In this chapter, we introduce the principles of mandatory DCF mechanism of IEEE 802.11 MAC and OFDM characteristics of IEEE 802.11a PHY. Relying on these understandings, we can further analyze the IEEE 802.11a systems in the later chapters.
Busy Medium DIFS Backoff DATA
SIFS ACK
DIFS Backoff DATA Busy Medium DIFS Backoff DATA
SIFS ACK DIFS
DIFS Backoff DATA
Busy Medium DIFS Backoff DATA ACK Timeout Backoff DATA Busy Medium DIFS Backoff DATA ACK TimeoutACK Timeout Backoff DATA
Busy Medium DIFS Backoff DATA
SIFS ACK
EIFS Backoff DATA Busy Medium DIFS Backoff DATA
SIFS ACK EIFS
EIFS Backoff DATA (a)
(b)
(c)
Figure 2.1: Timing of frame transmissions under basic access method (a) Successful frame transmission (b) Frame retransmission due to data frame failure (c) Frame retransmission due to ACK failure
Busy Medium DIFS Backoff RTS
SIFS CTS
SIFS DATA
SIFS ACK
DIFS Backoff Busy Medium DIFS Backoff RTS
SIFS CTS
SIFS DATA
SIFS ACK
DIFS Backoff
Busy Medium DIFS Backoff RTS CTS Timeout Backoff Busy Medium DIFS Backoff RTS CTS Timeout Backoff
Busy Medium DIFS Backoff RTS
SIFS CTS
SIFS DATA ACK Timeout Backoff Busy Medium DIFS Backoff RTS
SIFS CTS
SIFS DATA ACK Timeout Backoff
Busy Medium DIFS Backoff RTS
SIFS CTS
EIFS Backoff Busy Medium DIFS Backoff RTS
SIFS CTS
EIFS Backoff
Busy Medium DIFS Backoff RTS
SIFS CTS
SIFS DATA
SIFS ACK
EIFS Backoff Busy Medium DIFS Backoff RTS
SIFS CTS (a) Successful frame transmission (b) Frame retransmission due to RTS
failure (c) Frame retransmission due to data frame failure (d) Frame retransmission due to CTS failure (e) Frame retransmission due to ACK failure
MAC Layer
Variable number of OFDM symbols Coded/OFDM
(data rate is indicated in RATE) Coded/OFDM
(BPSK, R = 1/2)
Figure 2.3: Layer and sublayer defined in IEEE 802.11a standard
Figure 2.4: PPDU frame format defined in IEEE 802.11a standard
Signal detection,
Figure 2.5: Structure of PLCP preamble field defined in IEEE 802.11a standard
Figure 2.6: Bit assignment in SIGNAL field
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Scrambler Initialization Reserved SERVICE bits
"0""0""0""0" "0""0""0" R R R R R R R R R
Transmitt Order
Figure 2.7: Bit assignment in SERVICE field
Table 2.1: Rate-dependent parameters of IEEE 802.11a PHY
Mode Data rate
(Mbits/s) Modulation
Coding rate
(R)
Code bits per subcarrier
(NBPSC)
Code bits per OFDM
symbol (NCBPS)
Data bits per OFDM
symbol (NDBPS)
Data bytes per OFDM symbol
(BpS)
1 6 BPSK 1/2 1 48 24 3
2 9 BPSK 3/4 1 48 36 4.5
3 12 QPSK 1/2 2 96 48 6
4 18 QPSK 3/4 2 96 72 9
5 24 16-QAM 1/2 4 192 96 12
6 36 16-QAM 3/4 4 192 144 18
7 48 64-QAM 2/3 6 288 192 24
8 54 64-QAM 3/4 6 288 216 27
Table 2.2: Timing-related parameters of IEEE 802.11a PHY
Parameter Value NSD: Number of data subcarriers 48
NSP: Number of pilot subcarriers 4
NST: Number of subcarriers, total 52 (NSD + NSP)
∆F: Subcarrier frequency spacing 0.3125 MHz (=20MHz/64) TFFT: IFFT/FFT period 3.2 µs (1/∆F)
TSlot: Slot time 9 µs
TSIFS: SIFS time 16 µs
TDIFS: DIFS time 34 µs (=TSIFS + 2×TSlot) CWmin: minimum contention window size 15
CWmax: maximum contention window size 1023
TPREAMBLE: PLCP preamble duration 16 µs (TSHORT+ TLONG) TSIGNAL: Duration of the SIGNAL BPSK-OFDM symbol 4.0 µs (TGI + TFFT) TGI: Guard interval duration 0.8 µs (TFFT / 4) TGI2: Training symbol guard interval duration 1.6 µs (TFFT / 2) TSYM: Symbol interval 4 µs (TGI + TFFT ) TSHORT: Short training sequence duartion 8 µs (10 × TFFT / 4) TLONG: Long training sequence duartion 8 µs (TGI2 + 2 × TFFT)
Table 2.3: Contents of RATE field
Rate (Mbps) R1-R4
6 1101 9 1111 12 0101 18 0111 24 1001 36 1011 48 0001 54 0011
Chapter 3
Link Adaptation for IEEE 802.11a Systems
