Cross-Layer Design and Analysis of Wireless Geophone Networks Utilizing TV White Space

Traditional seismic data acquisition systems used for surveying during the exploration of oil and gas rely on cables between geophones and the data collection center. Despite the fact that cable-based systems provide reliable seismic data transfer, their deployment and maintenance costs increase substantially as the survey area increases in scale. Therefore, a three layer wireless network architecture is proposed in this work, which consists of wireless geophones (WG) and a data center with an intermediate wireless gateway node (WGN). This paper investigates the aggregate data throughput, transmission time, and energy consumption from WGs to the WGN in a wireless geophone network architecture based on the IEEE 802.11af standard. This standard is considered in order to have the maximum possible range and low power consumption due to operating in TV bands. Analytical expressions of the aforementioned quantities are derived using Markov chain models. Two Markov models are considered for this purpose: one for modeling the access method that allows multiple WGs to connect to a WGN and the other for representing a buffer in a WG. Since seismic data is recorded at regular intervals, arrivals of data packets in the buffer of the WG is deterministic. On the other hand, departure is random due to the multiple access method. Hence, in this work D/M/1/B queue is used for the first time to model the buffer in a wireless geophone. Furthermore, the physical layer constraints are also taken into account together with proper wireless path-loss channel models. The results obtained are useful for designing such wireless seismic networks without extensive simulations. In particular, the proposed joint medium access control, physical layer, and D/M/1/B model enables us to optimize the required number of WGNs. Finally, sectoring is also introduced in order to minimize the total number of WGNs needed to cover the whole surveying area.


