Every calculation in Module 9 described one link, alone in its band, using the whole channel. That link does not exist. A cell has hundreds of handsets, a WiFi channel has a dozen laptops, and all of them want the same slice of spectrum at the same moment. So the question this module opens with is not how to make one link work — M9-L4 settled that — but how to let many links work in one shared medium without destroying each other. That is the multiple access problem, and there have only ever been a handful of answers to it.
One Medium, Many Users
Think of the shared resource as a rectangle. One axis is frequency, and you own some total bandwidth of it. The other axis is time, and it runs forever. Every transmission occupies a patch of that rectangle, and two transmissions that overlap in both axes collide — each becomes interference to the other, exactly the interference M9-L3 priced. A multiple access scheme is therefore nothing more than a rule for cutting up the rectangle, plus the machinery to enforce it.
There are three ways to cut it, and they are not variations on a theme — they are genuinely different geometries:
The Resource, and the Three Cuts
R_{\text{total}} \;=\; B \times T \times S \quad\Longrightarrow\quad \text{FDMA: split } B, \;\; \text{TDMA: split } T, \;\; \text{CDMA: share both}
The same total resource, partitioned three ways. FDMA gives each user a narrow strip of frequency for all time. TDMA gives each user the whole bandwidth for a brief, repeating instant. CDMA gives every user all the bandwidth all the time and separates them by an algebraic property of their signals instead. The third row of the equation, S, is space — the fourth dimension, exploited by the sectorisation of M7-L3 and the multi-antenna methods of M7-L4, and taken up properly in M10-L3.
FDMA — frequency division multiple access. Each user gets their own carrier frequency. This is the oldest idea in radio: it is what M2-L3 and M3-L1 called frequency-division multiplexing, and it is how every AM and FM broadcast station on the dial coexists
TDMA — time division multiple access. Users share one carrier and take turns, in a repeating frame of slots. Digital only, because you cannot store and burst an analogue waveform cheaply
CDMA — code division multiple access. Every user transmits over the whole band simultaneously, tagged with a distinct spreading code; the receiver recovers one user by correlating against that code and treats the rest as noise
SDMA — space division, the fourth axis. Sectorised antennas (M7-L3) already do a crude version, and beamforming and MIMO (M7-L4, M10-L3) do it properly. It is orthogonal to the other three, so real systems combine it with all of them rather than choosing it instead
FDMA: Divide the Frequency
FDMA is the scheme you already understand, because it is how the radio dial works. Assign each user a channel of bandwidth Bch and a filter tuned to it, and the users never meet. It requires no synchronisation whatsoever — two FDMA users need not agree on the time of day — which is exactly why it was the only practical scheme in the analogue era. The cost is a guard band: a sliver of spectrum between channels, or at the band edges, that nobody may use, because real filters do not have vertical skirts and real transmitters spill energy sideways.
Worked example: AMPS, the first cellular system
The US AMPS allocation was 25 MHz in each direction (824–849 MHz up, 869–894 MHz down), with a channel spacing of 30 kHz
Channel count by simple division: 25 × 106 / 30 × 103 = 833.33, so 833 channels. The deployed numbering carried 832, one fewer, because the top of the band was left clear
That 25 MHz was split between two competing operators, 12.5 MHz each, with a 10 kHz guard band at each edge of an operator’s block. So per operator: (12.5 × 106 − 2 × 10 × 103) / 30 × 103 = 12.48 × 106 / 30 × 103 = 416 channels
Cross-check: 2 × 416 = 832, and the two 20 kHz guard allowances cost 40 × 103 / 30 × 103 = 1.33 channels out of 833.33 ✓
So the band-edge guard bands cost only 40 kHz of 25 MHz, which is 0.16%. The often-repeated claim that guard bands are the great waste of FDMA is, at least here, false
Now apply M9-L3’s frequency reuse. With a cluster size of N = 7, one cell gets 416/7 = 59 channels, and 21 of an operator’s channels were control channels rather than voice. Fifty-odd simultaneous calls per cell is the whole capacity of first-generation cellular
Why 30 kHz, and where did the intra-channel guard go? AMPS voice was narrowband FM with a peak deviation of 12 kHz and audio to 3 kHz, so Carson’s rule from M4-L2 gives 2(Δf + fm) = 2(12 + 3) = 30 kHz exactly. The channel is Carson-full: there is no spare sliver inside it. Adjacent-channel protection came instead from the roll-off of the FM spectrum plus a planning rule that neighbouring channels were never assigned in the same cell — which is a guard band paid for in reuse rather than in hertz. Notice how M9-L3’s adjacent-channel interference and its near-far problem are the reason that rule exists.