As mentioned in Section 2.1.2, one of the benefits of the RTS/CTS access method is to increase the system performance by minimizing the amount of time wasted when collisions occur on long data frames. On the other hand, the two additional frames without any payload (RTS and CTS) decrease efficiency. For that reason, the use of the RTS/CTS access method is under the control of the manageable object, RTS_Threshold, which indicates the data length under which the data frames should be sent without RTS/CTS. The data frame size is the only parameter that is used for deciding whether the mechanism is applied [2][3]. But what we are really concerned about is the transmission duration of the data frame not the length. However, the higher the PHY rate, the shorter the transmission time. Therefore, an integrated mechanism, which could consider both the length of the data frame and the used PHY rate, is needed.
In [10], a generic method to analyze the goodput (good throughput, excluding MAC/PHY overheads at MAC layer) performance of the IEEE 802.11a system is presented. Utilizing and extending this goodput analysis, we propose an link adaptation (LA) algorithm which could not only select the transmission rate but also
the MAC mechanism (the basic access method or RTS/CTS access method). In this LA algorithm, besides data payload length, we consider other parameters like the wireless channel condition and number of contending stations to select the best combination of the MAC mechanism and PHY mode.
In this chapter, we will analyze the collision probability of the IEEE 802.11a system in Section 3.1. Some detailed MAC and PHY characteristics including MAC/PHY overheads and error performance of IEEE 802.11a PHY modes will be introduced in Section 3.2 and 3.3, respectively. Section 3.4 shows the analysis of effective goodput of the 802.11a system. Based on the results obtained in Section3.4, a LA algorithm is proposed in Section 3.5 and evaluated in Section 3.6.
3.1 Collision Probability
In [2][21], Markov process is used to analyze the performance of the 802.11 system and show that the Markov chain analysis method is suitable for examining the performance of the IEEE 802.11 system, which captures the effect of the CW value and binary slotted exponential backoff procedure used by DCF in IEEE 802.11. The Markov model in [22] can be regarded as an extension of the model in [2][21], which takes the retransmission limit of MAC frames into account, therefore a more exact model is proposed. With this Markov model, the behavior of a station is examined, which we use to get the collision probability p that a transmitted frame collides with another. We put the obtained collision probability in the 802.11a system to the later use for computing the effective goodput.
In this section, the assumptions necessary for the presented analytical framework are as follows:
1. We ignore the effect of frame errors due to bit errors introduced by channel noise since the effect of frame errors is small (shown in later section).
Therefore, frames are received in error only when they encounter collisions due to other simultaneous transmissions.
2. No hidden stations and propagation delays are considered.
3. The network consists of a fixed number of contending stations n and every station always has a frame available for transmission (saturated conditions).
Moreover being all frames consecutive, each frame needs to wait for a random backoff time before transmitting.
4. The main approximation is that the collision probability of a transmitted frame is constant and independent of the number of retransmission that this frame has experienced in the past.
Let b(t) be the stochastic process representing the backoff window size for a
given station at slot time t. A discrete and integer time scale is adopted: t and t+1 correspond to the beginning of two consecutive slot times, and the backoff counter of each station decrements at the beginning of each slot time. Let s(t) be the stochastic process representing the backoff stage (0,…,m) of the station at time t. According to
the above assumptions, the bi-dimensional process {s(t), b(t)} is possible to be modeled with the discrete-time Markov chain, which is shown in Figure 3.1.
