Collaborative spectrum sensing for cognitive visible light communications

Zile Jiang; Zile Jiang; Xiaodi You; Chaoran Xiong; Gangxiang Shen; Biswanath Mukherjee

doi:10.1364/OE.427776

1. Introduction

Because of the ubiquity of light emitting diode (LED) lights, visible light communication (VLC) is emerging as a promising supplement to radio frequency communication (RFC) in upcoming 5G era [1,2]. This enables the integration of VLC and RFC systems to form a heterogeneous wireless access network [2–4]. In such an integrated architecture, VLC offers high-speed local transmission, while RFC provides wide coverage and stable connectivity.

For indoor VLC systems, although the visible light spectrum is ample, the available bandwidth of off-the-shelf LEDs is narrow (usually a few of tens of MHz) [5]. This limits the VLC system to carry out high-speed communication. Moreover, when the VLC system serves multiple users simultaneously, multiple access interference (MAI) becomes a major issue. To eliminate MAI, efficient resource allocation and scheduling schemes are required to share the limited VLC resources among multiple users. Extensive studies have been conducted in this direction. Some approaches focused on efficient transmission techniques. In [6], a precoding multi-user multiple input and multiple output (MIMO) system was proposed for indoor VLC to eliminate MAI by pre-processing user data at the transmitter. Orthogonal frequency division multiple (OFDM) with subcarrier reuse and power reallocation was employed for indoor VLC to improve the average bit rate [7]. There were also approaches focusing on improving the resource utilization by allowing resource sharing in the time domain [8].

Motivated by the concept of cognitive radio (CR) in the conventional RFC systems [9,10], cognitive VLC has been recently proposed to avoid VLC spectrum wastage [11]. The cognitive VLC system classifies users into primary (licensed) users (PUs) and secondary (unlicensed) users (SUs), where PUs have higher priorities of using the VLC system. To improve spectrum resource utilization, the cognitive VLC system allows SUs to share the spectrum with PUs in an opportunistic way. That is, when a PU is absent, SUs can use the spectrum resources allocated to the PU. However, when the PU returns, the SUs need to release the occupied spectrum resources immediately such that the PU can use them without degrading its quality-of-service (QoS). In [11], a cognitive VLC system was designed based on the prior knowledge of user locations. In [12], a cognitive multi-cell VLC system was developed to maximize the sum rate of SUs by allowing hybrid underlay or overlay resource allocation. However, all these schemes have ignored the information of PUs, i.e., whether they are absent or present. This therefore loses the opportunity of further improving spectrum resource utilization by allowing SUs to share the spectrum resources of PUs.

For the cognitive VLC, spectrum sensing is key to detect the presence of a PU and avoid interference from SUs. Although different spectrum sensing approaches have been proposed for cognitive RFC [9,13,14], to the best of our knowledge, there have been no related works specifically dedicated to the aspect of spectrum sensing in cognitive VLC. Because VLC systems have a different spectrum and usually employ intensity modulation and direct detection (IM/DD), their channels are different from RFC channels. Therefore, conventional sensing approaches for RFC channels cannot be directly reused or at least need to be modified for the cognitive VLC. Thus, new approaches are required for spectrum sensing in a cognitive VLC system.

In this paper, we propose a new scheme called collaborative sensing (CS) [13,15], in which multiple SUs collaboratively sense the visible light spectrum under the coordination of a central coordinator, which can be elected from the SUs or a dedicated equipment. The central coordinator first collects sensing information obtained by all the SUs that participate in CS. Then, based on the information received, it decides on whether PUs are present. Because SUs are scattered in different corners, they can provide richer sensing information than a single SU. Therefore, we expect such a collaborative scheme can effectively improve sensing performance. For performance evaluation, we first develop an analytical model for a scenario containing a single SU, subject to various system constraints such as indoor reflections and signal sampling size. Based on this analysis, we further consider a scenario with multiple SUs by extending the single-SU analytical model. By considering the central coordinator as a virtual user, and based on the sensing information that it collects, we reuse the previous single-SU model to analyze the performance in the multi-SU situation. To achieve optimal sensing performance, different weight coefficients are assigned for the information received from different SUs when the central coordinator aggregates the sensing information and makes decisions. Extensive simulations are conducted to evaluate the performance of the proposed CS scheme in comparison with local-sensing and conventional CS schemes. Results show that the proposed CS scheme is very efficient and can outperform the local-sensing and the conventional CS schemes significantly. Specifically, in a four-SU system, the proposed CS scheme can achieve a 100% detection probability (i.e., probability of successfully sensing the presence of PUs), while local-sensing and the conventional CS schemes can only achieve detection probabilities of 60% and 90%, respectively.

The rest of this paper is organized as follow. Section 2 analyzes the performance of spectrum sensing for the single-SU scenario. In Section 3, we introduce the proposed CS scheme, considering multiple SUs. Its performance is also analyzed by extending the analytical models of the single-SU scenario. Simulations and performance analyses are conducted in Section 4. We conclude the paper in Section 5.

2. Local spectrum sensing

2.1 Working principle

We first consider local (spectrum) sensing [13,14] in a cognitive VLC system, where there is only one SU and one PU. Figure 1 shows the functional diagram of this cognitive VLC system, which is divided into two parts: a VLC transmitter and a SU’s receiver. At the VLC transmitter, each random bit information transmitted from the transmitter to the PU is mapped to a bipolar on-off-keying (OOK) signal A_i, which follows a Rademacher distribution, namely Pr(A_i= 1) = Pr(A_i = −1) = 0.5 [16]. With a DC-bias, this signal is normalized to:

(1)$$s(t) = 1 + {M_{index}}{A_i}\quad t \in [{t_i},{t_{i + 1}}),$$

where M_index is modulation index, t_i is start time of A_i, and t_i₊₁ is end time of A_i. The symbol period T can be calculated as T = t_i₊₁ − t_i.

Fig. 1. Functional diagram of local sensing.

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Based on the configuration in Fig. 1, if we consider only the line-of-sight (LOS) channel, the channel impulse response (CIR) between the LED and the SU can be given by [17]:

(2)$$h(t) = H(0)\delta (t - {\tau _{LOS}}),$$

where H(0) is channel DC gain, τ_LOS is time delay of the LOS channel, and δ(t) is Dirac function. Then, after the transmitted signal is received by the SU’s photo-detector, the detected electrical signal is given by:

(3)$$r(t) = \gamma {P_t}h(t) \otimes s(t) + n(t),$$

where γ is receiver responsivity, P_t is LED launch power, and n(t) is additive white Gaussian noise. Here, the noise variance is given by:

(4)$${\sigma ^2} = \sigma _{shot,{\kern 1pt} {\kern 1pt} LED}^2 + \sigma _{shot,{\kern 1pt} {\kern 1pt} background}^2 + \sigma _{thermal}^2,$$

where σ²_{shot, LED}, σ²_{shot, background}, and σ²_thermal represent shot noise caused by LED light, shot noise caused by background light, and thermal noise of the photo-detector, respectively [17].

