在本篇論文中，我們提出了一種網路嵌入(network embedding) 方法，僅透過使用
行動用戶在LTE 網路中對基站的參考訊號接收功率(Reference Signal Received Power,
RSRP) 以追蹤及預測行動用戶。我們的方法之關鍵點在於將行動用戶與基站的RSRP
向量視為一個二分圖(bipartite graph): 左邊為行動用戶節點，右邊則為基站節點。接
著，我們將二分圖中行動用戶節點以及基站之節點投影到一個低維的歐氏幾何空間中。
透過將行動用戶的高維RSRP 向量轉換為低維之嵌入(特徵) 向量，我們便可以使用簡
單的追蹤方法，如有限脈衝響應(Finite Impulse Response, FIR) 濾波器來追蹤行動用
戶之位置。為了測試我們方法的有效性，我們使用了軟體模擬了一個包含54 個行動用
戶以及48 個基站之路網，並對此路網每隔一固定時間進行取樣快照(snapshots) 記錄
行動用戶之座標以及RSRP 向量。產生出的31 張快照中我們使用前30 張做為訓練集
(training set)，而最後1 張快照做為測試集(testing set)。實驗結果顯示，我們的網路
嵌入方法對最後1 張快照的預測誤差與常用之指紋定位法(fingerprinting) 對前30 張
快照的估計誤差相當。

In this thesis, we propose a network embedding approach for tracking/predicting mobile
users by only using the Reference Signal Received Power (RSRP) from mobile users to base
stations in an LTE network. The key insight of our approach is to view RSRP vectors as a
bipartite graph with mobile user nodes on the left and base station nodes on the right. We
then embed the mobile user nodes and the base station nodes in the bipartite graph into a
low-dimensional Euclidean space. By doing so, we transform high-dimensional RSRP vectors
of mobiles users into low-dimensional embedding (latent) vectors so that they can be tracked
by using simple tracking methods, such as the Finite Impulse Response (FIR) filters. To test
the effectiveness of our approach, we generate a synthetic data set for a community with 54
mobile users, 48 base stations, and 31 snapshots. We use the first 30 snapshots for training
and the last snapshot for testing. Our numerical results show that the prediction errors of our
network embedding approach for the last snapshot are comparable to the estimation errors of
the commonly used fingerprinting method for the first 30 snapshots.

Contents 1
List of Figures 3
1 Introduction 4
2 Problem formulation 7
2.1 Positioning problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Fingerprinting problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Tracking/prediction problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 The network embedding approach 10
3.1 Construction of a similarity matrix . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 The CAFE algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2.1 Modularity matrix and the modularity of a partition . . . . . . . . . . . 11
3.2.2 The network embedding problem . . . . . . . . . . . . . . . . . . . . 12
3.2.3 The softmax clustering algorithm . . . . . . . . . . . . . . . . . . . . 14
3.2.4 Learning the embedding vectors . . . . . . . . . . . . . . . . . . . . . 15
3.3 Using the embedding vectors for the fingerprinting problem . . . . . . . . . . . 16
3.4 Using the embedding vectors for the tracking/prediction problem . . . . . . . . 16
3.4.1 Tracking a mobile user . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.4.2 Predicting a mobile user . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 System architecture 19
4.1 Network embedder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Locator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.3 Tracker/Predictor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.4 Recommender . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5 A testing example 21
5.1 The RSRP vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2 The embedding vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.3 Effectiveness for the fingerprinting problem . . . . . . . . . . . . . . . . . . . 24
5.4 Tracking the embedding vectors . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.5 Predicting the coordinates of mobile users . . . . . . . . . . . . . . . . . . . . 29
5.6 Recommendation of base stations . . . . . . . . . . . . . . . . . . . . . . . . 30
6 Conclusion and Future Work 33

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