Spectrum Sensing Scheme Measuring Packet Lengths of Interfering Systems for Dynamic Spectrum Sharing

For the dynamic spectrum sharing (DSS), this paper proposes a spectrum sensing scheme that measures packet lengths of interfering systems. DSS requires spectrum sensing techniques to measure a length of time for which the interfering systems use a channel during observation time. A ratio of the length of time to the observation time is referred to as the channel occupation ratio (COR). When the observation time is limited, a conventional estimation scheme suffers from large errors of the measured COR. To cope with this problem, another conventional scheme divides the observation time into multiple short slots so as to estimate mean squared estimation errors of COR. However, this conventional scheme cannot accurately estimate errors, because it does not consider the time length of packets. Therefore, this paper proposes a scheme to estimate the variance of measured COR by measuring how long packets from the interfering systems can be observed, which can estimate errors much more accurately than the conventional scheme. Computer simulations evaluate how the observation time affects the standard deviation of the measured COR. It is also demonstrated that the theoretical results of the proposed scheme agree with those of the simulations when the true value of COR is less than 0.4.

Since the primary system does not use all the radio resources such as time, frequency, and space, some radio resources are not used during a short period. These vacant radio resources can impair frequency efficiency. DSS, which shares the radio resources with multiple systems, can improve the system throughput and frequency efficiency by exploiting the vacant radio resources. DSS in 5G, which aims to share the channel with the existing system such as LTE, has also been investigated [4]- [6].
Sharing the radio resources should prevent other systems from interfering with the target system. When each system exchanges control signals including information on the radio resource usage, a new-coming system can easily use vacant radio resources. On the other hand, when each system cannot recognize the control signals in the unlicensed band, each system needs to detect the radio resource usage by itself. For such detection without control signals, the spectrum sensing technique such as the listen before talk (LBT) [7] is required. LBT usually checks the radio condition before transmission.
However, it is more effective to observe the radio resource usage of the other systems during a certain period and to select channels with lower usage [8], [9].
The radio resource usage changes according to the time of day/week and the environment [10], [11]. Since the usage of radio resources depends on the users' behavior [12], it is possible to adequately predict the usage amount on a daily or weekly basis. However, the variations during a short period become large in towns and stations where many users frequently move. To observe the usage of radio resources during a short period, sensing techniques in the physical and MAC layers have been studied. In the physical layer, the energy detection can observe signals over channels [13], [14]. In the MAC layer, the usage period and kind of systems can be inferred from the MAC headers of observed packets [15]. A combination of techniques in the physical and MAC layers has also been investigated [16]. However, the detection technique in the MAC layer requires the MAC header to be correctly received. Furthermore, since it is necessary to recognize the MAC header, this approach cannot detect when a new system appears. In order to enable various systems to employ DSS in the unlicensed band, the spectrum sensing in the physical layer is preferable to that in the MAC layer.
The former spectrum sensing needs sufficient observation time in order to accurately detect the usage of radio resources. Since 5G is expected to develop the new frequency band [17], the number of channels used for the communication increases. As the number of observed channels increases, the observation time increases sharply and thus the frequency efficiency is degraded [18]. Since the number of RF circuits should be limited, all channels cannot be observed at the same time. As the observation time becomes longer, the usage of previously observed channels may change before selecting one channel. As the observation time becomes short, the channel usage cannot be measured accurately because the channel observer cannot receive a sufficient number of packets. To reduce the observation time, an adaptive spectrum sensing technique that selects the observed channel according to the usage of the interfering system has also been proposed [19]. However, this proposed technique cannot solve the following fundamental problem: When congested channels are selected for communications, the communication quality may deteriorate.
To overcome these problems, the estimation scheme that can evaluate estimation errors of the channel usage is required. A scheme proposed in [20] can theoretically estimate the observation error for the rendezvous schemes. However, the conventional scheme in [20] divides the observation time into multiple short slots and checks whether such slots are used or not, in order to estimate mean squared estimation errors. Such a conventional scheme cannot accurately estimate the mean squared estimation errors, because it does not consider the time length of packets from the interfering systems. Hence, this paper proposes a scheme to estimate the variance of measured channel usage by measuring how long packets from the interfering systems can be observed during one short  slot, which can estimate the mean squared estimation errors much more accurately than the conventional scheme. Since the proposed estimation scheme can measure the channel usage during sufficiently short observation time, DSS can operate well while improving the frequency efficiency. Note that the proposed scheme can be combined with the sensing techniques in [13]- [16], [19], because the proposed scheme aims to accurately estimate the variance of measured COR.
The rest of the paper is organized as follows. Section 2 presents the system model and discusses the problem of the short observation time. Section 3 describes the conventional and proposed estimation schemes for the measured channel usage. In Section 4, computer simulation results are detailed. Finally, Section 5 concludes the paper.