The electrical signal-to-noise ratio (SNR) of the output signal can be further derived as:

(5)$$SNR = {{{{(\gamma H(0){P_t}{M_{index}})}^2}} / {{\sigma ^2}}} \buildrel \Delta \over = {{{a^2}} / {{\sigma ^2}}}.$$

Here, a denotes signal amplitude (a ≥ 0). After the DC component is removed by the filter, the received signal can be expressed as:

(6)$$\tilde{r}(t) = {A_i} \cdot a(t) + n(t),{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} t \in [{t_i},{t_{i + 1}}).$$

Here, a(t) = a when the PU is present, and a(t) = 0, otherwise.

In the sampling unit, $\tilde{r}(t)$ is sampled to generate a total of N discrete data samples, represented as y_i (i = 1, 2, …, N). Based on these samples, we conduct spectrum sensing using a commonly-used detection mode, called energy detection [14,18]. Energy detection detects the PU’s presence based on the intensity of the received signal, with no need for the SU to obtain any prior knowledge. To implement energy detection, we create a detection metric M_E based on the sampled signals, which can be represented as:

(7)$${M_E} = \sum\limits_{i = 1}^N {y_i^2} .$$

To conduct spectrum sensing, we compare this detection metric with a decision threshold K_E to judge whether the PU is present. The probability that the PU is correctly detected, i.e., detection probability, is denoted as P_D, and the probability that the PU is falsely detected, i.e., false alarm probability, is denoted as P_F [13]. For energy detection, they are represented as:

(8)$${P_{D,\;E}} = \Pr ({M_E} > {K_E}|{{\cal H}_1});{P_{F,\;E}} = \Pr ({M_E} > {K_E}|{{\cal H}_0}).$$

Here, $\cal{H}$₁ represents the event that the PU is present, while $\cal{H}$₀ represents the event that the PU is absent.

Based on Eqs. (6), (7), and (8), the detection probability and false alarm probability of energy detection under decision threshold K_E can be further derived as:

(9)$${P_{D,{\kern 1pt} {\kern 1pt} E}} = 1 - G({{{K_E}} / {{\sigma ^2}}};N,{{{a^2}N} / {{\sigma ^2}}});{P_{F,{\kern 1pt} {\kern 1pt} E}} = 1 - F({{{K_E}} / {{\sigma ^2}}};N),$$

where F (x, k) and G (x; k, λ) are the cumulative distribution functions of central and non-central chi-square distributions, respectively [19].

According to Eq. (9), it is clear that the spectrum sensing performance largely depends on the setting of the decision threshold K_E. To determine an appropriate threshold, we adopt Neyman-Pearson (NP) criterion which is widely used in binary hypothesis tests due to its low complexity and little requirement for a prior knowledge [20]. In the NP criterion, the false alarm probability needs to be fixed to achieve acceptable spectrum sensing performance [14]. Thus, for the single-SU sensing scenario, we set P_{F, E} to be 0.1, which is a common practice in binary hypothesis tests [20]. Consequently, based on Eq. (9), the decision threshold for energy detection can be derived as:

(10)$${K_E} = {\sigma ^2}{F^{ - 1}}(1 - {P_{F,{\kern 1pt} {\kern 1pt} E}};N) = {\sigma ^2}{F^{ - 1}}(0.9;N).$$

2.2 Influence from indoor reflections

In a practical VLC system, there usually exist signal indoor reflections. However, the CIR in Eq. (2) does not consider the non-LOS (NLOS) channel caused by indoor reflections, and this therefore could lead to errors on the probabilities in Eq. (9). In this part, we evaluate the influence from indoor reflections on the local sensing performance.

After considering indoor reflections, Eq. (2) should be rewritten as [21]:

(11)$$h(t) = {h_{LOS}}(t) + {h_{NLOS}}(t){\kern 1pt} {\kern 1pt} {\kern 1pt} = H(0)\delta (t - {\tau _{LOS}}) + \int_{{\tau _{NLOS}} = 0}^\infty {{A_{NLOS}}} ({\tau _{NLOS}})\delta (t - d{\tau _{NLOS}}),$$

where A_NLOS (τ_NLOS) is the channel gain of the NLOS link with specific time delay τ_NLOS. Accordingly, in the sampling unit in Fig. 1, the received NLOS signal due to indoor reflections is also sampled, denoted as z_i (i = 1, 2, …, N). Now, we consider the following two cases.

When the LED is vacant (i.e., $\cal{H}$₀), indoor reflections do not impact the system performance since received NLOS signal only consists of DC components, which can be removed at the filter.

When the LED is occupied (i.e., $\cal{H}$₁), for a qualitative analysis on the influence from reflections, we assume that z_i is independent of y_i and follows a normal distribution (i.e., z_i ∼ ${\cal N}$ (0, ω²)). Such an assumption is common and a similar assumption was also made in [17]. Moreover, it is also common in many mathematical derivations or models to consider a zero-mean random variable with unknown properties to follow normal distribution. Thus, the expectation value of the decision metric M_E with indoor reflections is derived as:

(12)$$\mathbb{E}[{M_{E,{\kern 1pt} {\kern 1pt} w/\;ref}}] = \mathbb{E}[\sum\limits_{i = 1}^N {{{({y_i} + {z_i})}^2}} ] = \mathbb{E}[\sum\limits_{i = 1}^N {y_i^2]} + N{\omega ^2} = \mathbb{E}[{M_{E,{\kern 1pt} {\kern 1pt} w/o\;ref}}] + N{\omega ^2}{\kern 1pt} .$$

Here, we see that the expectation value $\mathbb{E}[{M_{E,{\kern 1pt} {\kern 1pt} w/\;ref}}]$ with reflections is always larger than the expectation value $\mathbb{E}[{M_{E,{\kern 1pt} {\kern 1pt} w/o\;ref}}]$ without reflections. This means that when the LED is occupied, indoor reflections can improve the detection probability, because according to Eq. (8), a larger expectation value of the decision metric means a higher detection probability.

Therefore, indoor reflections can enhance the spectrum sensing performance with the single-SU energy detection. This conclusion is quite different from that in a visible light communication [22] or positioning [23] system, in which indoor reflections usually degrade system performance.

