## 1 Introduction
Their scheme enhances the privacy level of the source node by setting two candidate domains and the proxy node that will serve as the source node to confuse an adversary. In [PERSON] et al. (2018), authors proposed a bidirectional location-based SLP scheme to protect both source and sink node. More existing random walk-based SLP solutions, their contributions, and their weaknesses are detailed in Section 2. Nevertheless, we noticed that the existing random walk-based solutions in SLP have either focused only on enhancing privacy, i.e., the safety period (see Section 6 for the definition) at the cost of reduced network lifetime, or have focused on enhancing privacy without hampering the network lifetime (NLT). However, enhancing both privacy and network lifetime together in a single solution does not exist in the literature. The objective of this work is to present a new random walk-based SLP routing protocol (SLP-E) that offers consistent privacy and improves both the safety period and network lifetime. No existing SLP solution based on random walks exhibits these combined improvements in the literature. This study also looks into how the radio range of sensor nodes affects network lifetime and privacy strength, which is not investigated in the existing SLP research. The existing works in the literature that tried to enhance both safety period and NLT in a single solution do not belong in the random walk-based category. The scheme suggested by the authors of [PERSON] et al. (2018) tried to maximize both the safety period and the network lifetime in a single solution. In addition to the introduction of phantom nodes in their scheme, fake sources are used to confuse a backtracking attacker to enhance privacy. In order to enhance NLT, the scheme tries to reduce energy consumption in the hotspot area (near the sink) by establishing diversionary routes that only use a lot of energy in non-hotspot areas. However, the introduction of fake sources can affect the NLT. Furthermore, it has been observed that their scheme does not take into account the energy level as a criterion when selecting a node from the forwarding group to relay the packet. Consequently, if nodes with lower energy continue to relay the packets, their batteries may eventually become depleted, resulting in a poor network lifetime (NLT). The work in [PERSON] et al. (2018) also proposed a scheme that improves both the privacy level and the network lifetime in a single solution, but the aim of this study is to mitigate the issues of black hole attacks and not to focus on SLP. In addition, we have also observed that the safety period in existing phantom routing schemes (random walk-based-SLP) exhibits a distance-dependent behavior, i.e., the closer the source node is to the BS, the smaller the safety period is. Further, as the distance between the source node and the BS becomes larger, the safety period value also becomes larger. The attacker might use this behavior to infer the asset information such as the location information. The proposed scheme (SLP-E) aims to address this problem by offering a constant level of privacy protection regardless of where the source node is located within the network, achieving enhanced privacy and network lifetime. Also, this work aims at answering the long-awaited question, i.e., _\"Is there any impact of sensors' radio range on safety period and NLT\"_ in SLP solutions? For achieving a prolonged network lifetime of the WSNs, a study was made in [31] to see the impact of sensors' radio range on the network lifetime. However, this work was not aimed at source location privacy (SLP). To the best of our knowledge, no research exists in the literature that aims at SLP that has studied the impact of the sensors' radio range on privacy level (safety period) and NLT. This article proposes a novel scheme that takes into account the backtracking attacker that initiates its backtracking process from the BS, as it is the final destination for all incoming packets, like in Ref. [22].