A. SYSTEM MODEL
Let us consider a system model shown in Fig. 1, which includes the target (proposed) and other wireless communication systems. These systems are assumed to use N Ch uncorrelated channels with the same bandwidth. It is also assumed that the other systems can randomly assign any user terminals (UTs) into each channel, and that an access point (AP) of the target system selects one channel from the N Ch channels to communicate with its UTs. The AP is equipped with a channel observer that monitors channel usage. The channel observer measures the total length of time, for which received signal strength of each channel exceeds a threshold during observation time T OBS , and the measured length of time is referred to as the channel usage time. As the threshold, the carrier sense level is usually used. Note that the target system can receive control signals from the interfering systems but cannot recognize them. Finally, the AP searches for the channel having the minimum channel usage time and selects such a channel for the communication.
where T ON (n Ch ) is the channel usage time at the n Ch -th channel. Here, the COR estimation is assumed to be unbiased, which means that the ensemble average ofρ(n Ch ) is equal to the true value. After measuring the channel usage of all the channels, the AP selects the channel that corresponds to the minimum COR. In Fig. 2, Ch#2 is selected and used for the communication. During the communication period T COM , the AP continues to communicate with UTs over the selected channel. After T COM , the AP measures the channel usage again and selects one channel corresponding to the minimum COR. Therefore, the period of the channel selection is equal to N Ch T OBS + T COM , which increases along with an increase in both the number of observed channels N Ch and the observation time T OBS . Although shorter T OBS is preferable, decreasing T OBS can damage the accuracy of the COR estimation. From now on, the dependence ofρ(n Ch ) on n Ch is omitted for simplicity. As an example of the COR measurement, Fig. 3 shows distributions of the measured COR when T OBS = 10, 10 2 , 10 3 ms and the true value of COR, ρ, is set to 0.32. The computer simulations also assumed that the traffic of the interfering systems follows the Poisson distribution and that the packet length is constant. It can be seen from Fig. 3 that the deviation of the measured COR increases along with a decrease in T OBS , which means that the AP is more likely to select worse channels as T OBS decreases. To overcome such a problem, this paper proposes a measurement scheme that can estimate the deviation of the measured COR. Another problem is that the channel observer of the AP cannot receive signals from hidden terminals. To solve this problem, UTs perform distributed sensing and send sensing results to AP, which has been proposed in [21], [22]. The amount of feedback information on the sensing results is considerable. To overcome this issue, Ref. [23] has proposed cluster of the channel observers and aggregation of the sensing results. However, the distributed sensing requires high cost when every UT is equipped with the channel observer. Considering the serious drawback, this paper does not consider the distributed sensing by UTs and installs the channel observer into only AP, which can hardly solve the above-mentioned problem. Note that the proposed scheme focuses on estimating the variance of the observed COR for the single channel observer, and can be combined with the above distributed sensing techniques.

III. ESTIMATION OF COR DEVIATION
This section discusses how to estimate the deviation of the measured COR. For comparison, the conventional scheme to divide the observation time into multiple short slots is explained at first. Next, the proposed estimation scheme is detailed under reasonable conditions with short T OBS .

