − 2 10 − 1 10 0 Number Epochs NMSE NLoS pre-trained NLoS LoS pre-trained LoS Fig. 6: Reachable NMSE o ver number of training epochs with 200 training samples between pre-trained and randomly initialized NN. about 1000 av ailable finetuning samples. Intuitiv ely , learning the channel transfer function for both the whole area, as well as for only the border area, is equally difficult since the channel exhibits a sort of random pattern in the NLoS case, as can be inferred from Fig. 2. After about 400 samples used for finetuning training, an accuracy of λ is reached, which means that if each spatial λ/ 2 a new channel is assumed, the room has been fully learned by the NN. This sho ws that the pre- trained NN system can easily be adjusted and trained with low ov erhead and, therefore, is even a viable solution in the NLoS case. B. Effect of pr e-training T o demonstrate the benefit of pre-training on a simulated LoS channel, we compare the performance of the pre-trained NN with that of a randomly initialized NN in the context of the number of epochs needed to achiev e a specific accuracy . Fig. 6 shows the NMSE performance of a pre-trained NN and a randomly initialized NN trained on 200 measured samples for both the LoS and the NLoS case. Also the final NMSE reached by the pre-trained NN in both cases is lower than the final NMSE of the randomly initialized NN. T o be fair , the randomly initialized NN can reach the NMSE performance of the pre-trained NN if it is trained with much more measured samples and/or epochs, b ut we consider the amount of av ailable training data as a limiting factor of a real world application. This leads to the conclusion that pre-training of the NN on a simulated LoS channel is advantageous, as the pre-trained NN requires less measured and labeled training data and, also, conv erges faster for all scenarios tested. V . O U T L O O K A N D C O N C L U S I O N In this work, we have shown that neural networks can be used for user localization in MIMO-OFDM systems. W e have in vestigated the amount of required training positions and showed that pre-training of the NN with simulated LoS data significantly reduces the required amount of training samples. As a result, an accuracy of less than 1% for real data can be reached within our spatial test area. For future work a multi- room measurement setup will be b uild to verify the results in a wider and more general setting. The NN complexity (i.e., the number of trainable parameters) may be reduced by using additional CNN layers. 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