LTE Link Budget & MAPL Calculator
Maximum allowable path loss (MAPL) for the LTE uplink and downlink, with uplink noise over the allocated resource blocks and the limiting direction named.
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Worked example: 256 kbit/s uplink on 4 resource blocks
Maximum allowable path loss: 126.80 dB
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How it works
LTE link budget and MAPL formula
The maximum allowable path loss (MAPL) is the most loss the path between a base station and a terminal can have while a terminal at the cell edge still gets its service. It is the EIRP less the receiver sensitivity, plus the gains at the receiving end, less the allowances for shadowing, building entry and interference. The uplink and the downlink each have one, and the smaller one sets the size of the cell.
The base station listens only to the resource blocks a terminal is scheduled, 180 kHz each, so the uplink noise floor is taken over those blocks rather than the whole channel. In the downlink the cell's power is spread evenly over every block of the carrier (3GPP TS 36.213 clause 5.2), so a user on some of them receives only that share. The required SINR comes from the cell edge data rate through the link level curve of 3GPP TR 36.942 Annex A.1, or is entered directly, and the shadow margin comes from the share of cell edge locations to be served.
MAPL = EIRP − S + Grx − Lrx + Gdiv − Mσ − BEL − Mi
S = kT₀ + 10 log₁₀(k × 180 000) + NF + SINR
SINR = 10 log₁₀(2^(η/α) − 1)
Mσ = σ × z(p)
Downlink EIRP on k blocks = EIRP − 10 log₁₀(N_RB / k)
- MAPL
- maximum allowable path loss, in dB
- EIRP
- uplink: the terminal's power class from 3GPP TS 36.101 Table 6.2.2-1 plus its antenna gain, less body loss; downlink: the base station power over all its ports, less feeder loss, plus antenna gain; in dBm
- S, NF
- receiver sensitivity in dBm, and the receiver noise figure in dB
- kT₀
- thermal noise density at the reference temperature T₀ = 290 K of ITU-R P.372-18: −173.975 dBm/Hz, often rounded to −174
- k, N_RB
- resource blocks allocated to the user, and on the whole carrier
- SINR
- signal to interference plus noise ratio the cell edge service needs, in dB
- η, α
- spectral efficiency the cell edge rate needs, in bps/Hz: the rate divided by k × 180 kHz, the share of subframes in that direction and the share of resource elements left after reference signals and control; and the TR 36.942 Table A.1 attenuation factor, 0.6 downlink and 0.4 uplink
- Grx, Lrx
- receiving antenna gain and the loss behind it: base station antenna and feeder in the uplink, terminal antenna and body loss in the downlink, in dB
- Gdiv
- uplink receive diversity gain, an assumption you enter, in dB; zero when the SINR comes from TR 36.942, whose curve already assumes two receive antennas
- Mσ, σ, z(p)
- shadow margin in dB: the shadowing standard deviation σ, 8, 10 or 12 dB for urban, suburban and open areas in ITU-R P.1546-6 Annex 5 section 12, or your own, times z(p), the normal quantile of the cell edge location probability p
- BEL, Mi
- building entry loss and interference margin, in dB
Standards
- 3GPP TS 36.101 Table 6.2.2-1: UE maximum output power by band and power class
- 3GPP TS 36.101 Table 7.3.1-1: UE reference sensitivity
- 3GPP TS 36.101 Table 5.6-1: channel bandwidth to resource blocks
- 3GPP TS 36.211 clause 6.2.3: resource block of 12 subcarriers at 15 kHz
- 3GPP TS 36.213 clause 5.2: downlink power allocation, reference signal power constant across the bandwidth
- 3GPP TR 36.942 Annex A.1: attenuated Shannon bound for cell edge rate to required SINR
- ITU-R P.1546-6 Annex 5 section 12: shadow fading standard deviation by environment
- ITU-R P.372-18 section 1.2.1: reference temperature of 290 K for thermal noise
Worked example
Worked example: 256 kbit/s uplink on 4 resource blocks
A class 3 handset (23 dBm in TS 36.101) with a 0 dBi antenna and 3 dB of body loss sends 256 kbit/s on 4 of the 50 resource blocks of a 10 MHz band 28 FDD carrier, to a base station with a 17 dBi antenna, 2 dB of feeder loss and a 5 dB noise figure, for 90 per cent of cell edge locations in open country with a 3 dB interference margin.