When the NLOS signal is considered, the decision threshold for energy detection is still derived based on Eq. (10), wherein noise variance σ² should include contributions from NLOS components.

2.3 Influence from signal sampling size

When carrying out spectrum sensing in a cognitive VLC system, we also want to minimize the time spent on sensing. Thus, the number N of data samples y_i (i = 1, 2, …, N) used for sensing is a crucial parameter. In this part, we evaluate the influence of signal sampling size N on sensing performance. Specifically, we focus on the relationship between the detection probability P_{D, E} and the sampling size N for energy detection.

Given a fixed false alarm probability P_{F, E}, based on Eq. (10) and Lindeberg–Lévy central limit theorem [16], we can obtain the following expression:

(13)$${{{K_E}} / {{\sigma ^2}}} \approx \sqrt {2N} {C_0} + N,$$

where C₀= Φ⁻¹(1 − P_{F, E}) and Φ(x) denotes the cumulative distribution function of the standard normal distribution. To get a concise mathematical form, we also apply “first approximation” for the non-central chi-square distribution, as follows [24]:

(14)$$G(x;k,\lambda ) \approx \Phi \left( {\left[ {{{({{x / {(k + \lambda )}}} )}^{\frac{1}{3}}} - 1 + {{\textrm{2(}k + 2\lambda \textrm{)}} / {9{{(k + \lambda )}^2}}}} \right] \cdot \sqrt {{{9{{(k + \lambda )}^2}} / {2(k + 2\lambda )}}} } \right).$$

Then, by substituting Eqs. (13) and (14) into Eq. (9), we can obtain the relationship between the detection probability, sampling size N, and SNR, which is expressed as:

(15)$${P_{D,{\kern 1pt} {\kern 1pt} E}} \approx 1 - \Phi \left( {{C_0} - {{SNR\sqrt N } / {\sqrt {2(1 + 2SNR)} }}} \right).$$

According to Eq. (15), for a given SNR, the detection probability is a strictly monotone increasing function of the signal sampling size. However, when SNR is very low, to achieve a desired P_{D, E}, the order of magnitude for the signal sampling size should be O(SNR⁻²), which means a long sensing time and which needs to be avoided.

3. Collaborative spectrum sensing

The spectrum sensing scenario in Sections 2 considers a single SU. In practical VLC environments, there could be multiple SUs, among which some could be located at regions with low SNR. These low-SNR SUs receive very weak signals, and therefore their accuracy of detecting the PU can be very low. To enhance the spectrum sensing accuracy, the SU can extend its sensing time, but this leads to extra time delay. Also, there can be situations where the links between the LED and the SUs are partially blocked, which makes the SUs fail to detect the presence of the PU. Under these situations, if the SUs improperly activate their data transmission, their signals will interfere with the PU’s communication. To tackle these issues, collaborative (spectrum) sensing (CS) [13,15] has been proposed as an effective solution. In CS, multiple SUs cooperate to detect the PU’s signal, thereby achieving better sensing performance, especially for the situations of low SNR.

In the conventional cognitive RFC network, CS is often conducted based on certain rules, including OR-rule, AND-rule, and Voting-rule [25]. Specifically, each SU first conducts local sensing independently. Then, they forward their sensing decisions to a fusion center to make a final judgement based on the aforementioned rules. However, when some SUs are located in regions with low SNR, their decisions based on local sensing will still be affected, leading to poor detection accuracy which further impacts the accuracy of the final judgement by the fusion center. To overcome this issue in conventional CS schemes, in this section, we propose a new CS scheme specifically for cognitive VLC.

3.1 Working principle

Figure 2(a) illustrates the proposed CS scheme for detecting the PU’s signal in the cognitive VLC system. The system is assumed to be a hybrid RFC/VLC network, in which VLC functions to transmit downstream data due to its high transmission capacity and RFC complements when VLC links are absent. There is one LED on the ceiling, with one PU and multiple SUs randomly distributed in the room. To enable CS, all the SUs first need to elect one SU to be a central coordinator, i.e., central SU (CSU), using their RFC network. Alternatively, a dedicated CSU (e.g., a fusion center in conventional CS schemes for the RFC network) can be set up to collect sensing information from all SUs. All SUs then periodically, or upon request, forward their sensing information (i.e., data samples y_i) to the CSU, and the latter combines all the information to judge whether the PU is present or not, which realizes collaborative sensing. The judgement will be then broadcasted to all the SUs that participate in CS. Note that the above describes a simple process or protocol for sensing information sharing among multiple SUs. There can be more sophisticated protocols or mechanisms to enhance the efficiency of sensing information sharing, which is out of the scope of this study, and an open problem for future research. Next, we analyze how the CSU calculates the decision metric based on the collected sensing information.

Fig. 2. (a) Schematic diagram of proposed CS scheme. (b) Functional diagram of CS at the receiver side.

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Figure 2(b) shows the functional diagram of the proposed CS scheme at the receiver side, which is divided into two parts: SUs’ receivers and a CSU’s receiver. We consider that a total of U SUs have the same signal sampling size and rate, and they can sample the received signal emitted from the LED to the PU synchronously using a time synchronization strategy at a sub-nanosecond level [26]. For the jth SU, the ith data sample at the output of the sampling unit is represented as:

(16)$$\;{y_{j,{\kern 1pt} {\kern 1pt} i}} = {\tilde{A}_i}{a_j} + \;{n_{j,{\kern 1pt} {\kern 1pt} i}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \;j = 1,2, \cdots ,U,\quad i = 1,2, \cdots ,N.$$

Here, Ã_i = ± 1 is normalized OOK signal received, a_j = γH_j(0)P_tM_index in which H_j(0) is channel DC gain between the LED and the jth SU, and n_j,i follows a normal distribution (i.e., n_j,i ∼ ${\cal N}$ (0, σ²)). According to Eq. (4), because the magnitude of σ²_{shot, LED} is much smaller than that of the constant terms σ²_{shot, background} and σ²_thermal [17], here we ignore σ²_{shot, LED} and treat the noise variance of n_j,i as a constant σ². This helps to simplify both theoretical analyses and practical implementations for the CS scheme.