FDMA Channel Count
N = \left\lfloor \frac{B_{\text{total}} - 2B_{\text{guard}}}{B_{\text{ch}}} \right\rfloor
The floor matters: a partial channel is not a channel. For the AMPS operator block, (12.5 MHz − 20 kHz)/30 kHz = 416.0, and the answer is a hard number. User 417 is refused. Hold on to that word — hardness is the property that CDMA gives up, and it is the deepest difference in this lesson.
What FDMA actually costs
An idle channel is wasted spectrum. A user holding a channel and saying nothing still owns it. Speech is silent roughly 60% of the time, so an FDMA voice network throws away most of what it allocates — and the scheme has no mechanism to notice
Every user needs a full RF chain. Continuous transmission on a private frequency means the handset’s power amplifier is on continuously, the duplexer must separate a transmit and receive band that are live at the same instant, and the filters must be sharp. That is silicon, current and cost per user
Narrow channels are fragile in a multipath channel. A 30 kHz channel is far narrower than the coherence bandwidth argument of M8-L2 permits you to ignore: the whole channel fades together, flat, so there is no frequency diversity to exploit and the fade margin is the brutal Rayleigh one M9-L4 quoted at ~20 dB
Narrow channels have good sensitivity, though. M9-L1’s noise floor scales as 10 log₁₀B, and 10 log₁₀(30 × 103) = 44.77 dB, so an AMPS receiver’s thermal floor sits at −174 + 44.77 = −129.2 dBm before noise figure. Compare the −101 dBm of a 20 MHz WiFi channel: 28 dB better, which is real coverage. FDMA is not a bad scheme, it is an old one
TDMA: Divide the Time
TDMA turns the rectangle on its side. All users share one carrier, and each gets the whole of it for a short slot inside a repeating frame. Because the slot repeats, a user who needs a steady 13 kbit/s can be served by a burst of 33 kbit/s occupying an eighth of the time — and the other seven eighths belong to somebody else. This only works digitally: the speech has to be encoded, buffered, and fired off faster than real time, which is why TDMA arrived with the second generation and not before.
Two divisions, and everything else in a TDMA system follows from them. The gross rate is set by the carrier bandwidth and the modulation (M6-L2 and M6-L3); the number of slots is a standards decision that trades users against per-user rate; and the slot duration then falls out. The overhead appears in neither formula, which is precisely why it has to be tracked separately.
Worked example: GSM, eight users per carrier
Carrier spacing 200 kHz, carrying GMSK at a gross bit rate of exactly 1625/6 = 270.833 kbit/s. Spectral efficiency 270.833/200 = 1.354 bit/s/Hz, which is the order M6-L3 would expect of a filtered binary scheme
Frame length 60/13 ms = 4.615 ms, divided into 8 slots, so a slot lasts 4.615/8 = 0.5769 ms = 577 µs
Bits per frame: 270.833 × 103 × 4.615 × 10−3 = 1250 bits, so bits per slot = 1250/8 = 156.25. The quarter bit is real, and it is why the frame is 60/13 ms rather than something round
Gross rate per user: 270.833/8 = 33.85 kbit/s. The full-rate speech codec produces 13 kbit/s, and channel coding expands that to a 22.8 kbit/s traffic channel — so 22.8/33.85 = 67% of a user’s gross allowance carries their coded speech
Where the other third goes, inside those 156.25 bits: 3 tail + 57 data + 1 stealing flag + 26 training + 1 stealing flag + 57 data + 3 tail = 148 bits, plus 8.25 bits of guard period. Check: 148 + 8.25 = 156.25 ✓
Payload fraction: 114/156.25 = 72.96%. The 26 training bits alone are 16.6% of the slot — and they are not waste, they are the channel estimate the equaliser needs in order to undo the multipath of M8-L2
Guard time in seconds: one bit lasts 1/270833 = 3.692 µs, so 8.25 bits = 30.5 µs, which is 8.25/156.25 = 5.28% of the slot
Guard time is a distance, and timing advance is how you beat it
Ask what that 30.5 µs is for and TDMA becomes a geometry problem. Two handsets in the same cell sit at different distances from the base station, so their bursts arrive at different delays, and a burst that arrives late lands on top of the next user’s slot. Radio covers 3 × 108 × 30.5 × 10−6 = 9.1 km in one guard period, so unaided, GSM tolerates a path-length spread of about 9 km — adequate for a small cell and useless for a large one. The fix is timing advance: the base station measures each handset’s round-trip delay and orders it to transmit that much early.
