Conventional Mechanism

In this subsection, both the saturation user throughput and the corresponding overhead for the conventional mechanism of the IEEE 802.16 network will be derived. Considering that 𝑆_𝑓 represents one frame duration in the unit of OFDM symbols, the total number of available OFDM symbols 𝑆_𝑎𝑣 within a frame can be obtained as

𝑆_𝑎𝑣= 𝑆_𝑓 − 𝑆_𝑡𝑡𝑔− 𝑆_𝑟𝑡𝑔, (2.14)

where 𝑆_𝑡𝑡𝑔 and 𝑆_𝑟𝑡𝑔 denote the durations of TTG and RTG in OFDM symbols respectively.

Without loss of generality, it is assumed that a frame duration is evenly partitioned by the DL and UL subframes for analytical convenience. Different durations of DL and UL subframes can also be analyzed in similar manner. However, the ratio of DL subframe to UL subframe should be a constant value for all the BSs in an IEEE 802.16 network. If the ratio is different for each BS, significant inter-cell interference will appear in the entire network. Therefore, the durations of both the DL subframe (𝑆_𝑓^𝑑) and the UL subframe (𝑆_𝑓^𝑢) in OFDM symbols can be represented as

𝑆_𝑓^𝑑=⌊ 𝑆𝑎𝑣

2

⌋

, (2.15)

𝑆_𝑓^𝑢 = 𝑆_𝑎𝑣− 𝑆_𝑓^𝑑. (2.16)

In order to obtain the user throughput, both the MAC and PHY overheads should be removed from the available raw bandwidth. According to the assumptions as mentioned above, the MAC and PHY overheads for a DL subframe in the conventional mechanism can be computed as

𝑆_𝑜ℎ^𝑑 = 𝑆_𝑙𝑝+ 𝑆_{𝑓 𝑐ℎ}+⌈ 2𝐵_𝑔𝑚ℎ+ 2𝐵_𝑐𝑟𝑐+ 𝐵_𝑚𝑎𝑝^𝑑 + 𝐵_𝑖𝑒^𝑑 + 𝐵_𝑚𝑎𝑝^𝑢 + 5𝐵_𝑖𝑒^𝑢 𝐶_𝑚𝑎𝑝

⌉

, (2.17)

where 𝑆_𝑙𝑝 and 𝑆_{𝑓 𝑐ℎ} are the durations of long preamble and FCH in OFDM symbols, which are regarded as the PHY overhead. The notations 𝐵_𝑔𝑚ℎand 𝐵_𝑐𝑟𝑐represent the size of generic

MAC header and CRC in bytes; while 𝐵_𝑚𝑎𝑝^𝑑 , 𝐵_𝑚𝑎𝑝^𝑢 , 𝐵_𝑖𝑒^𝑑, and 𝐵_𝑖𝑒^𝑢 are the size of DL-MAP, UL-MAP, DL-MAP IE, and UL-MAP IE in bytes respectively. It is noted that all these parameters are designated as the MAC overhead. Moreover, the bytes per OFDM symbol for transmitting these MAP messages is denoted as 𝐶_𝑚𝑎𝑝, whose value depends on the selection of the MCS. Since only two SSs are considered in the analytical model, three DL bursts are described in the FCH, i.e., for broadcasting MAP messages and transmitting data packets to 𝑆𝑆₁ and 𝑆𝑆₂ individually. The DL-MAP message contains only an end of map IE; while the UL-MAP message associated with UL-MAP IEs describe five bursts, including initial ranging, bandwidth request, two data grants for 𝑆𝑆₁ an 𝑆𝑆₂ individually, and end of map IE. Furthermore, both the DL-MAP and UL-MAP messages are individually attached with a generic MAC header and a CRC as denoted in (2.17). On the other hand, the MAC and PHY overhead for a UL subframe consists of two contention intervals (i.e., the initial ranging and the bandwidth request) and the short preambles. Since there are two SSs in considered, two short preambles will be transmitted in total by both 𝑆𝑆₁ and 𝑆𝑆₂. Therefore, the overhead for a UL subframe can be obtained as

𝑆_𝑜ℎ^𝑢 = 𝑆𝑐𝑖+ 2𝑆𝑠𝑝, (2.18)

where 𝑆_𝑐𝑖 and 𝑆_𝑠𝑝 are the durations of contention intervals and a single short preamble in OFDM symbols respectively.