Next, instead of forwarding sensing decisions as in the conventional CS schemes of cognitive RFC, SUs forward their data samples y_j,i to the CSU. Based on these samples, the CSU creates a virtual user (VU) whose data samples are the weighted sum of all the data samples from U SUs, denoted as:

(17)$$\;{y_{0,{\kern 1pt} {\kern 1pt} i}} = \sum\limits_{j = 1}^U {\;{w_j}{y_{j,{\kern 1pt} {\kern 1pt} i}}} = \sum\limits_{j = 1}^U {\;{w_j}({{\tilde{A}}_i}{a_j}} + {n_{j,{\kern 1pt} {\kern 1pt} i}}), \;\;\;{\kern 1pt} i = 1,2, \cdots ,N.$$

Here, w_j is normalized weight coefficient of the jth SU. There can be different methods to set the weight coefficients. A simple way is to use the same weight coefficients for all the SUs (i.e., w_j = 1 / U, j = 1, 2, …, U). However, this is not optimal and can only achieve a limited performance improvement. To enhance the sensing accuracy, we need to find the optimal weight coefficients that can maximize the SNR of the VU. Thus, the optimization of the weight coefficients w_j can be formulated as the following optimization problem:

(18)$$\textrm{maximize }SN{R_{VU}} = \;{\left( {\sum\limits_{j = 1}^U {{w_j}} {a_j}} \right)^2}{\left( {\sum\limits_{j = 1}^U {w_j^2{\sigma^2}} } \right)^{ - 1}},\;s.\;t.\;\;\sum\limits_{j = 1}^U {{w_j}} = 1.$$

According to Cauchy–Schwarz inequality [19], we can obtain the following relationship:

(19)$${\left( {\sum\limits_{j = 1}^U {{w_j}} {a_j}} \right)^2}{\left( {\sum\limits_{j = 1}^U {w_j^2{\sigma^2}} } \right)^{ - 1}} \le \mathop \sum \limits_{j = 1}^U {{a_j^2{\kern 1pt} } / {{\sigma ^2}}},$$

where “=” holds if and only if a₁ / w₁ = a₂ / w₂ = … = a_U / w_U. Therefore, the optimal weight coefficients can be uniquely determined as:

(20)$${w_j} = {{{a_j}} / {\sum\limits_{j = 1}^U {{a_j}} }},\;\;\;{\kern 1pt} j = 1,2, \cdots ,U,$$

where the optimal weight coefficient w_j depends on the value of a_j which can be estimated in advance by means of channel estimation.

According to Eqs. (1) and (3), the detected electrical signal received by the jth SU’s photo-detector can be written by:

(21)$${r_j}(t) = {{{a_j}} / {{M_{index}}}} + {a_j} \cdot \tilde{s}(t) + n(t),\;\;\;{\kern 1pt} j = 1,2, \cdots ,U,$$

where a_j / M_index is DC component, and ${\tilde{s}(t)}$ is the normalized waveform of s(t) denoted by ${\tilde{s}(t)}$ = [s(t) − 1] / M_index. Since M_index is a fixed parameter, a_j can be estimated from DC component without resorting to channel estimation. Because VLC systems usually employ IM/DD, a VLC channel has simple and stable characteristics. As long as the locations of SUs are fixed, the optimal weight coefficients are theoretically determinate and remain unchanged, which is different from a time-varying RFC channel.

After combining the SUs’ data samples with the optimal weight coefficients, the CSU implements the local-sensing scheme for the VU. With energy detection, the decision metric for the VU is calculated as:

(22)$${M_{CS}} = \sum\limits_{i = 1}^N {y_{0,{\kern 1pt} {\kern 1pt} i{\kern 1pt} }^2} .$$

Accordingly, based on Eq. (10), the decision threshold for the VU is derived as:

(23)$${K_{CS}} = \sum\limits_{j = 1}^U {w_j^2{\sigma ^2}{F^{ - 1}}(1 - {P_{F,{\kern 1pt} {\kern 1pt} CS}};N)} = \sum\limits_{j = 1}^U {w_j^2{\sigma ^2}{F^{ - 1}}(\textrm{0}\textrm{.9};N)} .$$

Finally, by comparing the decision metric M_CS with the threshold K_CS, the CSU can make a judgment and feed the decision back to all the SUs.

In Eqs. (17), (20) and (22), there are only linear computations, which means that the proposed CS scheme is computationally efficient. In Eq. (23), F⁻¹(0.9; N) is a non-linear term, which depends on signal sampling size N. Considering a range of discrete values of N, the CSU can establish a look-up table to store different values of F⁻¹(0.9; N) in advance. When calculating K_CS, the CSU just needs to look up the table according to N and this will not increase overall computational complexity. Moreover, there is no limitation on the number of SUs in the cognitive VLC system. As a special case, if there is only a single SU, the CS scheme can still work and is simplified to local sensing.

In the proposed CS scheme, we assume that SUs send their signals to the CSU via an ideal RFC network. Because VLC and RFC adopt different frequency bands, they do not interfere with each other. When using a RFC channel to transmit sensing information, non-ideal transmission conditions such as channel noise and quantization noise can affect the signal transmission quality, which is similar to the influence of NLOS components and is expected to increase the expectation value of decision metric M_CS.

3.2 Enhancement on detection probability

According to Eq. (19), when using the optimal weight coefficients, the VU’s SNR is the sum of SNRs from all the SUs. Because of this aggregated SNR, the sensing accuracy of the VU is significantly improved. Based on Eq. (15), the detection probability of the VU can be approximated as:

(24)$$\;{P_{D,{\kern 1pt} {\kern 1pt} CS}} \approx 1 - \Phi \left( {{C_{CS}} - {{SN{R_{VU}}\sqrt N } / {\sqrt {2(1 + 2SN{R_{VU}})} }}} \right),$$

where C_CS = Φ⁻¹(0.9) to ensure a fixed false alarm probability at 0.1 as in Eq. (15).

To evaluate the performance benefit of the proposed CS scheme in comparison with the conventional CS schemes based on OR-rule, AND-rule, and Voting-rule [25], we define the enhancement on detection probability as the difference between the detection probability of the proposed CS scheme and that of each conventional scheme, denoted by ΔP_D. We consider the scenario that a total of U SUs with similar low SNRs participate in CS, in which SNR_VU ≈ U·SNR. Compared with conventional CS scheme under OR-rule [25], based on Eq. (24), the theoretical enhancement on detection probability achieved by the proposed CS scheme can be derived as:

(25)$$\Delta {P_{D,{\kern 1pt} {\kern 1pt} OR}} = {P_{D,{\kern 1pt} {\kern 1pt} CS}} - {P_{D,{\kern 1pt} {\kern 1pt} OR}} \approx {\left[ {\Phi \left( {{C_{OR}} - SNR\sqrt {{N / 2}} } \right)} \right]^U} - \Phi \left( {{C_{CS}} - U \cdot SNR\sqrt {{N / 2}} } \right),$$

where C_OR = Φ⁻¹(0.9^1/U) to ensure a fixed false alarm probability at 0.1 for OR-rule [25].