In IEEE 802.11a PHY, CWmin and CWmax equal to 15 and 1023, respectively (as shown in Table 2.2). Therefore we have
(3.1)
where i ∈(0,m) is called backoff stage, W=(CWmin+1), and 2
]
m’W=(CWmax+1),
so for IEEE 802.11a PHY, we have m’ = 6. We use m to represent maximum backoff stage. As specified in IEEE 802.11, this value could be larger than m’ and the CW value will be hold after that, which is shown in equation (3.1). In fact, m is the ShortRetryLimit and equal to 7 according to the standard described in Section 2.1.1.
In this Markov chain, the only non-null one-step transition probabilities are
{ } [ ]
where we adopt the short notation:
{
1 1, | ,0 0} {
( 1) 1, ( 1) 1| ( ) 0, ( ) 0}
P i k i k =P s t + =i b t+ =k s t =i b t =k (3.3) These transition probabilities account, respectively, for: i) the decrements of the backoff timer; ii) after a successful transmission, the backoff timer of the new frame starts from the backoff stage 0, and thus the backoff is initially uniformly chosen in the range (0,W0 -1); iii) when an unsuccessful transmission occurs at backoff stage i-1, the backoff stage increases, and the new initial backoff value is uniformly chosen in the range (0,Wi -1); iv) at the maximum backoff stage, the CW value will be reset if the transmission is unsuccessful or restart for a new frame if the transmission is successful.
Let b P be the
stationary distribution of the Markov chain. First note that ( ) ( )
then
With (3.5) and transition in the chain, equation (3.6) can be simplified as
,0
Thus, by (3.5) and (3.7), all the value bi,k are expressed as functions of the value b0,0
and collision probability p. Impose the normalization condition for the stationary distribution as follows.
As any transmission occurs when the backoff counter is equal to zero, regardless of the backoff stage, the probabilityτthat a station transmits in a randomly chosen slot time can be expressed as
1 where b0,0 can be obtained from equation (3.9).
However, in general, depends on the collision probability p, which is still
unknown. To find the value of p, it is sufficient to note that the probability p that a transmitted packet encounters a collision is the probability that, in a time slot, at least one of the n-1 remaining stations transmit. The fundamental independence assumption given above implies that each transmission sees the system in the same state, i.e., in steady state. At steady state, each remaining station transmits a frame with probability
. This yields
Therefore, equations (3.10) and (3.11) represent a nonlinear system with the two unknown variables and p, which can be solved by the numerical technique. It is easy to prove that this system has a unique solution. In fact, inverting (3.11), we can obtain
1− −1 . This is a continuous and monotone increasing function in the range ), that starts from τ∗( )0 =0 and grows up to
( )1 =1 τ( )p ( )p
τ
. Equation defined by (3.10) is also continuous in the range . Moreover, is trivially shown to be a monotone decreasing function. Uniqueness of the solution is now proven noting that and
(0,1) p ∈
( )0
τ >τ∗( )0 τ( )1 <τ∗( )1 . Figure 3.2 shows the numerical solutions of both equations with varying values of n, the number of contending stations. For each value of n, the solution yields a unique value
for the collision probability p that we will utilize to compute the effective goodput in the later section. The value of the collision probability is sensitive to the number of stations, n. This is shown in Figure 3.2 and Figure 3.3 in which the value of p increases as we increase the number of stations, n. This is an expected result because the number of stations increases, there is more contention among all the stations.
3.2 MAC/PHY Layer Overheads
As shown in Figure 3.4(a), in IEEE 802.11 MAC, each MAC data frame, or MPDU, consists of the following components: the MAC header, variable-length information frame body (MAC service data unit, MSDU), and FCS. The MAC overhead due to the MAC header and the FCS is 28 octets in total. Actually, an additional field of Address 4 is used only for the wireless AP-to-AP communication, which is not common, and hence we assume that is not used. Besides, the information frame body (data payload) can be up to 2312 if encryption is used, but we assume that encryption is not used. Figure 3.4(b)~(d) illustrate the frame formats of the RTS, CTS, and ACK frames, which are 20, 14, and 14 octets long respectively.