Recall that the main objective of this study is to determine the saturation user throughput and the corresponding overhead of IEEE 802.16 PMP networks. The focus is to compute the maximum number of MAC PDUs that can be transmitted and received by a station within a frame respectively. It is assumed that there is always a packet to be transmitted in each the connection for any of the SS. Moreover, based on connection-oriented feature of the IEEE 802.16 MAC protocol, the resource scheduling within the BS is implemented on a per connection basis. Therefore, each connection is designed to receive a fair share of service.

In other words, the available bandwidth for an SS in a frame depends on the number of connections it possesses. Based on (2.12), (2.13), (2.15) and (2.17), the maximum number of

MAC PDUs that can be transmitted by the BS to 𝑆𝑆_𝑘during a DL subframe is computed as

where 𝐵_𝑝𝑘𝑡 represents the mean size of MAC service data unit (SDU) in bytes; while 𝐶_𝑘 is the bytes per OFDM symbol for 𝑆𝑆_𝑘 to transmit packets. Similarly, the maximum number of MAC PDUs that is transmitted by 𝑆𝑆_𝑘 to the BS during a UL subframe can be obtained as

According to the definition of the user throughput, only the packets that are received by the destination stations should be considered. The maximum number of effective MAC PDUs for 𝑆𝑆_𝑘 in a DL subframe will still be the same as (2.19), i.e.,

𝜀^𝑑_𝑘(𝐵_𝑝𝑘𝑡, 𝐶_𝑘) = 𝜑^𝑑_𝑘(𝐵_𝑝𝑘𝑡, 𝐶_𝑘). (2.21)

However, the maximum number of effective MAC PDUs for 𝑆𝑆_𝑘 in a UL subframe becomes

𝜀^𝑢_𝑘(𝐵_𝑝𝑘𝑡, 𝐶_𝑘) =

It is noted that the parameter 𝑚^𝑢_𝑘 as appeared in (2.20) is not counted since it denotes the number of two-hop intra-cell connections in the UL direction, which should not be considered in the computation of effective throughput in (2.22). Based on (2.21) and (2.22), the user throughput of 𝑆𝑆_𝑘 in the DL and UL subframes, respectively, can be derived as

𝑇_𝑘^𝑑(𝐵_𝑝𝑘𝑡, 𝐶_𝑘) = 𝜀^𝑑_𝑘(𝐵_𝑝𝑘𝑡, 𝐶_𝑘) ⋅ 8𝐵_𝑝𝑘𝑡

𝐿_𝑓 , (2.23)

𝑇_𝑘^𝑢(𝐵_𝑝𝑘𝑡, 𝐶_𝑘) = 𝜀^𝑢_𝑘(𝐵_𝑝𝑘𝑡, 𝐶_𝑘) ⋅ 8𝐵_𝑝𝑘𝑡

𝐿_𝑓 , (2.24)

where 𝐿_𝑓 denotes the duration of a frame in seconds. Combining (2.23) and (2.24), the saturation user throughput that is achieved in the IEEE 802.16 PMP network can therefore be computed as the sum of the user throughput of each SS, i.e.,

𝑇_{𝑐𝑜𝑛𝑣}^𝑚𝑎𝑥(𝐵_𝑝𝑘𝑡, 𝐶_𝑘) =

Furthermore, the corresponding overhead in terms of time per frame can be derived from (2.17) and (2.18) as

where 𝐿_𝑠is the duration of an OFDM symbol in seconds. It is noted that the second term in (2.26) represents the overhead caused by the duplication of the data packets; while the MAC overhead of the received data packets is specified in the last term.