Also, compared with conventional CS scheme under AND-rule [25], the theoretical enhancement on detection probability achieved by the proposed CS scheme can be derived as:

(26)$$\Delta {P_{D,{\kern 1pt} {\kern 1pt} AND}} = {P_{D,{\kern 1pt} {\kern 1pt} CS}} - {P_{D,{\kern 1pt} {\kern 1pt} AND}} \approx \textrm{1} - {\left[ {1 - \Phi \left( {{C_{AND}} - SNR\sqrt {{N / 2}} } \right)} \right]^U} - \Phi \left( {{C_{CS}} - U \cdot SNR\sqrt {{N / 2}} } \right),$$

where C_AND = Φ⁻¹(1−0.1^1/U) to ensure a fixed false alarm probability at 0.1 for AND-rule [25].

Finally, compared with conventional CS scheme under Voting-rule [25], the theoretical enhancement on detection probability achieved by the proposed CS scheme can be derived as:

(27)$$\begin{array}{l} \Delta {P_{D,{\kern 1pt} {\kern 1pt} Voting}} = {P_{D,{\kern 1pt} {\kern 1pt} CS}} - {P_{D,{\kern 1pt} {\kern 1pt} Voting}} \approx \\ 1 - \left[ {\sum\limits_{i = k}^U {\sum\limits_{\sum {{u_j}} = i} {\Phi {{\left( {{C_{Voting}} - SNR\sqrt {{N / 2}} } \right)}^{1 - {u_j}}}} } {{\left( {1 - \Phi \left( {{C_{Voting}} - SNR\sqrt {{N / 2}} } \right)} \right)}^{{u_j}}}} \right]\\ \ - \Phi \left( {{C_{CS}} - U \cdot SNR\sqrt {{N / 2}} } \right), \end{array}$$

where u_j is either 0 or 1, u_j = 0 represents that the jth SU does not detect PU’s signal, u_j = 1 represents that the jth SU has detected PU’s signal, k represents that the final decision is $\cal{H}$₁ if at least k SUs decide so, and C_Voting is solved from $\left[ {\sum\limits_{i = k}^U {\sum\limits_{\sum {{u_j}} = i} {\Phi {{({{C_{Voting}}} )}^{1 - {u_j}}}} } {{({1 - \Phi ({{C_{Voting}}} )} )}^{{u_j}}}} \right] = 0.1$ to ensure a fixed false alarm probability at 0.1 for Voting-rule [25].

In Section 4.2, without loss of generality, we will consider a typical scenario of four SUs (U = 4) and show that ΔP_D in Eqs. (25), (26), and (27) are always positive, which means the CS scheme can always outperform the conventional schemes under the aforementioned scenario. For other values of U (U ≥ 2), this conclusion also holds.

3.3 Influence from propagation delays

As discussed above, the proposed CS scheme assumes that the data samples from SUs are synchronized. In practice, there exists a signal propagation delay from the LED transmitter to each SU’s receiver. Since SUs may have different transmission distances from the transmitter, different SUs will have different propagation delays, which could lead to asynchronized data samples from SUs and further affect the sensing performance.

To evaluate this influence, we consider a scenario containing a total of U SUs with similar SNRs (i.e., a₁ ≈ a₂ ≈ … ≈ a_U ≈ a) and evaluate the spectrum sensing performance taking into account the propagation delays. Figure 3 shows the normalized bipolar OOK waveforms received by the first SU and the jth SU, respectively. Here, due to the propagation delays, the sampled data are asynchronized and tend to cancel each other. As a result, the expectation of the decision metric M_CS for the VU can be affected. For analyses, we set the time delay τ₁ of the first SU as a reference point and denote the time delay of the jth SU as τ_j (j = 1, 2, …, U). Thus, for the jth SU, the relative time delay with the first SU as a reference is τ′_j = τ_j − τ₁ (τ′₁ = 0). Here, we assume that τ′_j follows a uniform distribution between 0 and τ_max.

Fig. 3. Scenario of asynchronized data samples caused by propagation delays.

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Based on Eq. (22) and considering all the SUs, the relationship between the expectation of the decision metric M_CS and the upper bound τ_max of the relative time delay can be derived as:

(28)$$\mathbb{E}[{M_{CS}}]\left\{ {\begin{array}{{l}} {\textrm{ = }N\{ {a^2}[{U^2}(1 - \frac{{{\tau_{max}}}}{{2T}}) + \frac{{{\tau_{max}}}}{{2T}}\sum\limits_{j = 0}^{U - 1} {C_{U - 1}^j} {{(U - 2j)}^2}B(j + 1,U - j)] + U{\sigma^2}\} \quad {\tau_{max}} \le T,}\\ { \approx N\{ {a^2}[\frac{1}{2}{U^2} + \frac{{{\tau_{max}}}}{{2T}}\sum\limits_{j = 0}^{U - 1} {C_{U - 1}^j} {{(U - 2j)}^2}B(\frac{T}{{{\tau_{max}}}};j + 1,U - j)] + U{\sigma^2}\} \quad T < {\tau_{max}} \le 2T,} \end{array}} \right.$$

where B(a, b) and B(x; a, b) are complete and incomplete beta functions, respectively [19]. The derivation of Eq. (28) in detail can be found in Appendix A.

4. Simulation results and discussions

We evaluate the performance of the proposed spectrum sensing schemes in the context of indoor cognitive VLC systems. The following simulation conditions are assumed. There is only one LED transmitter, one PU, and multiple SUs which collaboratively sense whether the spectrum resource is being used by the PU. Figure 4(a) shows the simulated indoor VLC system and the location of the LED which is assumed to have a Lambertian radiation pattern [17]. Figures 4(b) and 4(c) show the locations of four SUs when conducting CS. The main parameters of the indoor VLC system are listed in Table 1. Other parameters are the same as those in [21]. For each test point, we conduct Monte-Carlo simulations 5000 times to calculate the detection probabilities, wherein the 1st indoor reflections are considered.

Fig. 4. (a) Simulated indoor VLC system. (b) Locations of the four SUs which are uniformly distributed at the corners. (c) Locations of the four SUs which are non-uniformly distributed at the corners.

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Table 1. Key parameters of VLC system.

