Sources of Interference

M9-L1 built a noise floor out of physics: −174 + 10 log₁₀B, plus a noise figure. M9-L2 turned that floor into an error probability and warned you about one failure mode it could not explain — a measured BER curve that stops following theory and flattens into a floor, so that adding power no longer helps. This lesson is that explanation. In almost every deployed radio system, the thing limiting the link is not thermal noise at all. It is other transmitters, and the shift from one to the other changes the design rules completely.

The Real Limit Is Interference, Not Noise

Thermal noise is a fixed, known, well-behaved adversary. You compute it once from bandwidth and noise figure and it never surprises you. Interference is none of those things: it is another radio’s wanted signal arriving where it is not wanted, it varies as that radio’s traffic and its user’s position vary, and — the part that matters most — it scales with the same transmit powers your own signal scales with. So the quantity a real receiver lives or dies by is not the signal-to-noise ratio but the signal-to-interference-plus-noise ratio, SINR, in which the two impairments are simply added as powers before the ratio is taken.

They add as powers, not as amplitudes and not in decibels, because interference and noise are statistically independent of one another. That single fact is the source of every arithmetic mistake made on this page by beginners: you cannot add or average decibels. Convert each term to linear power, sum, then convert back — the discipline M2-L4 established.

Work the case that motivates the whole lesson. A handset receives a wanted signal at S = −80 dBm, in a 20 MHz channel whose thermal floor M9-L1 computed as N = −101 dBm, while a neighbouring cell reusing the same frequency arrives at I = −90 dBm. Convert: I = 10^−90/10 = 1.000 × 10⁻⁹ mW, and N = 10^−101/10 = 7.943 × 10⁻¹¹ mW. Sum them: 1.000 × 10⁻⁹ + 0.0794 × 10⁻⁹ = 1.0794 × 10⁻⁹ mW, which is 10 log₁₀(1.0794 × 10⁻⁹) = −89.67 dBm. So SINR = −80 − (−89.67) = 9.67 dB, against an SNR of −80 − (−101) = 21 dB if the interferer vanished. Eleven decibels of the link’s quality has been eaten by a transmitter the designer of this receiver has no control over.

Two details in that arithmetic repay attention. First, the noise contributed almost nothing: interference alone would give SIR = 10 dB, and folding in the thermal floor cost only 10 − 9.67 = 0.33 dB. That is what “interference-limited” means quantitatively — when I sits 11 dB above N, the noise term is a rounding error, and the entire M9-L1 exercise of shaving a decibel off the noise figure buys you almost nothing. Second, look at what happens if every transmitter in the system, yours and the interferer’s alike, turns up by 10 dB. Now S = −70 dBm and I = −80 dBm while N stays at −101 dBm, so I + N = 1.0079 × 10⁻⁸ mW = −79.97 dBm and SINR = −70 + 79.97 = 9.97 dB. Ten decibels of extra power bought 0.30 dB.

Co-Channel Interference and the Reuse Trade

Co-channel interference (CCI) is interference on exactly your own frequency, from a transmitter that is deliberately using it somewhere else. It is the unavoidable price of frequency reuse, and no filter can touch it: a filter separates signals by frequency, and by construction there is no frequency difference to separate. Cellular systems manage it geometrically instead. Divide the available channels into N groups, assign one group per cell, and tile the plane with that pattern; N is the frequency-reuse factor, and for a hexagonal tiling the distance D between two cells sharing a channel group, in units of the cell radius R, follows a fixed rule.

Check the four that matter. N = 3 gives D/R = √9 = 3.00; N = 4 gives √12 = 3.46; N = 7 gives √21 = 4.58; N = 12 gives √36 = 6.00. Now attach that geometry to propagation. A cell’s six nearest co-channel neighbours all sit at roughly distance D, the wanted base station sits at distance R, and M8-L1 gave received power falling as d⁻ⁿ with a path-loss exponent n around 3 to 4 in built-up terrain. Take the six first-tier interferers as equal and the estimate falls out.

Worked example: N = 7 with n = 4

D/R = √21, so (D/R)⁴ = 21² = 441 exactly — the fourth power of a square root of 21 is just 21 squared, which is worth noticing because it lets you skip the decimal. Divide by six: 441/6 = 73.5. In decibels, 10 log₁₀(73.5) = 18.66 dB. That number is the reason N = 7 became the canonical cellular reuse pattern: the analog AMPS system needed about 18 dB of C/I for acceptable voice quality, and 18.66 clears it with almost nothing to spare. Here is the whole family, and the second exponent column is the sobering one.

