Two-dimensional downlink burst construction in IEEE 802.16 networks

2.1. IEEE 802.16 network

The IEEE 802.16 network consists of a base station (BS) and a number of subscriber stations (SSs). The BS provides connectivity, radio resource management, and control of SS, which supports the connectivity with the BS.

The two layers in the IEEE 802.16 protocol stack are the physical layer, which transfers raw data, and the MAC layer, which supports the physical layer by ensuring that the radio resources are used efficiently. The three duplex modes in the physical layer with OFDMA are Time Division Duplex (TDD), Frequency Division Duplex (FDD), and Half-duplex Frequency Division Duplex (H-FDD). The TDD is the most attractive duplex mode because of its flexibility. In addition, the modulation methods, that is quadrature phase shift keying (QPSK), 16 quadrature amplitude modulation (16QAM), or 64 quadrature amplitude modulation (64QAM), and the associated coding rate for data transmission are selected according to the channel quality, that is, signal-to-noise ratio (SNR).

An IEEE 802.16 frame for downlink and uplink transmissions is divided into downlink (DL) and uplink (UL) subframes in the time domain of the TDD mode (the right part of Figure 1). A burst is an allocated bandwidth assigned to one dedicated connection of one SS and is formed by slots. A slot is the minimal bandwidth allocation unit, and consists of one subchannel and one to three symbols. A subchannel is the smallest allocation unit in the frequency domain, and a symbol is the smallest allocation unit in the time domain. A number of other fields in a frame provide specific functions. For example, preamble synchronizes each SS, DL/UL-MAP describes the position and measure of each downlink/uplink burst, and frame control header specifies DL subframe prefix and the length of DL-MAP message.

In the IEEE 802.16, the SS must acquire bandwidth from the BS before transmitting or receiving data. On downlink, the BS broadcasts to all SSs, and each SS picks up its destined packets. On uplink, SSs must inform the BS of the bandwidth they require for data transmission by sending a bandwidth request (BWR). Upon receiving the BWRs, the BS allocates the bursts in an uplink subframe to each SS, and subsequently broadcasts this information through UL-MAP. After receiving UL-MAP, each SS uses the allocated burst to transmit its data.

Figure 1 demonstrates that, for efficient bandwidth use, the BS must consider several factors, including the power saving policy, quality of services (QoS) requirements, channel quality variation, DL/UL bandwidth ratio, and burst structure. Bandwidth allocation is generally performed in two phases, flow scheduling and burst construction, because it is difficult to consider all of these factors in a single step [9]. The objective of flow scheduling is to estimate the appropriate number of slots to assign to each connection and to subsequently schedule these connections according to their QoS requirements, power saving policy, DL/UL bandwidth ratio, and other related factors. Several algorithms for flow scheduling were evaluated in the literature (e.g., [12]). In burst construction, however, the burst for each connection must be constructed according to the number of the allocated slots, the burst structure, channel quality variation, and computational complexity. This study considered the burst construction in the downlink transmission, i.e., downlink burst construction.

2.2. Burst construction in downlink transmission

The downlink burst structure specified by the IEEE 802.16 standard is based on the downlink-partial usage of subchannels (DL-PUSC) method [1], in which the burst uses partial subchannels in the OFDMA frequency range. The downlink bursts have three distinct requirements. First, the burst must be a continuous area to minimize DL-MAP overhead because DL-MAP is transmitted at the lowest data rate for robustness (e.g., QPSK modulation) and to ensure that all SSs can decode their embedded contents even under poor channel conditions. Second, the shape of the downlink burst is a rectangle to allow a more flexible construction, although the uplink burst must be constructed with a multi-rectangular shape for reducing power consumption of SSs [9]. Third, the SS has various levels of SNR on various subchannels because of the variable noises on each subchannel. To minimize the overhead and the complexity of MAC control messages, each burst uses only one MCS based on the worst SNR of all assigned subchannels.

Figure 2 shows an example of the construction of a downlink burst for a connection with 15 slots allocated by the flow scheduler. For simplicity, the SNR of each subchannel is transformed into its corresponding MCS (bytes/slot). A downlink burst can be presented as a rectangle with a height-width pair (h,w) placed on a starting slot (y,x), which is represented by a row-column manner, for example, [(y,x),(h,w)] = [(0,0),(3,5)], as shown in Figure 2. The MCS used by this burst is 9 bytes/slot, which is the worst MCS of its occupied subchannels, i.e., subchannels 0 to 2.