View Table

4.1 Spectrum sensing by a single SU

Now, we evaluate the performance of local spectrum sensing in the cognitive VLC system. Considering that the SU is located on the diagonal line of the receiving plane in Fig. 4(a), Fig. 5(a) shows the analytical and simulated results of the probability that the PU is successfully detected (i.e., detection probability P_D). Note that for the case that ignores indoor reflections, the simulation results can accurately match the analytical results, thereby verifying the effectiveness of the analytical model. When indoor reflections are considered, NLOS components can enhance the performance of local sensing compared with the case ignoring indoor reflections. Specifically, when false alarm probability P_F= 0.1, indoor reflections can increase the detection probability by up to 0.09 when the SU is at a corner. However, when the SU is close to the center, the improvement becomes trivial. This is because, at a corner, there are stronger indoor reflections, enhancing NLOS components in the total channel response, compared with the central location. These results verify the theoretical conclusion that indoor reflections can enhance spectrum sensing performance for cognitive VLC in Section 2.2.

Fig. 5. (a) Comparison of analytical P_D and simulated P_D on the diagonal line. (b) Distribution of simulated P_D on the receiving plane. (signal sampling size N = 100, P_F = 0.1)

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We also evaluate the detection probability when the SU is located on the entire receiving plane, as shown in Fig. 5(b). We see that, when the SU is at the side or corner locations, the detection probabilities are quite low compared with central locations. This is because, at these locations, the SU’s SNR is low, leading to poor sensing accuracy. Specifically, we estimate the percentage of the area whose detection probability P_D reaches a certain threshold. It is found that around 59.3%, 55.2%, 50.3%, 45.1%, and 39.4% of indoor areas can reach a P_D of 0.5, 0.6, 0.7, 0.8, and 0.9, respectively, indicating that local sensing is incapable of achieving satisfactory sensing performance under different coverage requirements.

The NLOS signal can increase the false alarm probability theoretically, because it can add to noise variance at the receiver. With a fixed decision threshold, noise fluctuation is likely to cause false detection of the PU for energy detection. When the shot noise caused by LED light (i.e., σ²_{shot, LED}) is dominant, the false alarm probability will be deteriorated if NLOS components are strong, but at the same time the detection probability can be further improved due to increased expectation value of decision metric. However, when the shot noise caused by background light (i.e., σ²_{shot, background}) is dominant, NLOS components are comparatively weak, which can be ignored. In our simulation model, the orders of magnitudes of σ²_{shot, LED} and σ²_{shot, background} are around 10⁻¹⁷ A² and 10⁻¹⁴ A², respectively, where NLOS components only account for a very small proportion in σ²_{shot, LED}. For example, in a corner at (0.5, 0.5, 0.85), the total noise variance with and without NLOS components is 1.0373×10⁻¹³ A² and 1.0372×10⁻¹³ A², respectively. It is clear that the fluctuation of noise due to NLOS components is negligible and has almost no influence on false alarm probability.

Next, we evaluate how the signal sampling size impacts the detection probability and show the related results in Fig. 6. The blue curve corresponds to the situation when the SU is at the coordinate of (1, 1, 0.85), and the red curve corresponds to the situation when the SU is at the coordinate of (1.2, 1.2, 0.85). The analytical results calculated by Eq. (15) are also shown for comparison. We find that a larger signal sampling size can improve the detection probability, but at the cost of longer sensing time. Moreover, the simulated results can match the analytical results well, thereby verifying the effectiveness of the theoretical model in Section 2.3. For the first situation, the analytical results are slightly lower than the simulation results. This is due to the dominant indoor reflections at the corner which are ignored by the analytical model. For the second situation, the analytical results are slightly larger than the simulation results because of estimation errors in Eqs. (13) and (14), in which some approximations are adopted.

Fig. 6. Relationship between detection probability P_D and signal sampling size N. (P_F = 0.1)

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4.2 Collaborative spectrum sensing by multiple SUs

Here, we consider the scenario of collaborative spectrum sensing with one LED, one PU, and four SUs. The results in Fig. 7(b) correspond to the SUs’ locations shown in Fig. 4(b), and the results in Figs. 8 and 9(b) correspond to the SUs’ locations shown in Fig. 4(c).

Fig. 7. (a) Theoretical relationship between the enhancement of detection probability and the value of SNR·N^1/2 when using the CS scheme (P_F= 0.1). (b) Simulated ROC curves for the different CS schemes (N = 100).

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Fig. 8. ROC curves under different weighting strategies for the CS scheme. (N = 100)

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Fig. 9. (a) Theoretical relationship between E[M_CS] and τ_max when using the proposed CS scheme (P_F= 0.1). (b) Comparison of simulated ROC curves with and without consideration of propagation delays for the CS scheme. (N = 100)

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We first evaluate the enhancement of detection probabilities by the proposed CS scheme, i.e., ΔP_{D, OR}, ΔP_{D, AND}, and ΔP_{D, Voting}, using Eqs. (25), (26) and (27). Figure 7(a) shows the relationship between ΔP_D and value of SNR·N^1/2 calculated by the theoretical model in Section 3.2. We find that the enhancement ΔP_D is always positive, where the peak values of ΔP_{D, OR}, ΔP_{D, AND}, ΔP_{D, Voting} (k = 2), and ΔP_{D, Voting} (k = 3) are 0.57, 0.52, 0.49, and 0.48, respectively. This means that the proposed CS scheme is efficient to always outperform all the three conventional CS schemes: based on OR-, AND-, and Voting-rules. Specifically, when SUs are at the locations as shown in Fig. 4(b), the value of SNR·N^1/2 is 2.1, and the corresponding ΔP_{D, OR}, ΔP_{D, AND}, ΔP_{D, Voting} (k = 2), and ΔP_{D, Voting} (k = 3) are 0.21, 0.19, 0.11, and 0.11 relative to the OR-, AND-, and Voting-rules, respectively.

We also compare the performance for various test scenarios using the conventional and proposed CS schemes, including the conventional OR-rule-based scheme with two and four SUs, the conventional AND-rule-based scheme with four SUs, the conventional Voting-rule-based scheme (k = 2, 3) with four SUs, and the proposed scheme with two and four SUs.

Figure 7(b) shows the simulated receiver operating characteristic (ROC) curves [27] for these schemes when the SUs are at the locations shown in Fig. 4(b). The ROC curve is usually used to demonstrate the relationship between false alarm probability P_F and detection probability P_D. A larger area below the curve represents a better detection accuracy [28]. Clearly, all CS schemes demonstrate higher sensing accuracies than local sensing whose detection probability is only 0.61 when P_F = 0.1, which verifies the effectiveness of the CS schemes. Moreover, increasing the number of collaborative SUs can improve the detection probability. This is because a larger number of SUs can provide more sensing information from various locations, thereby increasing the chance of detecting the PU if it is present. Conventional CS scheme under Voting-rule usually adopts k = U/2 to optimize sensing performance, which is called majority decision [25]. However, compared with conventional CS schemes including majority decision, the proposed CS scheme can achieve significant improvement in sensing performance. Specifically, when P_F = 0.1, the detection probabilities of the proposed CS scheme with two and four SUs are 0.94 and 1, respectively. In contrast, the detection probabilities of the conventional CS scheme under the OR-, AND-, and Voting-rules (k = U/2) are only 0.82, 0.83, and 0.90, respectively, with four SUs. These enhancements on the detection probability are in line with the theoretical results in Fig. 7(a), thereby verifying the effectiveness of the analytical model in Section 3.2.