A. CONVENTIONAL ESTIMATION SCHEME BASED ON OBSERVED SHORT SLOTS
The estimation scheme proposed in [20] divides the observation time into N s observed short slots as shown in Fig. 4 (a). The interfering systems are assumed to randomly use the observed short slots. The channel observer monitors whether each observed short slot includes any signals. When the channel observer detects any signals (indicated by green blocks in Fig. 4 (a)), the corresponding observed short slots are classified into "ON". Otherwise (indicated by white blocks in Fig. 4 (a)), the corresponding observed short slots are classified into "OFF". On the assumption that the sensing results are statistically independent of each other, the probability thatρ = K ON /N s is given by where K ON (≥ 0) is the number of "ON" observed short slots. When N s ρ(1 − ρ) 1 holds, the binomial distribution can be approximated as the following Gaussian distribution according to the De Moivre-Laplace theorem [24]: When K ON is transformed intoρ = K ON /N s , (3) is rewritten as Let σ 2 denote the variance of the above Gaussian distribution and σ 2 is given by The variance is inversely proportional to N s . Therefore, when the length of the observed short slot is kept constant, longer observation time T OBS is required to reduce the variance of the measured COR.

B. PROPOSED ESTIMATION SCHEME MEASURING PACKET LENGTHS
In real packet transmission systems, the length of each packet is not the same but different. The conventional scheme proposed in [20] does not consider this situation because the length of the observed short slots is not determined. Conversely, the proposed estimation scheme considers the time lengths of the observed short slots and observed packets in order to estimate the variance of the measured COR. Therefore, the proposed scheme is expected to estimate the variance of the measured COR more accurately than the conventional one, and thus to avoid selecting worse channels. Fig. 4 (b) shows a time chart of the proposed scheme. Considering it,ρ of (1) can be rewritten aŝ where T SIG (k ON ) denotes the time length of the k ON -th (1 ≤ k ON ≤ K ON ) packet. For simplicity, the time lengths of the observed packets are assumed to be constant during T OBS . Since T EXP denotes an expectation of the constant time length, the following equation holds: Substituting (7) into (6) yieldŝ On the other hand, let T UNT be the time length of the observed short slot, and the observation time can be expressed as Substituting (9) into (8) results in Consideringρ = K ON /N s in the conventional scheme, the factor of T EXP /T UNT is also needed for ρ in the proposed scheme. Thus, σ 2 of (5) is modified into Let T NUL denote the time length for which the channel observer cannot detect any signals during T UNT , and T UNT is expressed as When T NUL T EXP holds, (11) can be approximated as where T EXP /T UNT 0 was used for the derivation.
Note that the value of T OBS can be obtained from (13) using target values of σ 2 , ρ, and T EXP .

IV. COMPUTER SIMULATION A. SIMULATION CONDITIONS
Computer simulations were conducted to verify the effectiveness of the proposed estimation scheme. Since the finite buffer model was employed, the packet generation of the interfering systems was assumed to follow the Poisson distribution. As the payload length of the observed packets was set to 512 bytes, the packet length varied according to the selected modulation and coding scheme (MCS) index. The control overhead was set in the same manner as [25] and each parameter was listed in Table 1. It was assumed that the channel observer can receive all packets from the interfering systems.
The following two conditions were considered. One keeps the packet length constant because the MCS index is fixed. The other employs the adaptive modulation and coding (AMC) and changes the packet length according to the selected MCS index. Let T DATA and T ACK denote the time lengths of data and acknowledgement (ACK) packets, respectively. Thus, the time length of the observed packet is denoted by T SIG and obtained as Under the former condition, T EXP is equal to T SIG . Under the latter condition, T EXP is the expectation of T SIG . Note that the packet length and measured COR were assumed to be perfectly estimated, because the purpose of the computer simulations is to clarify the basic performance of the proposed estimation scheme. It is also noteworthy that the above assumption can be considered reasonable. The reason is that the MAC header can be correctly decoded under considerable SNR conditions and that the packet length can be perfectly estimated from the decoded MAC header.