2.3. Related studies

Burst construction can be regarded as a process of placing items of variable heights, widths, and values into a two-dimensional area to maximize the total value of all items in the area. Thus, the burst construction problem can be regarded as a variant of the bin packing problem, the objective of which is to determine the optimal shape and position of each burst in the bandwidth area for maximizing the overall throughput of all constructed bursts. However, the traditional studies in operational research are not applicable for the burst construction because they focus on packing objects with fixed shapes and values [13–15]. Thus, a number of algorithms were proposed [10, 11, 16–21]. The eOCSA algorithm proposed by So-In et al. [10] constructs the first burst in the bottom right-hand corner of the available bandwidth area, and subsequently constructs another burst if the available bandwidth area above the previous burst is sufficient. Otherwise, eOCSA subsequently constructs the burst on the left-hand edge of the previous burst. The approaches [16–18] were designed in a method similar to eOCSA, but with minor modifications. Cicconetti et al. [19] further evaluated the internal fragmentation of the burst constructed in different directions, that is, vertical direction or horizontal direction, and subsequently selected the direction that experienced less fragmentation to construct the burst. Eshanta et al. [20] also proposed two approaches. One method constructs bursts with the fixed width in a vertical direction and the other constructs bursts with the fixed height in a horizontal direction.

The WLFF [11] constructs the burst on the best edge in the free bandwidth area. The best edge is the edge on which a burst is constructed, and generates the minimal variance of the sub-blocks in the free bandwidth area. Thus, constructing the burst on this best edge provides the most flexibility for the following burst construction. The greedy scheduling algorithm [21] was designed in a manner similar to WLFF. However, none of the bin packing solutions considers subchannel diversity.

Table 1 shows the summary of these methods. The complexity refers to the time complexity consumed by the burst construction algorithm. The required bandwidth implies that the algorithm not only considers the allocated slots, but also considers the requested bandwidth during burst construction. This is because the bandwidth provided by the allocated slots may exceed the required bandwidth of the connection when the burst is constructed on good-quality subchannels. Therefore, these unused slots can be further utilized by the other bursts if the algorithm extra considers the requested bandwidth.

3.1. Notations

A two-phase bandwidth allocation is used, as described in Section 2.1. Let C_all be the set of all downlink connections, and let L be the number of all downlink connections, i.e., L=|C_all|. In addition, let C _i represent the i th connection after flow scheduling. A _i and W _i denote the number of slots allocated by the flow scheduler and the requested bandwidth for C _i , respectively. Although the flow scheduler estimates A _i according to the requested bandwidth W _i , it also considers several other factors when performing this estimation. Thus, the throughput provided by A _i may be lower than W _i because the flow scheduler does not allocate sufficient slots in the current downlink subframe. Conversely, the throughput provided by A _i may exceed W _i because the burst allocator constructs the burst in an excellent block.

A two-dimensional matrix R represents the used MCSs on different subchannels for each connection in order to investigate the effects of subchannel diversity, where R(i, j) specifies the MCS used by C _i on the j th subchannel. A downlink subframe is composed of M×N slots, where M is the number of subchannels and N is the number of slots within one subchannel.

3.2 Problem and Issues

Problem statement: Given a downlink subframe of M×N slots, the set of C_all (all C _i , W _i , and A _i ), and the MCS matrix R, construct all B _i to maximize the overall throughput $\sum _{0\le i\le L-1}T{h}_i$.

Inefficient bandwidth usage must be eliminated to solve this problem. The following issues must be carefully considered when designing a downlink burst construction algorithm.

1. External fragmentation

A downlink burst with a rectangular shape may cause external fragmentation. External fragmentation refers to the division of available slots into small pieces that cannot meet burst requirements. Figure 3a shows an example of a connection C₁ with A₁ = 12 slots. The burst B₁ cannot be constructed because the free bandwidth was divided into pieces that were too small to accommodate B₁, although the total free bandwidth was sufficient for A₁.