GSM signals timing advance in whole bit periods, 0 to 63, so the largest correction is 63 × 3.692 = 232.6 µs of round trip
One way that is 116.3 µs, and 3 × 108 × 116.3 × 10−6 = 34.9 km. That is the origin of GSM’s famous ~35 km cell radius limit, and it is a protocol limit rather than a link-budget one — M9-L4’s budget would happily allow more
Bursting saves power. A handset transmitting one slot in eight has its power amplifier off 87.5% of the time. At 2 W peak the average is 250 mW, and the amplifier can be smaller and cheaper than a continuous one
Bursting also buys measurement time. In its idle slots a handset can retune and measure neighbouring cells, which is what makes GSM’s handover decisions possible at all — an FDMA handset transmitting continuously on one frequency cannot look anywhere else
DECT is the other TDMA system worth naming, because it makes different choices with the same machinery: a 1.728 MHz carrier at 1152 kbit/s gross, a 10 ms frame of 24 slots used as twelve transmit/receive pairs, so a slot is 10/24 = 0.4167 ms = 417 µs carrying 1152 × 103 × 417 × 10−6 = 480 bits. Its speech codec is 32 kbit/s ADPCM rather than 13 kbit/s, because a cordless phone in a house can afford bits that a cellular network cannot. Same scheme, different economics.
CDMA: Divide by Code
CDMA refuses to cut the rectangle at all. Every user transmits across the whole bandwidth for the whole time, and the separation is algebraic rather than geometric. Each user’s data stream is multiplied by a fast pseudo-random code unique to them — a process called spreading, because it takes a narrow signal and smears its energy across a wide band. The receiver multiplies by the same code again and integrates. The wanted user’s code correlates with itself and collapses back to a narrow, full-strength signal; everybody else’s code does not, and their energy stays spread out and looks like a small rise in the noise floor.
The whole scheme lives or dies on one number, the ratio of the fast code rate to the slow data rate. It is called the processing gain, and it says how much the despreading step improves the wanted signal relative to everything else in the band.
Rc is the chip rate, in chips per second — a chip is one symbol of the spreading code, and it is deliberately not called a bit because it carries no information. Rb is the user’s data rate. Since the occupied bandwidth W is set by the chip rate (M6-L2’s Nyquist argument applies to chips exactly as it does to symbols), the ratio is equally a bandwidth expansion factor. It is a power ratio, so it converts to decibels with 10 log₁₀, not 20 — the distinction M2-L4 insisted on.
Worked example: IS-95
Chip rate 1.2288 Mcps in a 1.25 MHz carrier; the full-rate vocoder runs at 9.6 kbit/s
Processing gain: 1.2288 × 106 / 9.6 × 103 = 128, and in decibels 10 log₁₀(128) = 21.07 dB
Cross-check without a calculator: 128 = 27, and a doubling is 3.0103 dB, so 7 × 3.0103 = 21.07 dB ✓
Where 1.2288 Mcps comes from is worth seeing, because nothing about it is arbitrary: 9.6 kbit/s through a rate-1/2 convolutional code gives 19.2 ksymbol/s, and each symbol is spread by a 64-chip Walsh code, so 19.2 × 103 × 64 = 1.2288 × 106 chips per second ✓
UMTS made the same choice at a larger scale: 3.84 Mcps in a 5 MHz carrier, so for 12.2 kbit/s AMR voice the processing gain is 3.84 × 106 / 12.2 × 103 = 315, i.e. 10 log₁₀(315) = 25.0 dB — about 4 dB more than IS-95, bought with four times the bandwidth
Note what the gain is not: it is not free capacity, and it is not coding gain. It buys nothing that a narrowband system with the same total bandwidth and the same coding could not also buy. What it buys is the ability to overlap, which is a different and more useful thing
The signal sits below the noise floor
Here is the consequence that makes CDMA feel like a trick. Take M9-L1’s relation between SNR in the occupied band and Eb/N₀: SNR = Eb/N₀ + 10 log₁₀(Rb/W). An IS-95 user needing Eb/N₀ = 7 dB therefore needs an in-band SNR of 7 + 10 log₁₀(9.6 × 103 / 1.2288 × 106) = 7 − 21.07 = −14.07 dB. The wanted signal is 14 dB below the noise and interference it is buried in, and it is still recovered perfectly, because the despreading operation supplies the missing 21 dB.