I. INTRODUCTION
For many years, oil and gas companies relied on cable-based architectures to transmit data from geophones to a data collection center. In land seismic surveys, cables are responsible for nearly 50% of total cost and 75% of total equipment weight [2]. Typically, data are collected by a large number of geophones deployed over an area of more than 20 km 2 [3]. Recently, there has been a growing interest to deploy wireless geophone networks for seismic acquisition especially The associate editor coordinating the review of this manuscript and approving it for publication was Wen Chen .
in large land surveys [2]- [8]. In [2], future potential of wireless geophone structure is discussed for high-density land seismic acquisition. In [4], a nodal system is proposed where geophones store the seismic data and then the crew collects the stored data from the field. The design requirements of a wireless geophone network are discussed in [5], where multiband orthogonal frequency division multiplexing (MB-OFDM) is adopted for radio transmission. A hybrid approach of the wired and wireless network is proposed in [6]. To date, suggested technologies are not utilizing the full potential of the wireless communication network that is capable of competing with cabled systems [5]. Due to power limitations, short-range and long-range transmissions are required to eliminate the cables. In short-range, wireless geophones (WG) send the recorded data to the wireless gateway node (WGN). The WGN then forwards all the received data to a storage and processing unit (recording cabin) in a long-range transmission.
For the design of wireless seismic acquisition system, it is necessary to understand the seismic data acquisition process. It consists of three main phases: shooting phase (source generates seismic waves), recording phase (geophones detect reflected waves from subsurface layers), and data delivery phase (synchronization, digitalization and forwarding). These phases are repeated at regular time intervals. In order to design a wireless geophone network for seismic acquisition, constraints such as transmission time, power limitation, and maximum attainable aggregate throughput need to be investigated keeping in view the fixed topology. Furthermore, the impairments introduced by the medium access control (MAC) and the physical (PHY) layers are very important, and hence, investigating the MAC and PHY layers for realistic conditions is essential for performance analysis. The analysis of throughput, transmission time, and power by considering MAC and PHY layers parameters is lacked in the aforementioned references. In this work, carrier sense multiple access method with collision avoidance (CSMA/CA) is considered for the communication between the WG and WGN. This medium access method is commonly used in such kind of networks, e.g., IEEE 802.11 and 802.15.4 standards.
There are three ways to test a network or a system; physical model (real test bed), a simulation model or a mathematical model. Mathematical/analytical models strive to reproduce the technical aspects and mechanisms that are widely seen in the standards (such as, IEEE 802.11 or 802. 15.4) in order to track the performance of a network. In this work, a mathematical model is adopted for the first time to test the wireless system performance that is proposed for the seismic field survey. The reason is to enable seismologists to design the wireless seismic network based on their requirements without using less familiar softwares.
Since the PHY and MAC layers contribute to the major performance degradation in the network, these layers are considered to be the most effective layers in the protocol stack. Therefore, this paper focuses on the analysis of these layers. In the literature, there are numerous mathematical models to investigate the MAC behavior and test its performance and functionality. These models can be broadly classified into saturated [9], [10] and unsaturated traffic models [11]. In saturated traffic, a node or a WG (in our case) always has a packet ready for transmission, i.e., the buffer in a node never gets empty. However, in a real situation, a node possibly becomes idle when there is no packet in the buffer to transmit, this is known as an unsaturated condition. The situation of seismic acquisition network is similar to unsaturated traffic condition, since after sending a packet to the centralized entity (WGN in our case), the WG can enter an idle state.
The aim of this work is to model the communication process between WG and WGN using Markov chains. A well-known MAC layer model in the literature is Bianchi's Markov chain model for IEEE 802.11 [10]. This model mimics the MAC layer functionalities while considering ideal channel conditions with saturated traffic. This model finds a basis for many analytical studies [12]- [19]. Bianchi's model has been extended to analyze the delay [12], [13], packet reception rate [20], throughput [16] and MAC layer service time [14], [15] of the IEEE 802.11. Bianchi's model also provides foundation for the IEEE 802.15.4 model [9], [21]. However, simulation results show weak matching with the analytical results under unsaturated traffic [11]. In [18] In this work, the proposed joint PHY, MAC and buffering model is built on the work of Daneshgaran et al. [18]. We extend this model so that it not only incorporates the general mechanisms at MAC and PHY layer, but also other PHY layer parameters and constraints, such as, Signal-to-Noise Ratio (SNR), encoding, modulation, and hardware and MAC layer functionality, i.e., request to send and clear to send (RTS/CTS) mechanism. This joint model enables us to analyze the throughput, transmission time and energy consumption of the network and to optimize parameters such as the number of WGs per WGN required to cover whole surveying area.
Furthermore, in unsaturated traffic model, it is required to find the probability of being idle. To calculate this probability, a buffer of size B is proposed in the WG and it is modeled as a D/M/1/B queue. It is worth mentioning that D/M/1/B is not observed in real applications, in particular, related to networks. This queue is used for the first time in this work. The reason is that this model is suitable for the scenario at hand, i.e., deterministic packet arrivals (seismic data is recorded at regular intervals) and random departure (communication between WG and WGN is carried out using CSMA/CA). This is in contrast to the previous works, in which the idle probability is either taken as input to the MAC model, i.e., considered to be known [11], or calculated using assumption of small buffer size with random arrivals [22].
Moreover, this work proposes to use IEEE 802.11af standard for communication between WGs and WGN. This standard operates in TV bands to achieve the maximum possible range and low power consumption among IEEE 802.11 family.
While many papers analyzed a certain functionality of IEEE 802.11 based network, the authors are not aware of any work that has performed cohesive analysis of the MAC, PHY and D/M/1/B model for seismic network presented in this work. In summary, unlike [1], the main contributions of this paper are the following: 1) Enhancing the MAC layer model by representing a buffering process in the wireless geophone with standard, which is proposed for the WG to WGN communications. This standard uses the TV white spaces for communication. The reason for considering these bands is to achieve larger transmission range with low power consumption, which reduces the required number of WGNs. The maximum range for this standard is 1 km.
3) The MAC model in [18] is extended for the RTS/CTS mode. This solves the hidden node problem and increases the throughput, since the collision only occurs on short RTS frames. Furthermore, more precise PHY error probability is provided by considering various path-loss models, modulation schemes, encoding schemes, noise within the hardware, and interference caused by neighboring WGNs. 4) In order to cover the whole seismic surveying area, frequencies allocated to the WGN are reused in a regular pattern. The joint MAC and PHY layer modeling together with queueing model enables us to analytically derive the interference due to frequency resuse and investigate its effect. Finally, cell sectoring is introduced to reduce the collision domain of CSMA/CA and to decrease the interference. The rest of this paper is organized as follows. Section II is devoted to the seismic data acquisition network. Analytical models of MAC, PHY and buffering process are presented in Section III, and expressions of throughput, transmission time and energy are derived in Section IV. Analysis of energy consumption is carried out in Section V, whereas Section VI discusses the interference noise modeling and mitigation. Results are presented in Section VII, and finally, Section VIII draws the conclusions.

II. WIRELESS SEISMIC ACQUISITION NETWORK
This section presents the seismic network topology, MAC protocol for wireless interface and transmission channels.

A. DEPLOYMENT OF GEOPHONES
There are various layouts for the geophones in the seismic survey field; however, the orthogonal layout/placement, shown in Fig.1a, is the most common. For such placement in a typical field, there are around 480 WGs, at distance of 25 meters along inline direction, whereas 30 such lines of geophones are placed at distance of 200 meters along crossline direction. Total inline distance and crossline distances are 12 and 6 km, respectively. These facts and parameters are obtained from leading oil and gas companies in the Middle East. The geophones considered in this work are assumed to be equipped with a wireless interface. Furthermore, a centralized network is assumed, in which WGNs are placed in between geophone lines in such a way to cover all the surveying area (see Fig. 1a). Each WG sends its collected data to the WGN to which it is connected. One cell (serving area) of WGN with connected WGs is shown in Fig. 1b. All WGNs transmit received data to the data collection center for storage. The medium to transmit the data from WGN to the data collection center can be wired or wireless. However, this stage of transmission is beyond the scope of this work.
Since, the acquired seismic data is very important, a buffer capacity is necessary in wireless geophones in order not to drop packets. For this purpose, D/M/1/B queueing model is proposed, for the first time, as packets arrive at regular fixed intervals and leave the queue in a random fashion.