4.1. Definition of corners

BCO avoids external fragmentation by constructing a burst starting from the corner and limiting it by the bounded width and height. The corner, bounded width, and bounded height are formally defined as follows: given the available bandwidth area before constructing the i th burst, the edge set, E _i , surrounding this area in a counterclockwise order is defined by $E_i=\left\{H_i^0,V_i^0,H_i^1,V_i^1,\dots ,H_i^j,V_i^j,\dots ,H_i^J,V_i^J\right\}$, where $H_i^j$ and $V_i^j$ are the j th horizontal and vertical edges, respectively. The corner, $C{R}_i^j$ is defined as an available slot, which is the intersection of $H_i^j$ and left-hand vertical edge $V_i^k$ of $H_i^j$. The corresponding bounded width and height are defined as $\left|H_i^j\right|$ and $\left|V_i^k\right|$, where $\left|H_i^j\right|$ and $\left|V_i^k\right|$ denote the lengths of $H_i^j$ and $V_i^k$, respectively. Therefore, constructing a burst in the corner indicates that one of the vertices of the burst lies in $C{R}_i^j$, and the width and height of this burst are restricted by $\left|H_i^j\right|$ and $V_i^k$, respectively. Figure 4a demonstrates that three corners are located on slot(0,4), slot(3,0) and slot(7,0) at constructing the i th burst, and their corresponding (height, width) pairs are (3,4), (5,4), and (5,8), respectively. Figure 4b presents an example of constructing burst B _i in the $C{R}_i^1$.

Lemma: Provided with a downlink subframe of M×N slots and number of connections, L, the available bandwidth area is continuous if each downlink burst is constructed in the corner.

Proof: Mathematical induction is applied to prove the claim. For L = 1, which indicates that only one burst is required to be constructed, the free slots are maintained as a continuous area after this burst is constructed in $C{R}_0^j$ and limited by $\left|H_0^j\right|$ and $\left|V_0^k\right|$.

Suppose that all free slots are maintained as a continuous area when L = s. When L = s + 1, the (s + 1)th burst is constructed in one of the corners (i.e., $C{R}_{s+1}^j$) and limited by the corresponding $\left|H_{s+1}^j\right|$ and $\left|V_{s+1}^k\right|$. Constructing burst in $C{R}_{s+1}^j$ maintains this burst adjacent to other constructed bursts. In addition, limiting the burst by $\left|H_{s+1}^j\right|$ prevents the horizontal division of the continuous free bandwidth area. Conversely, constructing burst in $C{R}_{s+1}^j$ and limiting it by $\left|V_{s+1}^k\right|$ prevent the vertical division of the continuous free bandwidth area. Consequently, the free slots, after constructing the (s + 1)th bursts, are not divided and are, therefore, maintained as a continuous area. Thus, by the mathematical induction, the available bandwidth area is always a continuous area.

4.2. Burst construction

BCO minimizes the internal fragmentation by exploring the optimal height-width pair of the burst constructed in the selected $C{R}_i^j$. The optimal height-width pair indicates that the burst with this pair provides the optimal throughput or the smallest area. To obtain the optimal height-width pair, BCO repeatedly constructs a temporary burst, B_tmp, with a possible height-width pair and calculates the throughput that this burst can provide. The steps are listed as follows:

Initialization: h = 1// set initial height

Step 1: Determine the width w for h by considering Ai, Wi, and the width $\left|H_i^j\right|$.

Step 2: B _tmp =[(y, x)(h, w)], where $\left(y,x\right)=C{R}_i^j$. In addition, calculate the throughput of B_tmp.

Step 3: Record the optimal burst $B_{\mathsf{\text{tmp}}}^{\mathsf{\text{best}}}$ with the optimal height-width pair obtained thus far.

Step 4: h = h + 1;

If $h\le \left|V_i^k\right|$, go to step 1.

When the loop ends, $B_{\mathsf{\text{tmp}}}^{\mathsf{\text{best}}}$ provides the optimal throughput among all B_tmp virtually constructed in $C{R}_i^j$.

In Step 1, A _i and W _i were used to calculate the width when the height was given, to alleviate internal fragmentation. BCO first calculated the width w_1, where (w₁×h) was equal to the allocated slots A _i . BCO calculated the width w₂ that the throughput provided by the burst (w₂×h) to satisfy the requested bandwidth W _i . Subsequently, BCO used the minimum of w₁, w₂, and $\left|H_i^j\right|$ as the width. This is because if w₂ is the minimum, constructing a burst with a larger width w₁ will exceed the requested bandwidth, resulting in internal fragmentation. In addition, $\left|H_i^j\right|$, as the minimum, indicates that the available bandwidth area located in this corner with the height h is insufficient to accommodate a burst with A _i slots. Therefore, the burst should be shrunk by using $\left|H_i^j\right|$ as its width. The exact calculations of w₁ and w₂ are described in the following section.