That is the same fact seen twice, and neither view is more true than the other. A spectrum analyser looking at the band sees no signal, only a slightly elevated noise floor — which is why spread spectrum began as a military technique for hiding transmissions, and why a CDMA carrier can be overlaid on a band that other services think is empty. It is also why a CDMA system has no channel you can point at. There is no 417th channel to be refused, because there were never any channels.
Capacity is soft, not hard
In FDMA and TDMA, an extra user beyond the count is refused and every existing user is unaffected. In CDMA, an extra user is admitted, and every existing user’s ratio gets slightly worse, because all the other users are the interference. This is the soft capacity of CDMA, and it means the capacity number is a design target rather than a physical count. Assume perfect power control so all N users arrive at the base station at equal power P. Then each user sees (N − 1)P of interference, so before despreading the ratio is 1/(N − 1), and after despreading Eb/N₀ = Gp/(N − 1).
Soft Uplink Capacity
N \;\approx\; 1 + \frac{G_p}{(E_b/N_0)_{\text{req}} \cdot \nu \cdot (1+f)}
ν is the voice activity factor — a talker is active about 40% of the time, and unlike FDMA, CDMA collects that saving automatically because a silent user simply stops adding interference. f is the fraction of interference arriving from other cells, typically about 0.6, and it exists because CDMA reuses every carrier in every cell. Thermal noise has been dropped from the denominator, so this is an interference-limited approximation and therefore an optimistic one.
Naive single-cell figure, continuous talkers: N − 1 = Gp/(Eb/N₀) = 128/100.7 = 128/5.012 = 25.5, so N = 26 users
Credit the voice activity factor ν = 0.4: 25.5/0.4 = 63.9, so N ≈ 65. This is the saving FDMA structurally cannot collect
Now pay for other-cell interference at f = 0.6: 63.9/1.6 = 39.9, so N ≈ 41 users per sector
Compare the same 1.25 MHz run as AMPS-style FDMA: 1.25 × 106 / 30 × 103 = 41.7 channels, and with N = 7 reuse that is 41/7 = 5.9 per cell. Three CDMA sectors at 41 give 123 per cell, and 123/5.9 = 21×
Treat that 21× with suspicion. It is the arithmetic the original CDMA capacity claims rested on, and it assumes perfect power control, perfect codes, a single-cell interference model patched with one correction factor, and no soft-handover overhead. Measured gains in deployed networks were smaller. The structural claim survives, though: CDMA reuses every carrier in every cell, so it never pays the factor-of-seven that reuse planning costs FDMA
Soft capacity cuts both ways. The pleasant half is graceful degradation: a stadium emptying into a cell does not produce a wall of blocked calls, it produces slightly worse quality for everyone and, eventually, dropped calls at the cell edge first — because the edge users are the ones with the least margin in M9-L4’s sense. The unpleasant half is that coverage and capacity are coupled. As users are added the interference floor rises, every user’s required received power rises with it, and the cell edge moves inward. This is cell breathing, and it has no analogue in FDMA or TDMA, where a cell’s radius does not depend on how busy it is.
The Near-Far Problem, and Why CDMA Is Hard
Every number in that capacity calculation assumed all users arrive at equal power. Drop the assumption and CDMA collapses. In FDMA a nearby shouting handset is on a different frequency, and M9-L3 showed it can still leak into yours — a genuine problem, worth 48.93 dB in that lesson’s example, but a filtering problem with a filtering answer. In CDMA there is no filter, because the near user is in your band by design. This is the near-far problem in its purest form, and it is the defining engineering constraint of the scheme.
Quantify it with M8-L4’s path-loss exponent. A user at 100 m and a user at 1 km, in terrain with n = 4, differ in path loss by 10 × 4 × log₁₀(10) = 40 dB. If both transmit at the same power, the near user arrives 40 dB — a factor of 104 — stronger. Against the interference budget computed above, where 40 nominal users share the floor, that single user contributes as much interference as 10,000 nominal ones. The cell does not degrade; it stops. Even a 20 dB error is fatal: 102 = 100 nominal users’ worth of interference from one handset, against a design total of 41.
