# SNR calculation with Noise Spectral Density

I am having difficulty in calculating the SNR for the following scenario:

In a cellular network

• Transmit power=36dBm
• Noise spectral density=-174dBm/Hz (AWGN)
• Bandwidth=10MHz

I have some other parameters such as pathloss and Rayleigh fading, but I think my biggest problem is the conversion of dB to power.

• Convert the noise spectral density to linear and multiply by the bandwidth to get the total noise power. Then, convert back to logarithmic domain and subtract from transmit power to gain the SNR. – jan Dec 11 '13 at 14:16
• I am stuck in a similar situation and I have parameters like FSPL and noise figure with same noise spectral density as mentioned above. My free space pathloss is given in db and converting it to linear gives me a huge number which when used to calculate received SNR results in a high SNR value for example 140 dB. I don't know where am i missing. Same is the case when i do calculations directly in decibels. I am using the formula: SNRreceived = [power transmitted(dBm) + FSPL(dB)]-[10log B(hz) * No(db) + 10log(KT) + NF(dB)] Could anyone point out where am I mistaken? I would be very thankful. – Srijan Mar 2 '14 at 22:35

The comment above already gave you a roadmap to get to an answer, but I'll flesh it out a bit:

• SNR is the ratio of signal power to noise power. To calculate the signal power at your receiver, you'll need to take the path loss and fading model into account, as you noted.

• The noise power at the receiver is described by a (flat) noise power spectral density and receiver bandwidth. To calculate the total noise power over that bandwidth, you simply multiply the amount of power per Hertz times the width of the band. When power is specified in logarithmic units (dB), you need to first convert it to a linear scale. Recall the relationship between mW and dBm: $$P|_{dBm} = 10 \log_{10}\left(\frac{P}{1\text{ mW}}\right)$$

That is, to convert a linear-scale power quantity to dBm, take ten times the base-10 logarithm of the ratio of that power quantity to 1 milliwatt. For example:

• 30 dBm: 1 W
• 0 dBm: 1 mW
• -30 dBm: 1 uW
• -60 dBm: 1 nW
• -90 dBm: 1 pW

To go the other way, invert the calculation: $$P = 10^{\frac{P|_{dBm}}{10}} * 1\text{ mW}$$

• So, to calculate the total noise power at your receiver, you would convert the noise power spectral density to linear units using the above equation: $$S_n = 10^{\frac{-174}{10}} \frac{\text{mW}}{\text{Hz}} = 3.981 * 10^{-18} \frac{\text{mW}}{\text{Hz}}$$ then multiply by the bandwidth to get the total amount of noise power: $$P_n = BS_n = \left(10 * 10^{6}\text{ Hz}\right)\left(3.981 * 10^{-18} \frac{\text{mW}}{\text{Hz}}\right)$$ $$P_n = 3.981 * 10^{-11} \text{ mW}$$

Then, use your model to predict the received signal power, take the ratio, and you've got your SNR.

N=N0.B Ndbm = 10log(N0.B/1mW) = 10log(KT0/1mW) + 10logB = -174 dBm/Hz + 10log(10*10^6) dB = -174 + 70 = -104 dBm => N = -104 dBm

• Can you please elaborate on the formula? Did you mean to post this as a comment perhaps? – A_A Jun 11 '18 at 10:02