# How to calculate bandwidth require for OFDM

I read LTE PHY profile and do not understand the relationship between number of FFT and bandwidth. For example LTE downlink channel bandwidth 1.25MHz and 5MHz have 128 FFTs and 512 FFTs accordingly. Another example is 802.11 a bandwidth 20MHz, FFT size 52.

I design an OFDM system system at carrier frequency 910MHz, with FFT size for example 64, how much coherent bandwidth that the system need? What is the formula? What other factors should be taken into account?

When I test a simple software defined radio OFDM system with parameters as FFT = 256, data carrier per symbol = 125, number of pilot = 25, bandwidth = 5MHz, carrier frequency = 910MHz, the channel estimation wouks fine. If I change bandwidth to 1MHz, then the channel estimation goes wrong. In this case I reduce sampling frequency 5 times, so carrier spacing is reduced 5 times too.

I think the carrier spacing must be greater than a limit so that intersymbol interference (or inter-carrier interference?) is small enough to not cause channel estimation failture. How to find the carrier spacing limit?

Or delay spread $\tau \ll T$ where T is symbol interval may cause the problem. How to calculate the limit $\tau$?

Thanks

• The edit has made the question unclear. Is it about bandwidth or channel estimation? Please consider asking seperate questions. – Deve Aug 19 '14 at 7:43

The channel bandwidth and FFT size alone don't provide enough information to describe the entire structure of the OFDM signal. Recall the following relationship:

$$\Delta f = \frac{f_s}{N}$$

where $\Delta f$ is the subcarrier spacing, $f_s$ is the sample rate used at the modulator input, and $N$ is the FFT size.

In your LTE examples, the two channel bandwidths must use the same subcarrier spacing, as it takes four times as much bandwidth to carry four times the subcarriers (512 versus 128).

For 802.11a, however, the FFT size is typically 64; with a sample rate of 20 MHz, this yields a subcarrier spacing of 312.5 kHz. Of these 64 potential subcarriers, 12 of them are unused (sometimes referred to as "virtual carriers"). Of the remaining 52 subcarriers, 4 contain pilot tones, so only 48 subcarriers carry information at any given time.

For your notional OFDM system, you can choose the amount of bandwidth required by your system, as required based on your throughput requirements. Choose the sample rate that you will input to the modulator, then choose a convenient FFT size. This defines your number of subcarriers and therefore the subcarrier frequency spacing.

• So just in case it hasn't become clear from Jason's answer: the OFDM bandwidth is approximately equal to the sample rate $f_\mathrm s$. – Deve Aug 17 '14 at 14:29
• 2 Deve. In general it isn't true. You can use only a few OFDM subcarriers to form OFDM signal of wishful bandwidth like it works in OFDMA systems. For example you have 1024 available subcarriers and use only 64 of them. So your bandwidth (I mean the bandwidth you occupy in radio spectrum) is obviously less than sample rate. – Serj Aug 18 '14 at 2:45
• @Serj You're right, zero (or virtual) subcarriers at the spectrum's margins reduce the bandwidth – Deve Aug 18 '14 at 7:45
• So how is the bandwidth calculated ? – Mike Feb 9 '16 at 8:33