B. MAC PROTOCOL
In the IEEE 802.11 standard, the fundamental medium access mechanism is called distributed coordination function (DCF). This random access scheme is based on CSMA/CA mechanism.
In DCF mode, the CSMA/CA algorithm adopts a binary exponential backoff mechanism to limit collisions and control the transmission from various stations/WGs. This scheme mainly depends on a parameter called contention window, w i . The number of backoff slots, i.e., how many slots a WG has to wait before it again assess the channel availability, is chosen randomly from the range 0 to w i −1. For the first transmission attempt, the value of w 1 is set to CW min . For each retransmission attempt, if the transmission is unsuccessful (due to the collision or transmission error), the value of w i is doubled until it reaches its maximum value, i.e., CW max = 2 m CW min , where m is the maximum number of backoffs. Mathematically, w i = 2 i CW min for 0 ≤ i ≤ m, and w i = 2 m CW min for i > m. When a WG is ready to transmit some frames, it starts the backoff timer with a randomly selected number in the range [0, w i ]. The timer is decremented as long as the channel is sensed idle. If a transmission by another WG is detected, then the timer is frozen and reactivated upon sensing the channel to be idle again for more than distributed interFrame space (DIFS) time period. After the backoff counter counts down to 0, the packets are transmitted in the next time slot.
A positive acknowledgement (ACK) is sent to the WG, upon successful reception of a packet at the destination and waiting for a period of time called short interFrame space (SIFS). Since the duration of SIFS (plus the propagation delay) is shorter than the DIFS, no other WG senses the channel idle. If ACK is not received in the specified duration (ACT_time) or a different packet transmission is detected by the WG, then it reschedules the transmission according to the backoff mechanism explained above. The above described two-way handshaking technique is called the basic access mechanism.
DCF also defines a four-way handshake procedure known as RTS/CTS. In this technique, if a WG wants to transmit a packet, it performs the backoff procedure explained above, senses the channel for DIFS and sends a short frame called RTS frame. The receiving node (WGN), after receiving the RTS, respond with a CTS frame. Upon successful reception of CTS, the transmitting WG sends the packet. The RTS and CTS frames contains the information about the packet duration. Therefore, stations that hear the RTS or CTS updates the network allocation vector (NAV), which contains the information about the duration of time the channel remains busy. Hence, a WG that is hidden from the transmitting WG, delays its transmission and avoids possible collision. This technique is effective when large packets are involved in the transmission, since the collision only occurs on the RTS frames and is detected by the transmitting stations if the CTS frame is not received. This technique manages to solve the hidden node problem and is considered in our work.

C. CHANNEL MODELS
In [18], a time-varying Rayleigh fading channel is assumed for calculation of the PHY layer errors. However, this channel model is not suitable for our case. Firstly, it is not appropriate for TV bands. Secondly, it considers only non-line-of-sight (NLOS) with no dominant path, however, chances of lineof-sight (LOS) is high for seismic wireless systems. Finally, it models the Doppler effect caused by mobile reception, transmission or scatterers that introduces time-dependence to the channel. In our case reception and transmission is not mobile. Hence, the aim is to calculate more precise PHY layer error probability and hence, more accurate throughput, transmission time, and energy consumption using proper channel models. There are quite a few propagation channel models in the literature which are proposed/validated for near-ground communication in very high frequency/Ultra high frequency (VHF/UHF) bands [26]- [28]. These models, summarized in Table 1, are suitable for our scenario.  counterpart [18]. The MAC model presented here captures the effect of the WG's backoff stage, the retransmission counter, the idle stage and the physical channel. As a contribution, a D/M/1/B queueing model is also inserted into the MAC model to represent the buffering process at each WG. The reason for using a D/M/1/B queueing model is that the input to the buffer of the WG is deterministic with fixed arrival rate, and output is random (due to exponential backoff). On one hand, the MAC Markov model is used to determine the steady state probability of sensing the channel to be idle for transmitting a frame, the probability of collision if more than one WG transmits in the same time slot, and the probability of failure due to constraints of the physical layer. On the other hand, the D/M/1/B queueing model facilitates finding the performance parameters, e.g, throughput, and transmission time. Specifically, the queueing model is used to find idle state probability. In the following subsections, details about the MAC model, the PHY model, and the D/M/1/B queueing model are presented.