The answer is fast closed-loop power control, and it has to be fast because it is chasing the fading of M8-L3, not just the geometry. IS-95 runs it at 800 Hz — sixteen adjustments per 20 ms frame — in steps of about 1 dB
Two loops, not one. An open loop lets the handset set its own power from the strength of what it receives, which handles the tens of decibels of geometry instantly; a closed loop lets the base station correct the residual, which is what the 1 dB steps are for
What matters is not the mean but the scatter. Every user being 1 dB high is harmless, since only ratios matter. Residual variance is not harmless: it raises the interference sum faster than it raises any wanted signal, so the standard’s ~1 dB accuracy target is a capacity specification wearing a control-loop costume
This is the honest answer to “why is CDMA harder than TDMA?” A TDMA system needs power control for battery life and for the adjacent-channel problem, and can tolerate several decibels of error. A CDMA system needs it to function, on every user, continuously, faster than the channel changes. That is a signalling load, a battery load and an algorithmic risk that TDMA simply does not carry
Orthogonality Only Holds When You Are Synchronised
Now the asymmetry that explains more about real CDMA systems than any other single fact. Two codes are orthogonal when their correlation is exactly zero, so despreading one removes the other completely. Walsh–Hadamard codes are perfectly orthogonal — a set of 64 length-64 sequences with zero mutual correlation — and that sounds like the end of the story. It is not, because Walsh codes are orthogonal only when aligned in time. Slide two Walsh codes past each other by a single chip and their correlation is no longer zero; it may be large.
So look at where alignment is available and where it is not. On the downlink one transmitter — the base station — generates every user’s signal, from one clock, so the codes leave the antenna in perfect step and arrive at any given handset having travelled one identical path. Alignment is free, so IS-95 uses the 64 Walsh codes to separate downlink users, and in the absence of multipath they do not interfere at all. On the uplink, every signal comes from a different handset, at a different distance, with a different clock. Aligning them at the base station to within a fraction of a chip — a chip lasts 1/1.2288 MHz = 814 ns, which is 244 m of propagation — would be a synchronisation problem far worse than TDMA’s guard time. So the uplink does not try.
Downlink: Walsh codes, orthogonal by construction. The price is that the set is finite — 64 codes, of which the pilot, sync and paging channels consume several — so the downlink has a hard-ish code limit sitting inside an otherwise soft system
Uplink: long pseudo-noise sequences, orthogonal only on average. IS-95 gives each user a different phase of a code of period 242 − 1 chips, which at 1.2288 Mcps repeats every 3.6 × 106 s = 41 days. Such codes are not orthogonal; they merely have low cross-correlation, so each interfering user contributes a small residue rather than zero. The capacity formula above is exactly the accounting of those residues
Multipath breaks the downlink too, which is the deep point. A delayed echo of the base station’s own signal arrives misaligned with the direct path, so the Walsh codes lose orthogonality against their own reflections. This is why a CDMA receiver has a rake: several correlators, each locked to a different echo, whose outputs are combined. The multipath M8-L2 treated as a hazard becomes a diversity source — the same reversal M10-L2 and M10-L3 will make with OFDM and MIMO
The Three Schemes Side by Side
None of the three is the winner, which is why all three shipped and two of them are still in service. Read the table down a column and you get a system; read it across a row and you get an engineering trade.