Review Section 2.2, during the transmission, a PLCP preamble and a PLCP header are added to an MPDU to create a PPDU. The PPDU format of the IEEE 802.11a PHY is shown in Figure 2.4, which includes the PLCP preamble, PLCP header, PSDU (i.e. MPDU conveyed from MAC), tail bits, and pad bits (if necessary). The PLCP preamble field, with the duration of TPREAMBLE, is composed of 10 repetitions of a short training signal (0.8 µs) and two repetitions of a long training signal (4 µs).
The PLCP header, except the SERVICE field, with the duration of TSIGNAL, constitutes a single OFDM symbol, which is transmitted with the BPSK modulation and rate-1/2 convolutional coding. The six zero tail bits are used to return the convolutional decoder to the zero state and the pad bits are used to make the resulting bit string into a multiple of OFDM symbols. Each OFDM symbol interval, denoted by TSYM, is 4 µs. The 16-bit SERVICE field of the PLCP header and MPDU (along with six tail bits and pad bits), represented by DATA, are transmitted at the data rate specified in the RATE field. Table 2.2 lists the related characteristics for IEEE 802.11a PHY.
Note that, while the data frame MPDUs can be transmitted at any supported data rate, all the control frames, including the RTS, CTS, and ACK frames, have to be transmitted at one of the rates in the BSS basic rate set so that they can be understood by all the stations in the same network. BSS basic rate set data rates are preset for all the stations in BSS. {6 Mbps, 12Mbps, 24Mbps} is the set of the IEEE 802.11a mandatory data rates, and it will be assumed to be the BSS basic rate set in our example and simulations. In addition, the RTS and CTS frame will be transmitted at the lowest rate in the BSS basic rate set (6Mbps) while the ACK frame transmitted at the highest rate in the BSS basic rate set that is less than or equal to the rate of the data frame it is acknowledging. For example, if a data frame is transmitted at the rate of 18 Mbps, the corresponding ACK frame will be transmitted at the rate of 12 Mbps.
Based on the above descriptions, to transmit a frame with an l-octet data payload over IEEE 802.11a PHY using the PHY mode m, the transmission duration is
( )
Note that the Bytes-per-Symbol information for the PHY mode m, BpS(m), is given in Table 2.1. Similarly, the transmission duration for a RTS frame and a CTS frame are
( )
( )
respectively. Note that the transmission rate of RTS and CTS is the lowest BSS basic rate, 6Mbps, i.e. PHY mode 1. And the transmission duration for an ACK frame using the PHY mode m’ is
The relation between m and m’ is discussed above.
3.3 Error Performance of PHY Modes 3.3.1 Bit Error Probability
The symbol error probability (SER) for an M-ary (M=4, 16, 64) QAM with the average received SNR per symbol, γ, can be calculated by [23]
( ) 1 1 ( )2
{ }
The Q-function is defined as
( ) 1 2 2
With a Gray coding, the bit error probability (BER) for an M-ary QAM can be approximated by
Note that the 4-ary QAM and QPSK modulation are identical. For the BPSK modulation, BER is the same as SER, which is given by Obviously, the error performance of a modulation scheme varies with different
received SNR values.
3.3.2 Frame Error Probability
In [24], an upper bound was given on the frame error probability under the assumption of binary convolutional coding and hard-decision Viterbi decoding with independent errors at the channel input. For an l-octet long frame to be transmitted using the PHY mode m, this bound is
(3.22) ( ), 1 1 ( )8l
em
P l γ ≤ − − P
where the union boundPum( )γ of the first-event error probability is given by
(3.23)
where dfree is the free distance of the convolutional code selected in the PHY mode m, ad is the total number of error events of weight d, and is the probability that an incorrect path at the distance d from the correct path being chosen by the Viterbi decoder. When the hard-decision decoding is applied, is given by
d( )
where is BER for the modulation scheme selected in the PHY mode m and given by (3.20) or (3.21). The value of a
ρ
d can be obtained either from the transfer function or by a numerical search [25]. Here, we use the ad coefficients provided in [26]. Figure 3.5 shows the upper bound BER performance, , of the different IEEE 802.11a PHY modes versus the average received SNR, .