A. MAC LAYER MODEL
The generalization of the analytical MAC model of slotted CSMA/CA mechanism for the IEEE 802.11 is presented in [18]. In this work, this model is extended to RTS/CTS mechanism along with introduction of D/M/1/B queue.
This work considers a scenario of N contending WGs that send the data to a sink. Suppose, the probability that a WG sends a frame in the randomly selected time slot, the collision probability, and the probability of transmission failure are denoted as τ , P col , and P fail , respectively. The method presented here aims to solve the non-linear system of equations representing τ , P col and P fail together with the estimation of the idle probability, p 0 . The idle probability is the probability of going back to the idle state if the buffer is empty by taking into account the offered load at each WG, i.e, λ. Consequently, our model enables the MAC model to determine this probability based on the arrival rate. Note that the capture effect in which a WG, with relatively high SNR, captures the channel in case of simultaneous multiple transmission, is not considered here. The reasons are: the RTS/CTS mode is insensitive to the capture, the transmission time is not influenced by the capturing effect and finally, capturing effect is only feasible to the indoor environment.
The IEEE 802.11 MAC discrete 2D Markov chain model is represented in Fig. 3, which shows the states and the transition probabilities. Fig. 3 is based on the following observation: • There is an idle stage and backoff stages (i, 0) to • The backoff counter is decremented with probability 1 at the beginning of each time slot.
• After a successful packet transmission in a time slot, if a WG has a packet in buffer to transmit then it starts the transmission from backoff stage 0 with probability 1 − p 0 .
• After each unsuccessful transmission (either due to packet collision or transmission error due to channel), the backoff stage is incremented to a new contention stage with probability P fail /w i . This increment seizes at backoff stage m, where WG keeps on trying with same contention window unless packet is successfully transmitted.
• If after a successful transmission, the buffer is empty then WG transits in the idle state waiting for a new packet. The probability of successful transmission P succ is the probability of having no collision and transmission errors and given as where P phy and P col are the probability of transmission error due to the wireless channel and probability of collision, respectively, and P fail = 1 − P succ . The probability that a WG sends a frame in the randomly selected time slot, τ , is given as (see Appendix A), (2), as shown at the bottom of the next page, where m is the maximum number after which the backoff timer is seized. The collision probability, that is needed to compute P fail , can be found by considering that the packet from the transmitting WG encounters a collision when at least N − 1 remaining WGs attempt to transmit simultaneously. Hence, the collision probability is given as

B. PHY LAYER MODEL
Next, the PHY channel error probability, i.e., P phy required in (1) where P data and P ACK are the probability of transmission error for packet and acknowledgement (ACK), respectively. The ACK frame is much smaller than the data frame and is transmitted at lowest rate (1.8 Mbits/s using BPSK). Hence, its transmission error probability is very low and can be ignored. Same is the case with RTS and CTS frames. Therefore, P succ,phy ≈ 1 − P data . The probability of packet loss due to transmission error can be expressed as The probability of transmission error for data packet is given as where H PHY , H MAC , and L b are the PHY header, MAC header, and frame payload length in bytes. P R (H PHY ) and P R (H MAC +L b ) are the transmission success probability of the PHY header and data plus MAC header, respectively, given by [33] for various packet encoding as and NRZ : where non-return-to-zero (NRZ), 4-bits-to-5-bits (4B5B), Manchester, and single error correction and double error detection (SECDED) are the encoding schemes, and P b is the probability of bit error.
In the IEEE 802.11af standard, OFDM is used at the PHY layer. Therefore, the received OFDM symbol Y is mathematically written as Y = HX + N , where X is the transmitted OFDM signal, N is the noise vector, H = diag(H ) = FhF * is the diagonal channel matrix, F is the FFT matrix, h is the channel impulse response, and (.) * is the Hermitian conjugate. At k th frequency bin, the received signal can be written as Y (k) =H (k)X (k) + N (k), where X (k) is the transmitted modulated symbol,H (k) is the channel effect and N (k) is noise corresponding to k th frequency bin. Now, considering the OFDM model and static channel h (Table 1), P b can be computed as [34] BPSK : where Q(.) is the Q-function which is found from lookup table [34], γ b = E b,r /N 0 is the received energy (Joules) per bit to noise power spectral density (Watt/Hz) ratio, and K = log 2 (M ). To find the bit error probability from (8), γ b is required, which can be related to the transmitted energy per bit, however, commercial radios do not provide this value, rather the transmitted power is provided. Hence, the relation of the transmitted power to γ b is presented next. The received energy per symbol to noise power spectral density ratio at the output of the receiver, i.e., γ s = E s,r /N 0 is given as, γ s = |H (k)| 2 E s N 0 , where E s is the transmitted energy per symbol and E s N 0 = C s P N T s B, where B is the channel bandwidth (Hz), T s is the symbol duration and C s /P N is the transmitted signal power to noise power ratio (power is in watt). Since, the symbol duration is related to bit duration as T s = log 2 (M )T b , where T b = 1/R and R is data rate, therefore, γ b = γ s /K to be used in (8). The noise power P N can be classified as, environmental noise (noise due to sources outside the receiver) P NE , interference noise (created from other users) P NI and receiver noise factor (due to noise generated by electronic components) P NR , i.e., P N = (P NE + P NI )P NR . The noise factor P NR (called as noise figure when expressed in dB) measures the degradation of the SNR caused by components in the receiver. The noise figure of an 802.11 receiver varies from 4 to 10 dB. Details about the interference noise is presented in Section VI. To conclude, the probability of VOLUME 8, 2020 transmission error P phy depends on modulation and encoding schemes, interference, environmental and receiver noise.