Furthermore, examining each possible height of a burst can avoid the phenomenon of throughput anomaly. The throughput anomaly indicates that a burst with a large height may anomaly cause lower throughput than a burst with a small height when the burst with a large height uses an inferior MCS. Figure 5 shows an example in which the throughput provided by the burst B(h = 3), referring to the burst with height 3, is considerably lower than that provided by the burst B(h = 2) because B(h = 3) used an inferior MCS, although B(h = 3) is larger than B(h = 2). In this case, a burst with a small height that provides large throughput should be constructed to avoid slot waste.

4.3. Pseudo code of the BCO algorithm

Figure 6 shows the pseudo code of BCO. To construct burst B _i for each connection C _i , BCO first uses the FindCorner function to obtain CRList, which contains the corners from the available bandwidth area. The FindCorner function returns the CRList by examining the horizontal and the vertical edges of the available bandwidth area. BCO subsequently explores the optimal corner by virtually constructing the burst in each corner to address the optimal block exploration (line 6-13), i.e., BCO repeatedly invokes the ConstructBurst function to virtually construct a burst $B_i^j$ in the corner $C{R}_i^j$. BCO subsequently compares $B_i^j$ with $B_i^{\mathsf{\text{best}}}$ to determine which is superior, i.e., which has higher throughput or which occupies the fewer slots under the same obtained throughput. If $B_i^j$ is superior, BCO sets $B_i^{\mathsf{\text{best}}}$ to $B_i^j$. After virtually constructing all $B_i^j$ and obtaining the best burst $B_i^{\mathsf{\text{best}}}$, BCO constructs B _i as $B_i^{\mathsf{\text{best}}}$.

The ConstructBurst function searches for the optimal height-width pair of the burst constructed in the chosen corner to minimize the internal fragmentation. Initially, the ConstructBurst function records (h^max,w^max) as the bounded height-width pair (line 18). The ConstructBurst function subsequently examines each possible height-width pair in lines 20-27 and returns the burst with the optimal height-width pair. In addition, when determining the width of the B^tmp for each height h, w₁ is calculated by $w_1=⌊\frac{A_i}{h}⌋$, where ⌊⌋ denotes the floor function, to ensure that the (w₁×h) slots do not exceed the allocated slots (i.e., A _i ). Conversely, w₂ is calculated by $w_2=⌈\frac{W_i}{\mathsf{\text{FindMCS}}\left(i,j,h\right)\times h}⌉$, where ⌈⌉ denotes the ceil function, to ensure that the burst with (w₂×h) satisfies the requested bandwidth requirement (i.e., W _i ). The function FindMCS(i,j,h) calculates the MCS used by the burst located in the corner j with the height h.

BCO evaluates the burst constructed in each corner by the NOSCal, MCSCal, and ThCal functions. The NOSCal(B) calculates the number of occupied slots for a burst B, and MCSCal(i,B) and ThCal(i,B) calculate the used MCS and achieved throughput of a constructed burst B for C _i , respectively. According to the definitions, for a specific burst, B=[(y,x),(h,w)], where (y,x) is the location of the starting slot and (h,w) is the height-width pair, NOSCal(B) and MCSCal(i,B) return h×w and $\underset{x\le p\le x+h-1}{min}R\left(i,p\right)$, respectively, and ThCal(i,B) returns min(NOSCal(B)×MCSCal(i,B),W _i ).

BCO applies a saving variable to efficiently use the unused allocated slots of each burst to improve throughput. This is because the flow scheduler usually allocates the total number of slots of the downlink subframe to each connection, indicating that the sum of all allocated slots equals the total number of slots in the downlink subframe. In this case, even when satisfying the requested bandwidth by fewer slots to avoid internal fragmentation, the saved slots are still not utilized. Therefore, BCO uses saving to record the number of total saved slots to allow subsequent bursts to use the saved slots conserved from the previous bursts. As shown in line 12, the unused slots after constructing B _i , i.e., A _i -NOSCal(B _i ), are added to the parameter, saving. Subsequently, the latter connection C _{i +1} has A _{i +1} +saving slots to construct B _{i +1}, as shown in line 21. Therefore, each burst not only uses its own allocated slots, but also applies the additional saving slots to fulfill its required bandwidth. The use of this parameter prevents two unfavorable phenomena, as follows: the waste of unused slots internal to the bursts constructed on optimal subchannels and the bandwidth dissatisfaction of connections whose bursts are constructed on inferior subchannels. Thus, this approach enhances the total throughput.

4.4. Time complexity analysis

However, the sum of occupied slots for all bursts does not exceed the total number of slots in the downlink subframe, i.e., $\sum _{0\le i\le L-1}\mathsf{\text{O}}\left(u\right)\le \mathsf{\text{O}}\left(MN\right)$, therefore, the time complexity of BCO is O(M²N).