Read the table twice. Down the n = 4 column is the trade every network planner makes: larger N pushes co-channel cells further apart and buys C/I, but it splits the same channels among more cells. With 336 channels in the system, N = 7 gives 336/7 = 48 channels per cell and N = 12 gives 336/12 = 28 — a 42% cut in capacity (28/48 = 0.583) to buy 23.34 − 18.66 = 4.68 dB. Across the n = 3 column is something more uncomfortable: in a low-exponent environment, such as a line-of-sight street canyon or an open suburb, no reuse factor in the table reaches 18 dB. This is why modern systems abandoned static planning altogether — LTE and 5G run N = 1, every cell on every frequency, with a raw first-tier C/I that this formula puts at 1/6 = −7.78 dB, and recover the link by scheduling, coding and coordination rather than by geometry.

Adjacent Channel Interference

Adjacent channel interference (ACI) is the opposite case: a transmitter on a different frequency whose energy nevertheless lands in your channel. It has two independent causes and both must be fixed. On the transmit side, no modulated signal has truly zero energy outside its nominal band — M6-L2’s pulse shaping controls the roll-off but cannot abolish it, and any non-linearity in the power amplifier broadens the spectrum further. On the receive side, no filter has an infinitely steep skirt, so some of the neighbour’s in-band power leaks through yours. The transmit half is specified as ACLR (adjacent channel leakage ratio, sometimes ACPR), measured in dBc — decibels relative to the carrier.

Now the arithmetic that makes ACLR intuitive. Suppose a transmitter meets ACLR = 45 dBc, so its leakage into the neighbouring channel is 45 dB below its own carrier. If that transmitter arrives at your receiver 30 dB stronger than the signal you want, its leakage arrives at 30 − 45 = −15 dB relative to your wanted signal — that is, 15 dB below it. Harmless. Nothing about the transmitter changed, but now let it arrive 50 dB stronger: the leakage lands at 50 − 45 = +5 dB, five decibels above your wanted signal, and your link is dead. The same compliant transmitter is either invisible or fatal depending entirely on a power ratio it does not control.

The near-far problem is a power-control problem

That power ratio is set by geometry, and geometry is brutal. Put your wanted base station 500 m away and an adjacent-channel transmitter of equal power 20 m away, in terrain with n = 3.5. The path-loss difference is 10 × 3.5 × log₁₀(500/20) = 35 × log₁₀(25) = 35 × 1.398 = 48.93 dB. With the 45 dBc transmitter above, its leakage now sits 48.93 − 45 = 3.93 dB above the signal you are trying to receive. This is the near-far problem, and notice where the fix has to live: you cannot filter it, because the interferer is not really out of band any more once it is 49 dB stronger, and you cannot demand a better ACLR indefinitely because amplifier back-off costs efficiency and battery life. What you can do is stop the near transmitter shouting.

Hence power control: every transmitter is commanded to use the least power that meets its own target, so that all signals arrive at the receiver at comparable strengths and the worst-case ratio in the paragraph above never occurs. In cellular uplinks this is a closed loop running hundreds of times a second, fast enough to track the fading of M8-L3, and it is not an optimisation but a precondition — a CDMA uplink without power control simply does not work, for exactly this reason. The static counterpart is the guard band: leave a slice of spectrum unused between allocations so the roll-off has room to fall. Guard bands are cheap engineering and expensive spectrum, which is why they are shrinking; the 2.4 GHz Wi-Fi band gives the clearest illustration, with channels spaced 5 MHz apart but signals about 20 MHz wide, so only the set 1, 6 and 11 — 25 MHz apart in centre frequency — avoids overlap altogether.

Inter-Symbol Interference

The third kind of interference does not come from another transmitter at all. It comes from your own previous symbols, and you have already met it twice. M6-L2 introduced inter-symbol interference as the consequence of squeezing symbols through too narrow a channel: the pulse tails spill onto their neighbours, and Nyquist’s 2W limit with raised-cosine shaping is the cure. M8-L3 introduced the other route to the same damage: delay spread. Multipath delivers copies of each symbol at different delays, so a copy of symbol k arrives while symbol k+1 is being decided. The criterion is a comparison of two times.