C. D/M/1/B QUEUE MODEL
For equation (2), the idle probability p 0 was taken as input in the previous studies, e.g., see [11]. Furthermore, an approximate analysis is presented to calculate the idle probability in [22] with the assumption of a small size buffer, Poisson arrival, heterogeneous traffic and empty inter-arrival queue. These assumptions are scenario specific, and hence, not suitable for the analysis of seismic data acquisition system. Hence, in this work, the idle probability is found by considering a D/M/1/B queue model to represent the buffer in each WG.
In D/M/1/B queueing model (state transition diagram is shown in Fig. 4), packets arrive at regular fixed intervals, however, leave the queue in a random fashion. Assuming that exactly one packet arrive in the queue after n th time step, i.e., nt, where one time step is equal to t sec. Furthermore, assume that the probability that a packet leaves the queue in one time step is p l , and hence, the probability that packet does not leave is p nl = 1 − p l . In Fig. 4, each column corresponds to the number of packets in queue, i.e., the j th column state probabilities s 0,j to s n−1,j shows the particular occupancy of the queue indicating there are j packets in the queue. The total number of columns J represents the size of queue and the number of rows n corresponds to number of time steps between packet arrivals. The last row is the state when packet arrives, while the leftmost and rightmost columns corresponds to the empty queue and full queue, respectively. This D/M/1/B queue model is inspired from [23], however, here it is extended to the general form by using the arbitrary number of queue size and time steps. Furthermore, in order to find the state probabilities, an iterative procedure is used in this work.
The state vector s can be written in the form of B sub-vectors as s = [s 0 , s 1 , . . . , s B ] T , where T is the transposition operator. The sub-vector s j (corresponds to j th column) is given by s j = [s 0,j , s 1,j , . . . , s n−1,j ] T . Corresponding to the state vector s, the 1-step transition matrix P has a dimension of n(B + 1) × n(B + 1). It is easy to write the transition matrix P in a composite matrix of dimension (B + 1) × (B + 1) as given in Appendix B.
From the transition matrix, the distribution vector s at the steady-state can be found from the following two equations Ps = s, where 1 is row vector of all 1s. The solution for the distribution vector s is found in an iterative fashion. For this purpose, the iterative equations can be written from (9) as follows.
The expressions (11)-(13) are solved iteratively as follows: Initially, assign value to each element in distribution vector s as 1 n(B+1) . Then, iterate through the equations (11)- (13) and stop when the distribution vector converges. The idle probability p 0 is given by and the average queue size Q can be found as Q = n−1 i=0 B j=1 js i,j . In order to find the inputs (t and p l ) to this queue model, the mean arrival rate λ (which is known from the acquisition rate), and the mean departure rate µ (which is equal to 1/E[T p ]) are needed. Using the arrival rate, the value of nt is calculated as nt = 1 λ . The queue leaving probability, p l , can be calculated from the departure distribution, which is a Poisson process, i.e., . Hence, probability that a packet does not leave the queue, p nl , is zero event in t sec, i.e., The value of n is found to be 25 in Section VII-A.

IV. THROUGHPUT AND TRANSMISSION TIME EXPRESSIONS
Using the models presented in Section III, throughput and transmission time expression are derived in this section. From the discussion in Section III, it can be seen that the probabilities τ , P col , and P fail are related by a three non-linear system of equations that resulted from steady state probabilities and given by (16)- (18), as shown at the bottom of the next page.
The above-mentioned probabilities are computed using the fsolve function of MATLAB.

A. THROUGHPUT
The solution of the equations (16), (17), and (18) enables us to compute the WG's throughput, which is defined as the fraction of time used to transmit payload bits over the channel and is given as (19), as shown at the bottom of the page, where σ s is the duration of time slot and E[L] is the average packet payload duration. P t is the probability that there is at least one transmission in the given time slot, while N WGs are contending and each transmit with probability τ , and is given by and P s is the conditional probability of success given at least one WG transmit, i.e., In (19), T c , T e , and T s are time duration the channel is sensed busy due to collision, transmission time of the error affected frame, and the successful frame transmission time, respectively. These times are given as, where H is the PHY and MAC headers duration, L is the packet payload duration (assuming all WG frames have same length, i.e., E[L] = L), τ p is the propagation delay, ACK timeout (CTS timeout ) is equal to SIFS + τ p + ACK (CTS), and DIFS (SIFS) is the waiting time of sender (receiver) before sending frame (acknowledgment). Here, transmission time of the error affected frame is calculated based on the assumption that CTS frame is much smaller than the data frame and transmitted at lowest rate (1.8 MHz using BPSK), hence its transmission error probability is very low. Note that, E[L], T c , T e , T s have same units for the normalized throughput. To get the throughput in bits/s, normalized throughput is multiplied by the data rate R. The throughput per WGN is NS.