5.1. Simulation model

The simulation environment was an IEEE 802.16 OFDMA system with a 20 MHz frequency band. The numbers of subchannels and symbols for a downlink subframe were set to 60 and 24, respectively. Thus, 1 subchannel had 12 downlink slots, and 1 downlink slot occupied 2 symbols. According to the received SNR, various MCSs were used, including QPSK1/2, QPSK3/4, 16QAM1/2, 16QAM3/4, 64AQM2/3, and 64QAM3/4 [1].

To simplify the simulation scenarios, each SS had only one downlink connection. All connections applied the same service class and QoS parameters because this study focused on total throughput. Therefore, the comparisons were conducted on the fair basis to measure the total throughput, although the issues of QoS were not considered. The SNR on each subchannel received by the SS followed the normal distribution, and the arriving traffic of each downlink connection followed the Poisson distribution. The default setting in the simulation was 20 downlink connections with an 800-kbps arriving data rate. The mean SNR of the subchannels received by each SS was set to 15 db, and the standard deviation was set to 5 db.

The flow scheduling used in the simulation was the algorithm with channel quality awareness and QoS guarantee (CQQ) [12], which is reportedly superior to other approaches. The CQQ applies a weighted fair queuing (WFQ) strategy to allocate total number of slots in the downlink subframe to each connection according to its assigned weight. The connection with higher average transmission rate and larger requested bandwidth is assigned a higher weight. The following discussion refers only to the results using CQQ because we conducted several previous simulations using various flow scheduling approaches and obtained similar results.

5.2. Average requested bandwidth

To investigate the effects of average requested bandwidth on total throughput, the arrival data rate was varied from 100 kbps to 1 Mbps. Figure 7a shows the total throughputs achieved by eOCSA, WLFF, and BCO. BCO outperforms eOCSA and WLFF on throughput because of two main reasons. First, eOCSA and WLFF often construct bursts with inferior MCSs because they do not consider subchannel diversity, and therefore, fail to address optimal block exploration. Second, internal fragmentation may occur using eOCSA and WLFF because they do not consider the requested bandwidth during burst construction.

eOCSA and WLFF cannot achieve the targeted bandwidth (200 kbps × 20 connections = 4 Mbps), even when the traffic is light, i.e., the requested bandwidth is smaller than 200 kbps. This occurs because the burst B _i has some unused free slots if the requested bandwidth is satisfied by fewer slots than A _i when B _i is constructed on high-quality subchannels and uses an optimal MCS. In this situation, eOCSA and WLFF does not shrink the area of B _i and, therefore, cannot release the unused slots to other bursts. In addition, eOCSA and WLFF may construct bursts on the subchannels with unacceptable channel quality, and thus, cannot use any suitable MCS to transmit data because they do not consider subchannel diversity. Consequently, all slots internal to the burst are invalid. Thus, several unused slots are wasted, as shown in Figure 7c, and cannot achieve the targeted bandwidth.

BCO alleviates internal fragmentation by shrinking the number of occupied slots. Figure 7c demonstrates that BCO experiences a maximum of 1.6% IUSR. The saved slots can be used by the following unconstructed bursts with insufficient allocated slots. In addition, BCO constructs a burst in the optimal corner to avoid external fragmentation and to explore an optimal block. Thus, it achieves a superior throughput than eOCSA and WLFF. Figure 7a,d reveals that, when the requested bandwidth is less than 700 kbps, BCO achieves the targeted bandwidth with fewer slots, and thus, owns higher EUSRs, because the constructed shrunken bursts already provide sufficient bandwidth, i.e., THCal(i,B _i )=W _i . However, the EUSR decreases when the required bandwidth increases because more slots are required to fulfill the increasing required bandwidth.

Although the requested bandwidth increases, the throughput should become stable when most slots are used (requested bandwidth exceeds 700 kbps for BCO). However, in this case, the situation is not actually saturated and their throughputs slightly increase, because, although most slots are used, the burst generally satisfies its requested bandwidth by fewer slots when using an optimal MCS and leaves the unused free slots of the allocated slots to other bursts that use inferior MCSs, i.e., the minority of slots in the downlink subframe use optimal MCSs, and the majority use inferior MCSs. The area of the burst using an optimal MCS increases in conjunction with the bandwidth to satisfy the requested bandwidth, and the unused slots, which are left to other bursts with lower MCSs, decrease. Consequently, more slots in the downlink subframe use optimal MCSs and fewer slots use inferior MCSs. Therefore, the throughput slightly increases. However, a saturated condition is eventually achieved when most slots are efficiently used. Some of the bandwidth area with inferior channel quality remains unused (approximately 10%) even when the traffic load is heavy, as shown in Figure 7d, because BCO shrinks the bursts to prevent throughput anomaly and achieves higher overall throughput, as explained in Section 4.2.