Put numbers on the urban case. M8-L3 quoted σ_τ ≈ 1 µs for an urban macrocell. Run a 5 MBd symbol rate through it, so T_s = 1/(5 × 10⁶) = 200 ns, and the delay spread covers 1000/200 = 5 symbol periods — each decision is contaminated by roughly five of its predecessors. The 0.1 criterion says you would need T_s > 10 µs, i.e. a symbol rate below 100 kBd, to ignore the problem: fifty times slower than the rate we wanted. The frequency-domain view agrees, as it must. That channel’s coherence bandwidth is B_c ≈ 1/(5σ_τ) = 200 kHz, while a 5 MBd signal with a raised-cosine roll-off of α = 0.25 occupies 5 × 1.25 = 6.25 MHz — 31 coherence bandwidths. Deeply frequency-selective, exactly as the time-domain count of five symbols predicted. For contrast, GSM ran at 270.833 kBd, so T_s = 3.69 µs and the same 1 µs spread is 0.27 T_s: still too much to ignore, which is why every GSM receiver contained a Viterbi equaliser spanning a handful of symbols.

There are three families of fix, and each is a Module 10 subject rather than this lesson’s. What matters here is knowing which problem each one attacks:

• Equalisation — estimate the channel’s impulse response and invert it, or search over symbol sequences as GSM’s Viterbi equaliser did. Cost grows sharply with the number of symbol periods spanned, which is why it stops being practical somewhere around the five of our worked example
• Multicarrier transmission with a guard interval — split the data across many slow subcarriers so each one’s T_s comfortably exceeds σ_τ, and prefix each symbol with a copy of its own tail so the multipath echoes land in the copy rather than in the data. This is OFDM and its cyclic prefix, and it is M10-L2’s entire subject
• Spreading — use a signal much wider than the data rate so that delayed copies become resolvable and can be combined constructively instead of interfering. This is direct-sequence spread spectrum, opened in M10-L1
• Diversity and multiple antennas — do not fight the multipath, exploit it. M10-L3 shows how several antennas turn the delay-spread channel from an impairment into extra capacity

One structural difference is worth flagging before we leave ISI, because it is the reason it shows up as a BER floor. Thermal noise is independent of your signal, so more transmit power always improves the ratio. ISI is made of your signal, so raising transmit power raises the interference by exactly as much and the ratio does not move at all — the same futility the SINR arithmetic showed for co-channel interference, arriving by a completely different route. An uncorrected ISI channel has a residual error rate that no amount of power will reduce, and that is precisely the flattened curve M9-L2 told you to look out for.

Man-Made and Impulsive Noise

Between the deliberate transmitters and the unavoidable thermal floor sits a third category: energy radiated by equipment that was never intended to be a radio at all. It is conventionally called man-made noise, though most of it is closer to interference in character, and unlike thermal noise it is neither uniform in frequency nor constant in time.

• Switching power supplies and LED drivers — a converter chopping at a few hundred kilohertz radiates that fundamental and a long harmonic comb reaching well into HF and VHF; a cheap unfiltered lamp driver can raise a receiver’s floor across an entire band
• Power lines and powerline communications — corona discharge on high-voltage lines produces broadband impulses synchronised to the mains cycle, while PLC modems deliberately inject signal across roughly 2–30 MHz on wiring that is an efficient accidental antenna
• Vehicle ignition — each spark is a wideband impulse; the classic VHF interference source, much reduced by modern shielded ignition but still measurable
• Microwave ovens — a magnetron at 2.45 GHz, in the middle of the same ISM band as Wi-Fi and Bluetooth, conducting on alternate mains half-cycles so it emits in bursts of about 10 ms every 20 ms at 50 Hz. Wi-Fi in the lower half of the 2.4 GHz band degrades measurably while an oven runs
• Electric motors, welders, thermostats and arcing contacts — anything that makes or breaks a current makes a broadband impulse, which is why an EMC standard exists for almost every product category

The frequency dependence is strong and useful. ITU-R Recommendation P.372 fits urban business-area man-made noise as roughly F_am = 76.8 − 27.7 log₁₀(f/MHz) decibels above the thermal reference, valid over the lower part of the spectrum. At 100 MHz that is 76.8 − 55.4 = 21.4 dB above thermal — a receiver there is not thermally limited by any stretch. At 250 MHz it has fallen to 76.8 − 66.4 = 10.4 dB, and the trend continues, which is the quantitative reason cellular bands at 2 GHz are usually thermal-noise-limited in the absence of other radios while an HF or VHF receiver almost never is.