B. TRANSMISSION TIME
The expected time taken to receive a packet successfully can be calculated from (19) and is given by (25), as shown at the botom of the next page. From (25), it can be seen that the time consists of three components. The first term represents the time spent to successfully transmit a packet T s . The second term represents the amount of time the channel is idle, and Moreover, the total time to transmit the whole data acquired in β sec with acknowledgments is given as: where λ is the offered load in frames/s.

V. ENERGY CONSUMPTION OF A WG
One of the greatest limitation of the seismic network is the finite energy resource. Hence, it is important to thoroughly investigate the energy consumption by a WG. This will help to predict the battery life and further design the acquisition system efficiently. The total energy consumption in order to observe the successful transmission of a packet, ξ T , can be written as where ξ s , ξ idle , ξ c , and ξ phy are energies utilized in transmitting the packet successfully, while being idle, when there are collisions and when packet transmission errors occur, respectively. These four terms correspond to the terms in (25) and, can be found by expanding T s , T c and T e and defining ρ tx , ρ rx and ρ idle as power consumption by WG for transmitting, receiving, and being idle, respectively. The energy spent in transmitting the packet successfully ξ s can be sub-divided into energy used for transmission (sending RTS and packet), reception (receiving CTS and acknowledgment) and being idle (during SIFS and propagation) and it is given as P fail = P col + P phy − P phy P col , S = P t P s (1 − P phy )E[L] (1 − P t )σ s + P t (1 − P s )T c + P t P s (1 − P phy )T s + P t P s P phy T e (19) VOLUME 8, 2020 The energy consumption due to collision ξ c can be divided into the energy spent in sending a packet and being idle when CTS times out and it is given as Similar to ξ s , the energy consumed while there is physical layer transmission error ξ phy consists of energy used in sending the RTS and data packets, receiving the CTS, and being idle (during SIFS, propagation and acknowledgment time out), i.e., Finally, the energy consumption when being idle ξ idle is It will be interesting to define the energy efficiency as fraction of energy used to successfully transmit a packet, i.e., For small number of WGs per WGN, the energy efficiency will be higher as less energy is consumed in collision and being idle.
The overall procedure of calculating required quantities is highlighted in flow chart (Fig. 5). This figure explains the procedure to calculate the throughput, transmission time, and energy consumption using MAC, PHY and D/M/1/B queueing model. The convergence is achieved when the mean square error between the values obtained from two successive iterations becomes equal to a predefined value, e.g., 10 −6 in this work.

VI. INTERFERENCE MODELING AND MITIGATION
In this section, interference noise is modeled and then cell sectoring is presented for interference reduction.

A. INTERFERENCE NOISE
Interference noise is the result of frequency reuse in the neighboring cells (a cell is coverage area of a WGN). Considering the cluster size, C, of 4 and radius of each cell as r, there are 6 immediate interference neighboring cells (indicated by arrows) at a distance of D = r √ 3C [24] as shown in Fig. 6a (far away interfering cells are not considered as their interfering signal is not significant). In CSMA, the probability of packet transmission by WG is τ . Therefore, the probability of having i interferers out of N WGs in a cell is Assuming that all the WGs transmit with the same power I t and I r i is the average received power (interference) from i th interferer in any cell from the neighboring 6 cells. Further, assume that the interference signal strength at any point decays as a power law of the distance separation between the transmitter and the receiver, i.e., I r i = I t 0 where I t 0 is the power received at a close-in reference point in the far field region of the antenna, i.e., at a small distance d o from the transmitting antenna. Here, d i is the average distance of i th interferer from the concern WG. Due to orthogonal geometry, the average d i is equal to D, and consequently, I r i = I r . Therefore, the average interference signal received from all the 6 neighboring cells can be written as A closer look at (34) reveals that the term in bracket is mean/expectation of a binomial random variable with parameter τ and 6N . Hence, (34) can be written in compact form as P NI = 6I r N τ .

B. CELL SECTORING
Cell sectoring can be used to increase the capacity (in terms of number of WGs per WGN) and the performance (in terms of throughput) by keeping the cell radius unchanged. Sectoring uses several directional antennas instead of the omidirectional antenna at the WGN, hence, reducing the interference. Each sector has its own collision domain. Hence, due to the directional antennas the collision domain within the cell is also reduced (WGs now contend within a sector instead of a cell), achieving better throughput performance. By using directional antennas, a given cell will receive interference from only fraction of the available interfering cells. This technique of reducing interference and collision domain by using directional antennas is referred to as sectoring. The reduction factor for interference and collision domain depends on the amount of sectoring used. A normal practice in cellular systems is to partition a cell into three 120 o or six 60 o sectors. When sectoring is employed, the channels used in a particular cell are broken down into sectored groups and are used only within a particular sector. Assuming a scenario of four-cell reuse (Fig. 6a), for the case of 120 o the number of interfering cells is reduced from six to two. This is because only two of (1 − P t )σ s + P t (1 − P s )T c + P t P s (1 − P phy )T s + P t P s P phy T e P t P s (1 − P phy ) the six co-channel cells receive interference with a particular sectored channel group. Similarly, for the case of 60 o the number of interfering cells is reduced from six to one as shown in Fig. 6b. Furthermore, the number of WGs per WGN causing interference will be reduced as well. Hence, for the 60 o sectoring case, P NI = I r N τ 6 . One of the drawback of the sectoring is increased number of handovers (switching from one to another cell/sector) in case of mobile network. However, thanks to our static environment that handover issue is not present.