B. CONSTANT PACKET LENGTH CONDITION
On the condition that the packet length is constant during T OBS , Fig. 5 shows how the observation time T OBS affects the standard deviation of the proposed estimation scheme with T EXP being a parameter. The true value of COR, ρ, was set to 0.32. T EXP was fixed at 0.68/0.37/0.22/0.11 ms that corresponds to 512-byte packets using MCS0/1/3/9. It can be seen that the theoretical results of (13) for the proposed estimation scheme agree with those of the computer simulation. The standard deviation, σ, decreases along with an increase in observation duration, T OBS . When T OBS > 5000 ms, σ becomes negligible and σ < 0.01. On the other hand, σ increases along with an increase in T EXP . This is because the number of packets decreases as T EXP becomes large even if the true value of COR is the same. When the number of packets is small, a large variation can be seen in the packet generation during the observation time. For comparison, the theoretical results of (5) for the conventional estimation scheme were also plotted in the figure. The results of the conventional estimation scheme are almost the same as those of the simulation when T EXP = 0.68 ms, but does not match the simulation results when T EXP = 0.37, 0.22, 0.11 ms. The reason is that as T EXP increases and approaches T UNT , the result of the conventional estimation scheme converges to that of the simulation. Evidently, from the above simulation results, the conventional estimation scheme cannot operate well when T EXP is much shorter than T UNT . Fig. 6 shows how the true value of COR, ρ, affects the standard deviation of the measured COR with T OBS being a parameter. T EXP was set to 0.68/0.11 ms. In all the cases, it can be seen that σ increases along with an increase in ρ when ρ < 0.5. On the other hand, when ρ > 0.5, σ decreases along with an increase in ρ. This is because the number of observed packets, which depends on the true value of COR, increases, and the deviation of the measured COR decreases. The theoretical results of the proposed estimation scheme almost agree with the results of the simulation when ρ ≤ 0.4. However, the former results do not match the latter results when ρ > 0.4. For comparison, the results of the conventional estimation scheme were also plotted in Since the proposed estimation scheme assumes that one packet falls within one short slot, the results of the proposed estimation scheme deviate from those of the simulation when the number of observed packets increases. Although the proposed estimation scheme is not effective in such a case, the communication quality is degraded even if the channel whose COR is larger than 0.4 is selected. When ρ > 0.4, the longer observation time and the shorter communication time are preferable.

C. VARIABLE PACKET LENGTH CONDITION
Next, computer simulations were conducted under the condition that the packet length varies. The packet length, T SIG , ranged from 0.11 ms to 0.68 ms in which the MCS index was randomly selected from MCS0 through MCS9. The true value of COR was kept constant during the observation time. The other parameters were the same as those of the previous simulation. Fig. 7 shows the distributions of the measured COR under the condition of the variable packet length. The true value of COR was set to 0.32 in the same manner as Fig. 3 while T OBS was set to 100 ms. For comparison, the results with T SIG being constant 0.37 ms were plotted. It can be seen that the observed results with the variable packet length are almost the same as those with constant T SIG . This is because the expected packet length, T EXP , of the variable packet length is the same as that with T SIG of 0.37 ms. Fig. 8 (a) shows the standard deviation of the COR while Fig. 8 (b) shows differences in the standard deviation of COR between the simulation result and the proposed or conventional estimation schemes, where T EXP of the proposed scheme was set to 0.37 ms. It can be seen from these figures that the conventional estimation scheme suffers from larger errors because the conventional scheme does not consider the variable packet length condition. When ρ ≤ 0.4, the proposed scheme can reduce the difference or error of the standard deviation below 0.05. On the other hand, when ρ > 0.4, the result of the proposed scheme becomes large, which does not cause any problems for the following reasons: When the true value of COR is equal to 0.5, it is evident from Fig. 8 (a) that the standard deviation is near 0.055. In this case, the probability that the measured COR lies within [0.39, 0.61] reaches 95%, which can be inferred from the Gaussian distribution with the standard deviation of 0.055 and the mean of 0.5. Therefore, excluding the channels with the measured COR being greater than 0.4 0.39 can prohibit the channels with larger COR from being selected. When the measured COR is less than 0.4, however, the proposed estimation scheme can select the channels with smaller COR.

V. CONCLUSIONS
In this paper, the novel spectrum sensing technique that can estimate the standard deviation of the channel usage time has been proposed for the dynamic spectrum sharing. The proposed scheme divides the observation time into multiple short slots and measures how long packet from the interfering systems can be observed during one short slot, in order to deal with the case of short observation time. Computer simulations have shown that how the observation time affects the standard deviation of the measured COR. It has also been demonstrated that the theoretical results of the proposed estimation scheme agree with those of the simulation when the true value of COR is less than or equal to 0.4. Although the standard deviation increases along with a decrease in the observation time, it has been verified that the proposed estimation scheme can detect the channels with smaller COR even under a short observation time condition.