Figure 7b demonstrates that the improvement ratios of BCO increased in conjunction with the requested bandwidth because eOCSA and WLFF reached a saturated condition, whereas BCO did not reach a saturated condition. Under the heavy load of 1 Mbpps, BCO achieved 2 and 9 times the throughput achieved by eOCSA and WLFF, respectively.

5.3. Number of connections

The effects of the number of connections on the total throughput were also investigated. The number of connections was varied from 10 to 50 with the same overall data arrival rates, i.e., 16 Mbps. Figure 8a reveals that the total throughputs of BCO, eOCSA, and WLFF increased in conjunction with the number of connections. Under the same overall data rate, the larger the number of connections, the smaller the bandwidth requested by each connection and the smaller the area of each burst. A burst with a smaller area provides all algorithms with more opportunities to construct bursts on high-quality subchannels. It also enables all algorithms to decrease the numbers of unused slots internal and external to the bursts, as shown in Figure 8c,d, respectively, resulting in the increase of the throughput. Figure 8b demonstrates that, the smaller the number of connections, the larger the improvement ratios achieved by BCO, because, when the burst is larger, eOCSA and WLFF are more likely to construct this burst on low-quality subchannels, whereas BCO attempts to avoid this problem.

5.4. Channel quality

The effects of the channel quality on the total throughput were investigated. In this simulation, the mean SNR of the subchannels received by each SS was varied from 10 to 20 db, and the standard deviation was maintained at 5 db. Figure 9a reveals that the total throughputs of BCO, eOCSA, and WLFF increase because a high mean SNR provides bursts with more opportunities to use better MCSs. Figure 9b demonstrates that the improvement ratios of BCO decreased as the channel quality increased. Two main reasons were determined for this occurrence. First, eOCSA and WLFF did not consider subchannel diversity, and thus, failed to address optimal block exploration. Therefore, the increase of throughput was caused by the higher channel quality. However, because BCO considered optimal block exploration, it achieved satisfactory throughput, even when the mean SNR was low. Therefore, as the mean SNR increased, the increasing slope on throughput in BCO was smaller than that in eOCSA and WLFF. Second, when the mean SNR increased, the larger throughputs achieved by eOCSA and WLFF lowered the improvement ratios obtained by BCO.

Figure 9c indicates that a high mean SNR provided fewer opportunities for eOCSA and WLFF to construct bursts on the subchannels with unacceptable channel quality, thereby causing a decreased in the IUSRs of eOCSA and WLFF. Conversely, Figure 9d indicates that the EUSRs of all algorithms remained stable, even as the mean SNR increased, because the overall required bandwidth and the number of connections were fixed.

5.5. Variation of channel quality

The effects of variation of the channel quality between subchannels on the total throughput were investigated. In this simulation, the mean SNR of the subchannels received by each SS was maintained at 15 db, and the standard deviation was varied from 0 to 10 db. Figure 10a reveals that BCO surpassed eOCSA and WLFF when the standard deviation was 0, i.e., all subchannels had the same channel quality. In this case, eOCSA and WLFF generated internal and external fragmentations; however, BCO alleviated these problems, as shown in Figure 10c,d, respectively.

In addition, Figure 10a demonstrates that the total throughputs of eOCSA and WLFF decreased considerably as the standard deviation of the SNR increased, whereas that of BCO changed slightly. Consequently, the improvement ratio of BCO increased considerably, as shown in Figure 10b. The numbers of subchannels with optimal SNRs and subchannels with inferior SNRs increased in conjunction with the standard deviation of the SNR. Because one burst only uses a MCS based on the worst SNR of all assigned subchannels, eOCSA and WLFF do not consider the channel quality and will construct the bursts on the subchannels with inferior or unacceptable SNRs, resulting in a high IUSR (Figure 10c) as the standard deviation of the SNR increases. However, in this case, the throughput of BCO decreased slightly because it considered optimal block exploration at constructing bursts. Figure 10d reveals that the EUSR of BCO slightly increased in conjunction with the variation of the channel quality.