VII. RESULTS AND DISCUSSION
In this section, the throughput and time for the transmission of data is investigated in wireless seismic acquisition system for various densities of geophones per WGN to cover the whole surveying field shown in Fig. 1a. The important questions here are: how many WGs can be served by one WGN and how many WGNs are required to serve the whole surveying area. To answer this question, various parameters are considered in the ensuing subsections.

A. PARAMETERS AND VALIDATION
The parameters used for our scenario are listed in Table 2 and 3. These adopted system parameters are based on the 802.11 standard [25]. The offered load is calculated as: the sampling frequency for the seismic acquisition systems is f s = 2 kHz with 24 bits/sample, hence the data acquisition rate comes out to be 48 kbits/s per component of a three component (3C) geophone [5]. For 802.11, the MAC frame  payload size is taken as 9000 bits/frame, therefore, the offered load is 16 frame/s. The recording phase duration is 14 s.
In D/M/1/B queue model, value of n is required. In order to find the suitable value of n, it is plotted against utilization for various values. Utilization is the ratio of the arrival rate to the departure rate, i.e., λ/µ. Figure 7a shows that for the higher values of n ( 25), the behavior of the D/M/1/B model is not changing. Hence, the value of n is taken as 25.
Next, the theoretical and simulation results are compared in Figs Figure 8a shows the mapping between the coverage radius of the WGN to the number of WGN required to cover the whole serving area and to the number of WGs served by a single WGN. It is direct to see that as the coverage range increases, the required number of the WGNs decreases.
Here, TV white spaces are considered for the transmission in order to have maximum possible coverage of WGN. The coverage range of 802.15.4 is 20 m, which is very small for our scenario. On the other hand, the recently proposed IEEE802.11af standard (that uses TV white spaces) has a maximum range of 1000 m. With 1 km of coverage range, the number of WGs per WGN are around 600 and 22 WGNs (Fig. 8a) are needed to serve the whole surveying area. This means that the maximum number of WGs supported by a WGN based on its coverage range is N r = 600 WG.

C. AGGREGATE THROUGHPUT
Next, the throughput per WGN is shown in Fig. 8b. From this figure, it is concluded that there is a saturation point after  a point where the decrease in throughput due to collisions overcomes the increase in throughput due to the increase in the number of WGs per WGN. This saturation point is very useful in the analysis and can be used to find the number of WGs that can be covered by a WGN so that the throughput is maximized. From this figure, it is concluded that the maximum value of throughput occurs at N TH = 312 WGs per WGN for two-ray channel model. It can be noted from Fig. 8b that the effect of path-loss model is not noticeable when WGs are close to WGN.

D. TRANSMISSION TIME OF DATA
The timing diagram [30] for seismic data acquisition process is shown in Fig. 9a. It shows that data is recorded for 14 s. The acquisition process is repeated after 16 s. Hence, the time required to transmit the data from WG to WGN is investigated for various number of WGs supported by WGN. Fig. 9b shows that number of WGs versus the transmission time to transfer the data from all WGs to the respective WGN. The total time to transmit the whole data acquired in 14s (total recording time) with acknowledgment by a WGN is given as: T = N * 14 * 16 * E[T p ] (from (26)). The useful information about the transmission time in the figure can be use to optimize the number of WGs in a coverage area of WGN. For example, a restriction on the time can be placed and calculate the number of WGs served by a WGN. The restriction is useful as the shooting and recording process for seismic acquisition is repeatedly done for days. For rest of the figures, one-slope channel model is used, unless otherwise stated.

E. MAC PAYLOAD SIZE
For the Figs. 8b and 9b, the MAC payload size was taken as 9000 bits. It will be interesting to see the effect of payload size on throughput. Figure 10a shows that as the MAC payload size increases, throughput increases for a fixed number of WGs. Therefore, the MAC maximum payload size of 18000 bits can be taken.