| Step | Working | Result |
|---|---|---|
| Noise floor on 4 blocks | −173.975 + 10 log₁₀(720 000) + 5 | −110.40 dBm |
| Spectral efficiency needed | 256 000 / (720 000 × 12/14) | 0.415 bps/Hz |
| Required SINR | 10 log₁₀(2^(0.415/0.4) − 1) | 0.22 dB |
| Shadow margin | σ × z(0.9) = 12 × 1.282 | 15.38 dB |
| Maximum allowable path loss | 23 + 0 − 3 − (−110.40 + 0.22) + 17 − 2 − 15.38 − 3 | 126.80 dB |
The 12/14 is the uplink reference signal taking 2 of the 14 symbols in each subframe, and on an FDD carrier every subframe carries uplink. TR 36.942 fits its curve for two receive antennas, so no diversity gain is added on top. Taken over all 50 blocks, 9 MHz, the noise floor would be 10.97 dB higher and the MAPL 10.97 dB lower.
What is MAPL in an LTE link budget?
MAPL is the maximum allowable path loss: the most loss the path between the base station and a terminal can have while the cell edge still gets its service at the stated location probability. It is the EIRP less the receiver sensitivity, plus the receiving antenna gain, less the losses and margins. The uplink and the downlink each have one, and the smaller sets the cell. A propagation model turns it into a range: this calculator uses Okumura-Hata or COST 231 Hata only inside 150 to 2000 MHz, base station heights of 30 to 200 m and terminal heights of 1 to 10 m, and flags a range outside 1 to 20 km, or outside 1 to 100 km up to 1500 MHz, where ITU-R P.529-3 extends it. The LTE Cell Range tool takes the same MAPL to the 3GPP TR 38.901 models as well.
What is wrong with using the channel bandwidth for uplink noise?
The base station receiver integrates noise over the resource blocks a terminal is scheduled, not the whole carrier. Using the channel bandwidth overstates the uplink noise floor by 10 log₁₀ of the ratio, which is about 14 dB for four resource blocks on a 20 MHz carrier. The error is pessimistic, so it can lead to more sites than a network needs.
Is the uplink always the limiting direction?
No. At a wide uplink allocation the uplink usually limits, because the terminal has much less power than the base station. As the allocation narrows the uplink noise falls with it, and at some point the downlink becomes the limiting direction. With a typed SINR the calculator reports the allocation where that happens; with a cell edge data rate it reports the allocation that gives the uplink the most. A narrower downlink allocation does not help the downlink in the same way: the user receives only its share of the cell power, so the signal falls with the noise.
How does a cell edge data rate become a required SINR?
The calculator takes the data rate over the allocated resource blocks, allows for the frame share and overhead of the resource grid, and inverts the attenuated Shannon bound from 3GPP TR 36.942 Annex A.1. That curve is a generic 3GPP link level model rather than a particular vendor's equipment, so if you have a measured vendor figure you can enter the SINR directly instead.
How is the shadow margin worked out from a location probability?
Shadow fading is treated as log normal around the median path loss, so the margin is the standard deviation times the normal quantile for the chosen probability. For example, 90 per cent of cell edge locations needs about 1.28 standard deviations. The standard deviation comes from ITU-R P.1546-6 Annex 5 section 12 for the environment, or you can enter your own.
Does it account for terrain?
No. The range comes from a clutter based propagation model that does not see terrain, which suits a first estimate of cell size. For terrain aware prediction, use the Coverage Predictor.
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