m( ) Pu γ γ
Consider the RTS/CTS access method, the only frame will suffer the collision is the RTS frame. Thus, , the RTS frame error probability, can be calculated by
where n represent the number of contending stations. Note that the term
( )
(
1 24 8 20 16 6 8,
Pe + + + γ
)
represents the PCLP SIGNAL field (24-bit long) plus the length of the RTS frame format (20-octet long) along with the 16-bit SERVICE field, six tail bits, and pad bits, which are transmitted with the BPSK modulation and rate-1/2 convolutional coding, i.e. PHY mode 1.On the other hand, , the CTS frame error probability, , the data frame error probability, and , the ACK frame error probability are shown below
3.4 Effective Goodput Computation
In this section, we focus our analysis on the effective goodput of the RTS/CTS access method. Our objective is to calculate the maximum throughput achievable with the IEEE 802.11a WLAN at the MAC layer for a given SNR by taking into consideration of the MAC, PHY, and retransmission overheads. In our analysis, we make following assumptions: i) the transmitter generates, at an infinite rate, l-octet long data payload (MSDU); ii) the MSDU is not fragmented; iii) the propagation delays are neglected; iv) the constant wireless channel condition throughout the entire frame delivery period. After a station makes the PHY mode selection and starts transmitting, the selected PHY mode will be used for all the potential retransmissions.
In brief, a frame with l-octet data payload is to be transmitted using the PHY mode m
over the wireless channel with condition γ . Let m’ denote the PHY mode used for the
corresponding ACK frame transmission and it is determined based on m according to the rule specified in Section 3.2.
To simplify the analysis, we separate the transmission phases of the RTS/CTS access method into two stages: i) channel reservation ii) data transmission. The first stage, channel reservation, includes the DIFS deferral phase, backoff phase, RTS transmission phase, SIFS deferral phase, CTS transmission phase, and SIFS deferral phase. The remained phases belong to the data transmission stage. Now, let’s consider the entire delivery progress of the frame transmission. Since the maximum numbers of transmission attempt to deliver the RTS frame and the data frame are specified by ShortRetryLimit, denoted as ns, and LongRetryLimit, denoted as nl, respectively.
Recalling Section 2.1.1, every station maintains an SSRC as well as an SLRC.
Whenever a CTS frame is received in response to the RTS frame, the SSRC is reset to 0. On the other hand, SLRC is reset to 0 when an ACK is received in response to a data frame. That is to say two counters are independent to each other. An example will make it clearer. Let ns be 7 and nl be 4. At beginning, we send the RTS frame but unfortunately it fails, i.e. it fails at the channel reservation stage, for first 6 times. At the 7th attempt, it succeeds. So there are 7 retries in total so far. Now the data frame is sent afterwards, but the transmission fails at the data transmission stage. Then one retry count for the data frame is consumed, i.e. there are 3 more left. Again, the RTS frame is sent, and it will get 7 more chances. Therefore, for a single data frame, there may be totally 28 (7×4) RTS frames and 4 data frames sent in the transmission progress in the worst-case scenario. We illustrate all discussions above with Figure 3.6.
stands for the probability of a successful channel reservation within the
, ( ,
succ ch
P γ n)
retry limit and it can be calculated by
is the probability of a successful channel reservation. represents the probability of a successful data transmission and it can be computed by
, , ( ,
By referring to Figure 2.2(a), a successful channel reservation duration is equal to a backoff delay, plus the RTS transmission time, plus an SIFS time, plus the CTS transmission time, and plus an SIFS time. However, whenever the channel reservation fails, the station has to wait for a CTS_Timeout period or an EIFS interval, and then execute a backoff procedure before the retransmission (see Figure 2.2(b) and (d)).
According to the IEEE 802.11 MAC standard, an EIFS interval is equal to an SIFS time plus a DIFS time plus the ACK transmission time at the most robust 6 Mbps and a CTS_Timeout is equal to an SIFS time plus a CTS transmission time plus a Slot_Time.
Therefore, the average transmission duration of the channel reservation can be
Therefore, the average transmission duration of the channel reservation can be