F. ENCODING
In all the previous results, NRZ encoding is used. It is interesting to see the effect of packet encoding schemes, as in (7), on throughput. Figure 10b shows that the NRZ encoding achieves the maximum throughput, since it does not have any redundant information. On the other hand, encoding method SECDED has the lowest throughput. The reason of less throughput of the encoding schemes as compared to NRZ is that they have redundant information for self clocking and/or bit error correction. Hence, throughput can be compromised for other advantages. The maximum number of WGs per WGN that give the maximum throughput is same for all the encoding schemes. Furthermore, for less number of WGs per WGN (<=100) the encoding performance is same.
G. MODULATION SCHEME 4-QAM modulation scheme with data rate of 3.6 Mbits/s is used for the throughput analysis in all the previous figures. In equation (8), probability of bit error is given for various modulation schemes. In reality, standards use adaptive modulation schemes, i.e., a modulation scheme is selected based on the channel condition. The setup is evaluated for various modulation schemes and data rates given in Table 3. Figure 10c depicts the throughput for various modulation and data rates. It shows that as the number of bits per symbol is increased by using the higher order modulation scheme, the maximum number of WG per WGN decreases. However, the throughput increases up to 4-QAM with data rate of 5.4 Mbits/s and then decreases for higher order QAM. The reason for this behavior is as follows: when more bits per symbol are transmitted, throughput per WGN increases. On the other hand with more bits per symbol bit error rate also increases, which decreases the throughput. The aim is to select the modulation scheme and data rate that gives maximum throughput and maximum number of WGs per WGN among all the modulation schemes. For this purpose, the product of maximum throughput per WGN over the range of 1 − 1000 m for a specific modulation scheme and data rate, S mod , and the corresponding value of WGs per WGN,  Fig. 10d. The values of S mod and N T are obtained from Fig. 10c. It is concluded from Fig. 10d that BPSK with data rate of 1.8 Mbits/s gives best results for one-slope and Egli channel models, whereas 4-QAM with 5.4 Mbits/s and 7.2 Mbits/s are best for two-ray and two-slope channel models, respectively.

H. SECTORING
Next, the performance is measured using sectoring. The 120 o and 60 o sectoring are used. It can be seen from Fig. 11a, that using sectoring increases the throughput (due to reduce collision domain and less interference) and, hence, more WGs per WGN can be accommodated. Similarly the time required to send the data is tremendously reduced as shown in Fig. 11b,where BPSK with data rate of 1.8 Mbits/s is used. Figure 11c depicts the energy efficiency per WGN, η ξ . It can be noted from the figure that sectoring increases the energy efficiency tremendously. Since there are less collisions and interference in case of sectoring, therefore, the efficiency improves as compared to the no sectoring case. For 60 o sectoring, energy efficiency is almost close to one. In order to achieve even better performance in terms of energy efficiency, WGs with in a sector can be grouped together and a master WG can be selected to transmit data to WGN [32].

J. OPTIMUM NUMBER OF WGs PER WGN
The analysis presented above is useful for designing seismic wireless acquisition networks. For instance, 384 WGs can be assigned to one WGN in case of one-slope channel model. The value is obtained when the upper bound on the time is set to 16 seconds (sweep plus listen plus move-up time), i.e., WGs must finish sending data to respective WGN before the next shot. The other parameters used in this case are 16-QAM modulation (10.8 Mbits/s), NRZ encoding, payload size of 18000 bits, and 60 o sectoring. These parameters are selected to get the maximum possible aggregated throughput. The results are shown in Figs. 12a and 12b.

VIII. CONCLUSION
In this work, a wireless seismic acquisition network is examined and investigated using Markov chain models. In particular, the MAC and PHY layer protocols are discussed for the transmission between WGs and WGN, and throughput, transmission time and energy consumption are analyzed. The proposed model incorporates the proper path-loss channel models, encoding and modulation schemes, and packet payload size. The buffer in a WG is modeled using D/M/1/B queue. It is shown that these results are useful for designing such wireless seismic acquisition networks, in particular, to find the optimal number of WGs served by a WGN, and the total number of WGNs to serve the whole surveying area. In order to have a minimum number of WGNs, the IEEE 802.11af standard is considered which have a maximum range of 1 km. Finally, sectoring is also introduced for maximizing the number of WGs per WGN and hence, minimizing the total number of WGNs needed. It is worth to mention here that the energy constraint, the timing constraint and the quick quality check (QC) required in wireless seismic acquisition are some of the issues in wireless acquisition that are open to research. Wires are also responsible for providing power to the geophones, hence an efficient energy system (possibly using energy harvesting technology) is needed for self-sustainable wireless geophone.

APPENDIX A STEADY STATE PROBABILITIES AND τ
In this appendix, some results are repeated from [18] for the sake of self-containedness and clarity.
In order to get the closed form solution for the Markov chain, all the steady state probabilities are expressed as a function of b 0,0 and then the normalization condition is used, i.e., sum of all the state probabilities is equal to one, to find b 0,0 . From Fig. 3, it can be noted that Owing to the Markov chain regularities, for 1 ≤ k ≤ w i −1, we have The normalization condition, i.e., m i=0 W i −1 k=0 b i,k + b idle = 1, yields the equation for computation of b 0,0 as (40), shown at the top of the next page. By taking into the fact that transmission starts when backoff counter reaches zero, τ is given (41), as shown at the top of the next page.