Now the caveat that genuinely matters, and it is a caveat about M9-L2 rather than about this lesson. Impulsive noise is not Gaussian, so the Q-function analysis does not apply to it, and the direction of the error is the dangerous one: Q understates the damage. Model a channel as background noise of standard deviation σ for 99% of the time and 10σ for the remaining 1%. Gaussian analysis at a decision distance of 4σ predicts Q(4) = 3.17 × 10⁻⁵. The true error rate is 0.99 × Q(4) + 0.01 × Q(0.4) = 3.14 × 10⁻⁵ + 3.45 × 10⁻³ = 3.48 × 10⁻³ — a factor of 110 worse, and dominated entirely by the 1% of the time nobody modelled. The total noise power rose by only 10 log₁₀(0.99 + 0.01 × 100) = 10 log₁₀(1.99) = 2.99 dB, so a link budget that averaged the noise would predict a mild 3 dB penalty. To recover the original 3.17 × 10⁻⁵ by brute force you would need the decision distance out at 27.3σ, which is 20 log₁₀(27.3/4) = 16.7 dB more signal. Averaged noise power is the wrong statistic for impulsive interference; so is the independent-bit-errors assumption behind M9-L2’s PER formula, since impulse errors arrive in bursts, which is exactly what interleaving exists to break up.

Interference the receiver makes itself

Not all of it arrives from outside. A receiver front end is only approximately linear, and its non-linearity manufactures interference from signals that would otherwise be harmless. Two strong signals at f₁ and f₂ produce third-order intermodulation products at 2f₁ − f₂ and 2f₂ − f₁, and the reason third order is singled out is that those two frequencies land close to the originals — often inside your own channel, where no filter can remove them. Two carriers at 2110 and 2120 MHz put products at 2100 and 2130 MHz, 10 MHz either side. The figure of merit is the third-order intercept point, IP3.

Take an LNA with IIP3 = −10 dBm fed two tones at −30 dBm each. Then P_IM3 = 3(−30) − 2(−10) = −90 + 20 = −70 dBm, which is 40 dBc below each tone — equivalently 2(−10 + 30) = 40 dBc, the same number by the shortcut. Raise the tones by 10 dB to −20 dBm and P_IM3 = −60 + 20 = −40 dBm, now only 20 dBc down. Ten decibels of extra input cost twenty decibels of rejection, so the interference a receiver generates internally grows far faster than the signals causing it — and this is why a receiver can be perfectly quiet on the bench and unusable next to a transmitter mast.

The related failure is desensitisation, also called blocking. A strong signal, even one entirely outside your channel, drives the front end toward compression: gain falls, the effective noise figure rises, and your wanted signal is degraded without the interferer ever appearing in band. The relevant specification is the 1 dB compression point, and standards test for it explicitly, defining blocker levels tens of decibels above the wanted signal that a receiver must tolerate with only a stated loss of sensitivity. Notice that blocking, intermodulation and ACI are all consequences of dynamic range rather than of noise, which is why a low noise figure is necessary and nowhere near sufficient.

Mitigation, and Who Owns Each Fix

There is no single interference remedy, and the useful way to organise the toolbox is by who can deploy each tool. Some live inside the radio and are the physical-layer designer’s business; some are decisions about where to put base stations and which frequencies to give them, which is network planning; and a few are neither, being regulatory or mechanical.

Two of those rows deserve emphasis because they are the ones beginners reach for in the wrong order. Filtering is the instinctive answer to interference and it is the only tool on the list that cannot help with co-channel interference — and co-channel interference is the dominant impairment in every modern cellular network, since they all run N = 1. Conversely, sectorisation looks like a mere hardware detail and is one of the largest single wins available: 4.77 dB for three sectors, 10 log₁₀(6) = 7.78 dB for six, obtained purely by not radiating where you do not need to. The directivity that M7-L2 defined and the arrays that M7-L4 built are, seen from here, interference-management devices.

Two smaller honesty points close the toolbox. First, several of these techniques trade one interference type for another rather than removing interference outright: narrowing a filter to reject ACI eats into your own signal, and sectorising a site raises the handover rate, which raises signalling load. Second, some interference is neither accidental nor negotiable — deliberate jamming exists, and radio-frequency spectrum is shared by treaty and licence rather than by physics, which is why M11 spends its time on standards and coexistence rules and not only on waveforms.