Exercises — Wi-Fi (IEEE 802.11) — CSMA - CA, bands

The medium is half-duplex (and broadcast): a radio can transmit or receive, not both at once, because its own transmitter drowns its receiver. So collision detection mid-send is impossible → Wi-Fi uses CSMA/CA, not CSMA/CD.

(a) DIFS — the longer gap for ordinary data. (b) SIFS — the shortest gap, guaranteeing the handshake reply wins the channel. Shorter wait = higher priority.

The NAV (Network Allocation Vector). This is virtual carrier sense: you trust a neighbour's announced duration instead of listening. See MAC Layer and ARQ / ACK for where the ACK fits.

Backoff time $=\text{counter}\times \text{slotTime}=5\times 9\mu s=45\mu s$. Each idle slot decrements the counter by one; $5$ slots of $9\mu s$ each = $45\mu s$. (This ignores DIFS itself, which is the fixed gap before counting begins.)

$C{W}_{\text{new}}=2(15+1)-1=32-1=31$. The cap $1023$ is not reached, so no clamping. Why the $+1$ then $-1$? A window "$0$ to $15$" has $16$ slots; doubling slots ($16\to 32$) gives range "$0$ to $31$". The algebra just re-encodes "double the number of slots."

$CW=2(31+1)-1=64-1=63$. Slot count went $32\to 64$, so the range is now "$0$ to $63$."

(a) X has the smaller count, so X reaches $0$ first — after 4 idle slots ($4\times 9=36\mu s$). (b) While X counts $4\to 0$, Y counts $7\to 3$. The moment X starts transmitting the channel is busy, so Y freezes at counter $=3$. (c) Y resumes from 3 (freeze, not reset). It needs only $3$ more idle slots — it kept its lead, giving fairness and avoiding starvation. Contrast this with ALOHA and Slotted ALOHA, which has no countdown memory at all.

Physical carrier sense only reports what you can hear. A and C are hidden from one another, so each honestly measures "idle" while their frames still collide at B. The rescue is RTS/CTS: A sends a tiny RTS, B replies with a CTS that both A and C hear; C then sets its NAV and stays quiet. Virtual carrier sense fixes what physical sensing cannot. Full treatment in Hidden and Exposed Terminal Problems.

No 5 GHz signal: higher frequency ⇒ shorter wavelength ⇒ waves are more strongly absorbed and scattered by walls, so the energy dies before reaching the laptop. Slow-but-stable 2.4 GHz: longer wavelength diffracts around and penetrates obstacles (reach), but 2.4 GHz has only 3 non-overlapping channels and is crowded by Bluetooth/microwaves, capping throughput. This is a range-vs-throughput trade-off — see Frequency, Wavelength and Attenuation and Bandwidth vs Throughput.

Apply $2(CW+1)-1$ four times:

• After 1st: $2(16)-1=31$
• After 2nd: $2(32)-1=63$
• After 3rd: $2(64)-1=127$
• After 4th: $2(128)-1=255$ Sequence: $15\to 31\to 63\to 127\to 255$. None hits the cap $1023$. The final window "$0$ to $255$" offers 256 slot choices, so two retrying stations now have only a $1/256$ chance of picking the same slot — doubling the window each time makes repeat collisions exponentially unlikely.

Add the pieces in order (look at figure s01's timeline): $\text{DIFS}+(\text{backoff}\times \text{slot})+\text{DATA}+\text{SIFS}+\text{ACK}$ $=34+(3\times 9)+200+16+24=34+27+200+16+24=301\mu \mathbf{s}.$ Note the ACK waits only SIFS (16), not DIFS — that short gap is what keeps the handshake from being pre-empted.

No. RTS/CTS is worth it only when the data frame is large, because then a collision wastes a lot of airtime and the small handshake cost is cheap insurance. For tiny frames, the RTS+CTS+SIFS overhead can rival or exceed the frame itself, so you pay more than a collision would cost. That is why real stacks use an RTS threshold: apply the handshake only above some frame size.

A fixed $p$ is tuned for one load. If many stations suddenly contend, a fixed $p$ keeps producing the same collision rate — no self-correction — so throughput collapses (the classic ALOHA and Slotted ALOHA instability). Binary exponential backoff is feedback-driven: each collision doubles the window, cutting each station's effective transmit probability, which spreads retries and lowers pressure exactly when congestion rises. When traffic clears, a successful ACK resets $CW$ to its minimum, restoring responsiveness. It self-tunes; fixed $p$ cannot.

Priority in CSMA/CA is inverse to waiting gap: shorter gap → wins. To beat ACK (which uses SIFS) it must wait less than SIFS. So define a new interframe space $\text{XIFS}<\text{SIFS}<\text{DIFS}$. Constraint: $\text{XIFS}$ must still be longer than the receiver's turnaround time (the time to switch from receive to transmit), otherwise the reply starts before the radio is physically ready. So $\text{turnaround}<\text{XIFS}<\text{SIFS}$. (Real 802.11e uses exactly this idea with AIFS values per traffic class.)

Same countdown ⇒ both reach $0$ after 2 idle slots ($18\mu s$) and transmit simultaneously → collision at the receiver. Neither gets an ACK within the SIFS window, so both assume loss. Each doubles its window: $C{W}_{\text{new}}=2(15+1)-1=31$. They then re-draw backoff from "$0$ to $31$" — now $32$ choices, so the chance they collide again drops to $1/32$. This is the avoidance loop closing: random draw → tie → collision → widen window → re-draw.

Recognition ::: half-duplex radio ⇒ CA not CD; SIFS < DIFS; NAV = virtual sense. Application ::: backoff time = counter × slot; $C{W}_{\text{new}}=2(CW+1)-1$ capped at $C{W}_{\max }$. Analysis ::: smaller count wins, loser freezes (fairness); hidden terminals need RTS/CTS. Synthesis ::: full timeline DIFS+backoff+DATA+SIFS+ACK; RTS/CTS only for big frames. Mastery ::: exponential backoff self-tunes; IFS ordering encodes priority.