In Fig. 7(b), the distances from SUs to the LED are the same, resulting in equal weight coefficients w_j for the proposed CS scheme. Next, we consider a scenario that four SUs have different distances from the LED, as shown in Fig. 4(c). Figure 8 compares the simulated ROC curves of the proposed CS scheme by using equal weight coefficients (w_j = 0.25, j = 1, 2, 3, 4) and the optimal weight coefficients obtained by Eq. (20) (w₁ = 0.12, w₂ = 0.15, w₃ = 0.21, w₄ = 0.52), respectively. For comparison, we also show the analytical results of the detection probability for the CS scheme calculated by Eq. (24) that ignores indoor reflections. We find that adopting the optimal weight coefficients can achieve the best sensing performance. Specifically, when P_F = 0.1, the detection probabilities of the proposed CS scheme with the optimal weight coefficients and the equal weight coefficients are 0.97 and 0.88, respectively, while that of the conventional Voting-rule-based CS scheme is only 0.53. Although the proposed CS scheme with equal weight coefficients is not optimal, it can still outperform the conventional CS scheme significantly, due to the significantly improved SNR of the VU. On the other hand, compared with the optimal weight coefficients, it is much operationally simpler to assign equal weight coefficients. Thus, adopting the CS scheme with equal weight coefficients is also an acceptable alternative for spectrum sensing even though there is some performance penalty compared with the situation with optimal weight coefficients.

Finally, we evaluate the influence of propagation delays on the proposed CS scheme, which are caused by different transmission distances from the LED to the SUs. Considering different numbers of SUs, Fig. 9(a) shows the theoretical relationship between the normalized E[M_CS] and the value of τ_max / T according to Eq. (28). We see that E[M_CS] has a negative correlation with τ_max. Specifically, E[M_CS] decreases linearly when τ_max ≤ T and sub-linearly when T < τ_max≤ 2 T, indicating that propagation delays will deteriorate the sensing performance of the CS scheme, but still within certain limits.

When the four SUs are at the locations as shown in Fig. 4(c), Fig. 9(b) compares the simulated ROC curves under the scenarios with and without consideration of propagation delays for the proposed CS scheme. We see that the asynchronized data samples resulting from propagation delays will degrade the sensing performance. Specifically, when P_F = 0.1, the detection probability decreases from 0.88 to 0.83 and from 0.97 to 0.94 with equal weight coefficients and optimal weight coefficients, respectively. However, these detection probabilities are still much higher than the conventional Voting-rule-based CS scheme whose detection probability is only 0.53. Therefore, in addition to high effectiveness, the proposed CS scheme is also robust for spectrum sensing in cognitive VLC systems.

5. Conclusion

We proposed a collaborative sensing (CS) scheme for indoor cognitive visible light communication (VLC) systems. For the scenario of a single secondary user (SU), we conducted a performance evaluation by proposing an analytical model, and considered the impact of indoor reflections and signal sampling size on performance. For the scenario of multiple SUs, by extending the single-SU analytical models, we evaluated the detection performance enhancement by CS. Results showed that the proposed CS scheme can significantly enhance the sensing accuracy in terms of detection probability by about 40% and 10% compared with the local-sensing and conventional CS schemes, respectively, when a typical four-SU scenario is considered. Moreover, it is expected that the sensing accuracy can be further enhanced if there are a larger number of SUs. Such a performance benefit was further verified under the situation that the SUs have different signal propagation delays from the LED.

Appendix A. Derivation of Eq. (28)

Based on Eq. (22) and considering all the SUs, the expectation of the decision metric M_CS can be derived as:

(29)$$\mathbb{E}[{M_{CS}}] = \mathbb{E}[\mathop \sum \limits_{i = 1}^N y_{0,i}^2] = N\mathbb{E}[{(\mathop \sum \limits_{j = 1}^U a \cdot \tilde{s}({\tau _0} + \tau _j^{{\prime}}) + {n_j})^2}],$$

where τ₀ is the start time of data samples for the first SU (τ₀ ∼ U(0, T)).

When τ_max≤ T, without loss of generality, we assume that ${\tilde{s}}$(τ₀ + τ′₁) = 1, whose adjacent symbol value has a 1/2 probability to be either 1 or −1. When the adjacent symbol corresponds to 1, received signal energy will not be influenced. When the adjacent symbol corresponds to −1 and τ₀ + τ_max ≤ T, the time delay is acceptable and will not result in asynchronized data samples as in Fig. 3. Thus, we define the cases that received signal energy will not be influenced as event O, whose probability is Pr(O) = 1/2 + 1/2 × (T − τ_max) / T = 1 − τ_max / 2T. When the adjacent symbol corresponds to −1 and τ₀ + τ_max > T, received signal energy is likely to be influenced, in which Pr(${\tilde{s}}$(τ₀ + τ′_j) = 1) = (T − τ₀) / τ_max, and Pr(${\tilde{s}}$(τ₀ + τ′_j) = −1) = 1− (T − τ₀) / τ_max. Therefore, for the scenario of τ_max≤ T, Eq. (29) can be further derived as:

