ECE4024 Chap.1 Cellular Systems and Wireless Channels
Cellular Systems and Wireless Channels
This chapter establishes the physical and network views of a wireless link. It separates path loss, shadowing, multipath, noise and interference, then connects a received-power calculation to cellular coverage and frequency reuse.
The practical goal is to identify the mechanism before choosing an equation, keep gains and losses in consistent logarithmic units, and finish every range or margin result with the assumptions that make it valid.
What this chapter covers
- 01
Cellular reuse and the distinction between coverage and capacity
- 02
Transmitters, propagation channels and receiver thresholds
- 03
Free-space loss and wavelength dependence
- 04
Log-distance path loss and environmental exponents
- 05
Log-normal shadowing, fade margin and outage
- 06
Antenna gains, effective aperture and EIRP
- 07
Thermal noise, interference and SINR
- 08
Link closure, cell radius and physical-sense checks
Worked example · free
Audit a complete link budget
- +1Write the logarithmic balance with gains positive and losses negative: received level equals 21 + 5 + 4 - path loss - 2.
- +2Set received level to -90 dBm and isolate path loss: 21 + 5 + 4 - 2 - (-90) = 118 dB.
- +1Substitute the predicted 113 dB loss to obtain received level 21 + 5 + 4 - 2 - 113 = -85 dBm.
- +1Subtract the threshold: -85 - (-90) = 5 dB of margin.
- +1Interpret the result as a model-based median margin that still needs a shadowing or fading reliability calculation when outage is requested.
Key terms
- Path loss
- The reduction in average received power caused by propagation, expressed as a positive loss that grows with distance under the chosen model.
- Shadowing
- Slow location-dependent variation around a mean path-loss trend, commonly represented as a Gaussian quantity in decibels.
- Fade margin
- The difference between a predicted received level and the minimum receiver threshold, used with a variation model when assessing outage.
- EIRP
- Transmitter power multiplied by transmit-antenna gain in linear units, or their sum in logarithmic units, referenced to an isotropic radiator.
- Frequency reuse
- The repeated use of the same spectrum in sufficiently separated cells to increase spatial capacity while controlling co-channel interference.
- SINR
- The desired received power divided by interference plus noise power, the appropriate quality measure when other transmitters contribute unwanted energy.
Cellular Systems and Wireless Channels FAQ
What is the difference between path loss and shadowing?
Path loss describes the average distance trend under a propagation model. Shadowing describes slower random variation around that trend because different locations encounter different obstructions. They belong to different layers of the coverage calculation.
Why is receiver sensitivity subtracted in an allowable-loss calculation?
Sensitivity is a negative received-power threshold. Solving the received-power balance for path loss subtracts that negative value, increasing the amount of loss the link can tolerate. Writing the balance before rearranging prevents a sign mistake.
Does a positive fade margin guarantee coverage?
No. It says the predicted level exceeds the threshold by a stated amount. Reliability still depends on the shadowing or fading distribution, interference conditions and whether the propagation model describes the actual environment.
Why can smaller cells increase capacity?
Smaller cells can reuse the same spectrum more frequently across a region, serving more simultaneous users. The benefit comes with more sites, handovers, backhaul and interference coordination, so it is not a free improvement.
When should I use SINR instead of SNR?
Use SINR when co-channel users or other transmitters contribute significant unwanted power. An SNR-only calculation treats thermal noise but ignores interference, which can produce an optimistic performance prediction in a reused cellular band.
Exam move
Draw the transmitter, channel and receiver before calculating. Label every gain, loss and threshold with its unit. Practise isolating allowable path loss and then independently recomputing received power. Keep free-space, log-distance and shadowing models separate, because each answers a different question. For cellular prompts, distinguish link coverage from frequency-reuse capacity and state whether interference is included.
End every numerical response with the model boundary and a physical-sense check: added loss should lower received power, a stricter threshold should shorten range, and a greater fade margin should reduce outage only under the stated statistical model. Build a three-column revision sheet for coverage, capacity and reliability. Under coverage, place wavelength, free-space loss, log-distance range and receiver sensitivity.
Under capacity, place cells, reuse clusters, co-channel separation and sectorisation. Under reliability, place shadowing, fade margin and outage probability. This prevents a familiar formula from being used for the wrong system question. Rehearse a complete link budget in both directions: first calculate received power from a specified distance, then solve the same model backwards for maximum distance.
Keep dBm as absolute power, dB as a gain or loss and dBi as antenna gain; do not convert a sum of decibel terms into watts halfway through. For a reuse problem, sketch the reference cell and the co-channel tier before substituting a cluster size. State whether the calculation assumes omnidirectional cells, equal transmit powers and a path-loss exponent model.
Finally, challenge every result with a controlled change: raise the carrier frequency, add feeder loss, tighten sensitivity, increase the reuse distance or introduce a shadowing margin. Predict the direction before recalculating. If the number moves the other way, inspect the sign convention and the exponent rather than polishing the final sentence.
A strong written response separates a deterministic median path-loss prediction from random local fading and never promises guaranteed coverage from a single nominal budget.
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