Property
FDMA
TDMA
CDMA
How it divides
Frequency — a permanent private strip
Time — a repeating slot on a shared carrier
Neither. All users, all band, all the time, separated by code
Overhead type
Guard bands, plus channel spacing above the occupied bandwidth
Guard times, plus training and tail bits; GSM 8.25 of 156.25 bits = 5.28% guard, 27% total
No guard region at all — the overhead is the interference other users add, priced by the processing gain
Capacity behaviour
Hard. 416 channels means user 417 is refused
Hard. 8 slots per carrier, and the ninth caller waits
Soft. User 42 is admitted and everyone’s SINR drops a little. Graceful degradation, and cell breathing
Synchronisation needed
None between users
Tight — to a fraction of a slot, hence timing advance
Downlink tight and free; uplink deliberately abandoned in favour of low-correlation codes
Handset complexity
Low logic, but a sharp filter, a duplexer and a continuously-on amplifier
If your constraint is that receivers must be cheap and asynchronous — broadcast, or a legacy analogue estate — choose FDMA. It is the only scheme that works with no shared clock and a single filter, which is why the AM and FM dials of M3 and M4 will outlive most of this lesson
If your constraint is battery life and predictable capacity — a voice network that must quote a channel count to a regulator and run for a week on a handset battery — choose TDMA. Bursting turns off the amplifier 87.5% of the time and hands you idle slots for measurement, and the capacity number is a number you can defend
If your constraint is spectrum, and you can afford tight power control — a dense urban network with no more bandwidth to buy — choose CDMA. You escape the factor-of-seven reuse penalty, you collect the voice activity saving for free, and you get soft handover and graceful overload. You pay for it in every handset’s complexity and in a control loop that must never fail
If your constraint is wideband data over a badly dispersive channel, none of the three is the answer, and that is the honest verdict of this lesson. Wide TDMA bursts need an equaliser whose difficulty grows with bandwidth; wide CDMA needs a rake with more fingers than is economic. The scheme that solves it is OFDM, and it is the next lesson
Where This Goes
Module 10 is about how one medium is shared, and this lesson has covered only the first three answers. The rest of the module supplies the fourth, the modern reworking of the first, and the question this lesson quietly ignored:
M10-L2 — OFDM and OFDMA. Take FDMA’s idea of narrow strips, make the strips so narrow that each one fades flat, make them mathematically orthogonal so they need no guard bands between them, and then hand groups of them to different users. It is FDMA rebuilt on the insight that orthogonality is cheaper than separation
M10-L3 — MIMO. The fourth axis, space. Several antennas at both ends send parallel streams through the same frequency at the same time, which is a partition the rectangle in this lesson cannot even draw
M10-L4 — duplexing. Notice that this whole lesson discussed how users share, and never how a single user’s two directions share. Splitting uplink from downlink by frequency (FDD) or by time (TDD) is the same two ideas applied at right angles to the problem
Module 11 — the standards. GSM chose TDMA, IS-95 chose CDMA, UMTS chose CDMA, LTE and 5G chose OFDMA, and each choice was made under the constraints of its decade. The table above is the argument they were all having
Key Takeaways
Multiple access is a rule for partitioning one time–frequency resource. FDMA splits frequency, TDMA splits time, CDMA splits neither and separates by code. Space is the fourth axis, and it belongs to sectorisation (M7-L3) and MIMO (M10-L3) rather than to this lesson.
FDMA, worked: 25 MHz of AMPS at 30 kHz spacing gives 25 × 106/30 × 103 = 833 channels; per 12.5 MHz operator block with 10 kHz edge guards, (12.5 × 106 − 20 × 103)/30 × 103 = 416. Guard bands cost 0.16%; the real costs are idle channels and one RF chain per user.
TDMA, worked: GSM’s 200 kHz carrier at 1625/6 = 270.833 kbit/s, 8 slots in a 4.615 ms frame, so a slot is 4.615/8 = 577 µs and 1250/8 = 156.25 bits. Per user 270.833/8 = 33.85 kbit/s gross for a 13 kbit/s codec. Guard period 8.25 bits = 30.5 µs = 5.28% of the slot = 9.1 km of propagation.
Timing advance extends that 9.1 km: 63 bits × 3.692 µs = 232.6 µs round trip, so 116.3 µs one way and a 34.9 km cell radius — a protocol limit, not a link-budget one.
CDMA, worked: processing gain Gp = Rc/Rb = 1.2288 × 106/9.6 × 103 = 128 = 21.07 dB (and 27 × 3.0103 dB ✓). At Eb/N₀ = 7 dB the in-band SNR is 7 − 21.07 = −14.07 dB: the signal sits below the noise floor and is still recovered.
Capacity is soft. N ≈ 1 + Gp/((Eb/N₀)ν(1+f)) = 1 + 128/(5.012 × 0.4 × 1.6) ≈ 41 per sector, against 41/7 = 5.9 per cell for the same 1.25 MHz as FDMA. Treat the resulting 21× as the optimistic end of a real structural advantage.
The near-far problem is why CDMA is hard. At n = 4, a 10× distance ratio is 40 dB, so one uncontrolled near handset supplies 104 nominal users’ worth of interference. Hence two-loop power control at ~1 dB and ~800 Hz, whose scatter, not its mean, is what costs capacity.
Walsh codes are orthogonal only when synchronised. So the downlink — one transmitter, one clock — uses them, while the uplink abandons orthogonality for long PN sequences with low cross-correlation. Multipath desynchronises the downlink against its own echoes, which is what the rake receiver exists to exploit.