Resource Grid

Imagine a table where its rows are units in frequency domain and its columns are units in time domain. In this table, each unit in frequency is equivalent to one subcarrier (defined by the subcarrier spacing) and each unit in time is one OFDM symbol. Each cell in this table is called a Resource Element (RE), and this table is called a Resource Grid. The resource grid is normally presented for one subframe in the time domain and the whole bandwidth of the corresponding bandwidth part in the frequency domain. 12 consecutive REs in the frequency domain is called a Resource Block (RB). Hence, the table below shows the RB size in kHz for different subcarrier spacings.

Subcarrier Spacing (kHz)	RB Size (kHz)
15	180
30	360
60	720
120	1440
240	2880
480	5760
960	11520

3GPP defines the minium guard band from the total channel bandwidth to get the transmission bandwidth as given in the table below. If the value of the guard band for a subcarrier spacing $\Delta$ and bandwidth $B$ is presented by the function $g(\Delta, B)$, then the number of REs per each symbol in the time domain is given by the equation below and the number of RBs per symbol is given by the equation below.

$$N_{RE} = \frac{B - 2g(\Delta, B)}{\Delta} N_{RB} = \lfloor \frac{n_{RE}}{12} \rfloor$$

From here to calculate the number of RBs per frame, we should multiply the number of RBs per symbol by the number of symbols per frame, calculated by the equation below.

$$N_{Sym} = 14 \times 10 \times 2^{\mu}$$

Bandwidth (MHz)	SCS 15 kHz	SCS 30 kHz	SCS 60 kHz
5 MHz	242.5	505	N/A
10 MHz	312.5	665	1010
15 MHz	382.5	645	990
20 MHz	452.5	805	1330
25 MHz	522.5	785	1310
30 MHz	592.5	945	1290
40 MHz	552.5	905	1610
50 MHz	692.5	1045	1570
60 MHz	N/A	825	1530
70 MHz	N/A	965	1490
80 MHz	N/A	925	1450
90 MHz	N/A	885	1410
100 MHz	N/A	845	1370

Let us have an example:

• Subcarrier spacing: 30 kHz
• Number of OFDM symbols: 14
• Bandwidth: 40 MHz

Given the equations, we can calculate the number of REs per symbol as follows:

$$N_{RE} = \frac{40000 - 2 \times 905}{30} = 1273 N_{RB} = \lfloor \frac{1273}{12} \rfloor = 106$$

Finally, given the equations, we can calculate the number of RBs per frame as follows:

$$N_{RB} = 106 \times 14 \times 10 \times 2^1 = 29680$$