(30)\begin{align} &N\mathbb{E}[{(\mathop \sum \limits_{j = 1}^U a \cdot \tilde{s}({\tau _0} + \tau _j^{^{\prime}}) + {n_j})^2}]\nonumber\\ &= N\{ {a^2}[\Pr (O) \cdot {U^2} + (1 - \Pr (O)) \cdot \frac{1}{{{\tau _{max}}}}\mathop \smallint \nolimits_{T - {\tau _{max}}}^T \mathbb{E} [{(\mathop \sum \limits_{j = 1}^U \tilde{s}({\tau _0} + \tau _j^{^{\prime}}))^2}]\textrm{d}{\tau _0}] + U{\sigma ^2}\} \nonumber\\ &= N\{ {a^2}[{U^2}(1 - \frac{{{\tau _{max}}}}{{2T}}) + \frac{1}{{2T}}\mathop \smallint \nolimits_{T - {\tau _{max}}}^T \mathop \sum \limits_{j = 0}^{U - 1} {(U - 2j)^2}\textrm{C}_{U - 1}^j\Pr {(\tilde{s}({\tau _0} + \tau _j^{^{\prime}}) = 1)^j}\Pr {(\tilde{s}({\tau _0} + \tau _j^{^{\prime}}) ={-} 1)^{U - j - 1}}\textrm{d}{\tau _0}] + U{\sigma ^2}\} \nonumber\\ &= N\{ {a^2}[{U^2}(1 - \frac{{{\tau _{max}}}}{{2T}}) + \frac{1}{{2T}}\mathop \smallint \nolimits_0^{{\tau _{max}}} \mathop \sum \limits_{j = 0}^{U - 1} {(U - 2j)^2}\textrm{C}_{U - 1}^j{(1 - \frac{{{\tau _0}}}{{{\tau _{max}}}})^j}{(\frac{{{\tau _0}}}{{{\tau _{max}}}})^{U - j - 1}}\textrm{d}{\tau _0}] + U{\sigma ^2}\} \nonumber\\ &= N\{ {a^2}[{U^2}(1 - \frac{{{\tau _{max}}}}{{2T}}) + \frac{{{\tau _{max}}}}{{2T}}\mathop \sum \limits_{j = 0}^{U - 1} \textrm{C}_{U - 1}^j{(U - 2j)^2}\mathop \smallint \nolimits_0^1 {(1 - x)^j}{x^{U - j - 1}}\textrm{d}x] + U{\sigma ^2}\} \nonumber\\ &= N\{ {a^2}[{U^2}(1 - \frac{{{\tau _{max}}}}{{2T}}) + \frac{{{\tau _{max}}}}{{2T}}\mathop \sum \limits_{j = 0}^{U - 1} \textrm{C}_{U - 1}^j{(U - 2j)^2}B(j + 1,U - j)] + U{\sigma ^2}\} .\end{align}

When T < τ_max≤ 2T, the time delay is likely to impact two adjacent symbols. For simplicity, we only consider the influence on the most adjacent one. When the adjacent symbol corresponds to 1, received signal energy will not be influenced and Pr(O) = 1/2. When the adjacent symbol corresponds to −1, we still have Pr(${\tilde{s}}$(τ₀ + τ′_j) = 1) = (T − τ₀) /τ_max, and Pr(${\tilde{s}}$(τ₀ + τ′_j) = −1) = 1− (T − τ₀) /τ_max. Therefore, for the scenario of T < τ_max≤ 2T, Eq. (29) can be further derived as:

(31)$$\begin{aligned} &N\mathbb{E}[{(\mathop \sum \limits_{j = 1}^U a \cdot \tilde{s}({\tau _0} + \tau _j^{^{\prime}}) + {n_j})^2}]\\ &\approx N\{ {a^2}[\Pr (O) \cdot {U^2} + (1 - \Pr (O))\frac{1}{T}\mathop \smallint \nolimits_0^T \mathbb{E} [{(\mathop \sum \limits_{j = 1}^U \tilde{s}({\tau _0} + \tau _j^{^{\prime}}))^2}\textrm{]d}t] + U{\sigma ^2}\} \\ &= N\{ {a^2}[\frac{1}{2}{U^2} + \frac{1}{{2T}}\mathop \smallint \nolimits_0^T \mathop \sum \limits_{j = 0}^{U - 1} {\textrm{(}U - 2j\textrm{)}^2}\textrm{C}_{U - 1}^j\Pr {(\tilde{s}({\tau _0} + \tau _j^{^{\prime}}) = 1)^j}\Pr {(\tilde{s}({\tau _0} + \tau _j^{^{\prime}}) ={-} 1)^{U - j - 1}}\textrm{d}{\tau _0}] + U{\sigma ^2}\} \\ &= N\{ {a^2}[\frac{1}{2}{U^2} + \frac{1}{{2T}}\mathop \smallint \nolimits_0^T \mathop \sum \limits_{j = 0}^{U - 1} {\textrm{(}U - 2j\textrm{)}^2}\textrm{C}_{U - 1}^j{\textrm{(}1 - \frac{{{\tau _0}}}{{{\tau _{max}}}}\textrm{)}^j}{(\frac{{{\tau _0}}}{{{\tau _{max}}}})^{U - j - 1}}\textrm{d}{\tau _0}] + U{\sigma ^2}\} \\ &= N\{ {a^2}[\frac{1}{2}{U^2} + \frac{{{\tau _{max}}}}{{2T}}\mathop \sum \limits_{j = 0}^{U - 1} \textrm{C}_{U - 1}^j{\textrm{(}U - 2j\textrm{)}^2}\mathop \smallint \nolimits_0^{T/{\tau _{max}}} {\textrm{(}1 - x\textrm{)}^j}{x^{U - j - 1}}\textrm{d}x] + U{\sigma ^2}\} \\ &= N\{ {a^2}[\frac{1}{2}{U^2} + \frac{{{\tau _{max}}}}{{2T}}\mathop \sum \limits_{j = 0}^{U - 1} \textrm{C}_{U - 1}^j{\textrm{(}U - 2j\textrm{)}^2}B(\frac{T}{{{\tau _{max}}}};j + 1,U - j)] + U{\sigma ^2}\} . \end{aligned}$$

According to Eqs. (30) and (31), Eq. (28) can be obtained.

Funding

National Natural Science Foundation of China (62001319); Open Fund of IPOC (BUPT) (IPOC2020A009); Priority Academic Program Development of Jiangsu Higher Education Institutions; Support from Jiangsu Engineering Research Center of Novel Optical Fiber Technology and Communication Network.

Acknowledgments

Most of this work was carried out at Soochow University when Zile Jiang was visiting there.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Room size (length × width × height)	5 m × 5 m × 3 m
Height of receiving plane	0.85 m
Launch power of LED transmitter (P_t)	2 Watt
LED semi-angle at half power	60°
Modulation index (M_index)	0.1
Effective area of photo-detector	0.5×10⁻⁴ m²
Receiver responsivity (γ)	0.35 A/W
Reflection coefficient of wall	0.83
OOK data rate	100 Mb/s

Collaborative spectrum sensing for cognitive visible light communications

Abstract

1. Introduction

2. Local spectrum sensing

2.1 Working principle

2.2 Influence from indoor reflections

2.3 Influence from signal sampling size

3. Collaborative spectrum sensing

3.1 Working principle

3.2 Enhancement on detection probability

3.3 Influence from propagation delays

4. Simulation results and discussions

4.1 Spectrum sensing by a single SU

4.2 Collaborative spectrum sensing by multiple SUs

5. Conclusion

Appendix A. Derivation of Eq. (28)

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Tables (1)

Equations (31)

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