4G/LTE - PHY Channel

Physical Layer Parameter - DL, FDD

Followings would be a quick cheatsheet if you are DSP engineer or FPGA engineer working in LTE PHY.

Let's get into further details for some of the important parameters.

• Sampling Rate
• Sampling Time
• Frquency Spacing between FFT bin
• Number of Samples for each CP and OFDM Symbol
• BandWidth/Guardband Width
• Application

Sampling Rate

• 20 Mhz BW Case :  Subcarrier spacing x FFT size = 15000 (15 Khz) x 2048 = 30.72 Mhz
• 15 Mhz BW Case :  Subcarrier spacing x FFT size = 15000 (15 Khz) x 1536 = 23.04 Mhz
• 10 Mhz BW Case :  Subcarrier spacing x FFT size = 15000 (15 Khz) x 1024= 15.36 Mhz
• 5 Mhz BW Case :  Subcarrier spacing x FFT size = 15000 (15 Khz) x 512= 7.68 Mhz
• 3 Mhz BW Case :  Subcarrier spacing x FFT size = 15000 (15 Khz) x 256 = 3.84 Mhz
• 1.4 Mhz BW Case :  Subcarrier spacing x FFT size = 15000 (15 Khz) x 128 = 1.92 Mhz

Sampling Time

• 20 Mhz BW Case :  1 sec / 30.72 Mhz = 1,000,000 us/30,720,000 Hz = 0.0326 us = 32.6 ns
• 15 Mhz BW Case :  1 sec / 23.04 Mhz = 1,000,000 us/23,040,000 Hz = 0.0434 us = 43.4 ns
• 10 Mhz BW Case :  1 sec / 15.36 Mhz = 1,000,000 us/15,360,000 Hz = 0.0652 us = 65.2 ns
• 5 Mhz BW Case :  1 sec / 7.68 Mhz = 1,000,000 us/7,680,000 Hz = 0.1302 us = 130.2 ns
• 3 Mhz BW Case :  1 sec / 3.84 Mhz = 1,000,000 us/3,840,000 Hz = 0.2604 us = 260.4 ns
• 1.4 Mhz BW Case :  1 sec / 1.92 Mhz = 1,000,000 us/1,920,000 Hz = 0.5208 us = 520.8 ns

Frquency Spacing between FFT bin

• 20 Mhz BW Case : 30.72 MHz / 2048 = 0.015 Mhz = 15 Khz = 1 RE(Resource Element) in Frequency Domain  
• 15 Mhz BW Case : 23.04 MHz / 1536 = 0.015 Mhz = 15 Khz = 1 RE(Resource Element) in Frequency Domain  
• 10 Mhz BW Case : 15.36 MHz / 1024 = 0.015 Mhz = 15 Khz = 1 RE(Resource Element) in Frequency Domain  
• 5 Mhz BW Case : 7.68 MHz / 512 = 0.015 Mhz = 15 Khz = 1 RE(Resource Element) in Frequency Domain  
• 3 Mhz BW Case : 3.84 MHz / 256 = 0.015 Mhz = 15 Khz = 1 RE(Resource Element) in Frequency Domain  
• 1 Mhz BW Case : 1.92 MHz / 128 = 0.015 Mhz = 15 Khz = 1 RE(Resource Element) in Frequency Domain  

Number of Samples for each CP and OFDM Symbol

Following illustration shows the number of samples in each CP and OFDM symbols for 20Mhz case. I will calculate the number of samples for other BW case by taking the ratio of FFT site of 20 Mhz and the FFT size of other BW.

In short, I will list up the value of A,B,C,D for each system BW.

Followings are A,B,C values for each BW

• 20 Mhz BW Case :
• A = 160
• B = 144
• C = 2048

• 15 Mhz BW Case :
• A = 160 x (FFT size for 15 Mhz/FFT size for 20 Mhz) = 160 x (1536/2048) = 120
• B = 144 x (FFT size for 15 Mhz/FFT size for 20 Mhz) = 144 x (1536/2048) = 108
• C = 2048 x (FFT size for 15 Mhz/FFT size for 20 Mhz) = 2048 x (1536/2048) = 1536

• 10 Mhz BW Case :
• A = 160 x (FFT size for 10 Mhz/FFT size for 20 Mhz) = 160 x (1024/2048) = 80
• B = 144 x (FFT size for 10 Mhz/FFT size for 20 Mhz) = 144 x (1024/2048) = 72
• C = 2048 x (FFT size for 10 Mhz/FFT size for 20 Mhz) = 2048 x (1024/2048) = 1024

• 5 Mhz BW Case :
• A = 160 x (FFT size for 5 Mhz/FFT size for 20 Mhz) = 160 x (512/2048) = 40
• B = 144 x (FFT size for 5 Mhz/FFT size for 20 Mhz) = 144 x (512/2048) = 36
• C = 2048 x (FFT size for 5 Mhz/FFT size for 20 Mhz) = 2048 x (512/2048) = 512

• 3 Mhz BW Case :
• A = 160 x (FFT size for 3 Mhz/FFT size for 20 Mhz) = 160 x (256/2048) = 20
• B = 144 x (FFT size for 3 Mhz/FFT size for 20 Mhz) = 144 x (256/2048) = 18
• C = 2048 x (FFT size for 3 Mhz/FFT size for 20 Mhz) = 2048 x (256/2048) = 256

• 1.4 Mhz BW Case :
• A = 160 x (FFT size for 1.4 Mhz/FFT size for 20 Mhz) = 160 x (128/2048) = 10
• B = 144 x (FFT size for 1.4 Mhz/FFT size for 20 Mhz) = 144 x (128/2048) = 9
• C = 2048 x (FFT size for 1.4 Mhz/FFT size for 20 Mhz) = 2048 x (128/2048) = 128

BandWidth/Guardband Width

• 20 Mhz BW Case :
• A = Occupied Subcarriers (including DC)  x 15 Khz = 1201 x 15 Khz = 18015 Khz = 18.015 Mhz
• B = Occupied Subcarriers (including DC) = 1201
• C + D = Guard Subcarriers = 847

• 15 Mhz BW Case :
• A = Occupied Subcarriers (including DC)  x 15 Khz = 901 x 15 Khz = 13515 Khz = 13.515 Mhz
• B = Occupied Subcarriers (including DC) = 901
• C + D = Guard Subcarriers = 635

• 10 Mhz BW Case :
• A = Occupied Subcarriers (including DC)  x 15 Khz = 601 x 15 Khz = 9015 Khz = 9.015 Mhz
• B = Occupied Subcarriers (including DC) = 601
• C + D = Guard Subcarriers = 423

• 5 Mhz BW Case :
• A = Occupied Subcarriers (including DC)  x 15 Khz = 301 x 15 Khz = 4515 Khz = 4.515 Mhz
• B = Occupied Subcarriers (including DC) = 301
• C + D = Guard Subcarriers = 211

• 3 Mhz BW Case :
• A = Occupied Subcarriers (including DC)  x 15 Khz = 151 x 15 Khz = 2265 Khz = 2.265 Mhz
• B = Occupied Subcarriers (including DC) = 151
• C + D = Guard Subcarriers = 105

• 1.4 Mhz BW Case :
• A = Occupied Subcarriers (including DC)  x 15 Khz = 76 x 15 Khz = 1140 Khz = 1.140 Mhz
• B = Occupied Subcarriers (including DC) = 76
• C + D = Guard Subcarriers = 52
 

Application

These kind of information may sound too much detail, but they are the most basic information required for digital signal processing at the first step processing of LTE PHY signal. Examples on sharetechnote are

• LTE Physical Layer Signal : PSS