NR Prach

Physical random access channel 38.211 §6.3.3

Tc = 1 / (480.103 * 4096) = 0.509 nS
Ts = 1 / (15.103 * 2048) = 32.55 nS
ĸ = Ts / Tc = 64
CP = Cyclic prefix
GT = Guard time
Note: cell range is not a reference, just a computation estimate

Long PRACH preamble formats for LRA = 839
Format LRA ΔfRA
 NCPRA Nu GT CP length
[μs]		 Seq length
[μs]		 GT length
[μs]		 Max cell
range		 Support for
restricted sets
0 839 1.25 kHz 3168 ĸ 1 . 24576 ĸ 2976 ĸ 103.125 1 . 800 96.875 14.5 km Type A, Type B
1 839 1.25 kHz 21024 ĸ 2 . 24576 ĸ 21024 ĸ 684.375 2 . 800 684.375 102.7 km Type A, Type B
2 839 1.25 kHz 4688 ĸ 4 . 24576 ĸ 4688 ĸ 152.604 4 . 800 152.604 22.9 km Type A, Type B
3 839 5 kHz 3168 ĸ 4 . 6144 ĸ 2976 ĸ 103.125 4 . 200 96.875 14.5 km Type A, Type B

Short PRACH preamble formats for LRA = 139
μ = 1 (30 kHz)
Format LRA ΔfRA
 NCPRA Nu GT CP length
[μs]		 Seq length
[μs]		 GT length
[μs]		 Max cell
range		 Support for
restricted sets
A1 139 15 . 2μ kHz 288 ĸ . 2-μ 2 . 2048 ĸ . 2-μ 144 ĸ 4.688 2 . 33.33 4.688 700 m -
A2 139 15 . 2μ kHz 576 ĸ . 2-μ 4 . 2048 ĸ . 2-μ 288 ĸ 9.375 4 . 33.33 9.375 1400 m -
A3 139 15 . 2μ kHz 864 ĸ . 2-μ 6 . 2048 ĸ . 2-μ 432 ĸ 14.063 6 . 33.33 14.063 2100 m -
B1 139 15 . 2μ kHz 216 ĸ . 2-μ 2 . 2048 ĸ . 2-μ 108 ĸ 3.516 2 . 33.33 3.516 520 m -
B2 139 15 . 2μ kHz 360 ĸ . 2-μ 4 . 2048 ĸ . 2-μ 108 ĸ 5.859 4 . 33.33 3.516 520 m -
B3 139 15 . 2μ kHz 504 ĸ . 2-μ 6 . 2048 ĸ . 2-μ 252 ĸ 8.203 6 . 33.33 8.203 1230 m -
B4 139 15 . 2μ kHz 936 ĸ . 2-μ 12 . 2048 ĸ . 2-μ 396 ĸ 15.234 12 . 33.33 12.891 1930 m -
C0 139 15 . 2μ kHz 1240 ĸ . 2-μ 1 . 2048 ĸ . 2-μ 620 ĸ 20.182 1 . 33.33 20.182 3020 m -
C2 139 15 . 2μ kHz 2048 ĸ . 2-μ 4 . 2048 ĸ . 2-μ 1024 ĸ 33.333 4 . 33.33 33.333 5000 m

NR PRACH long format length

NR RACH long length

NR PRACH short format length

NR RACH short length

RACH configuration
RACH-ConfigGeneric ::= SEQUENCE {
   prach-ConfigurationIndex INTEGER (0..255),
   msg1-FDM ENUMERATED {one, two, four, eight},
   msg1-FrequencyStart INTEGER (0..maxNrofPhysicalResourceBlocks-1),
   zeroCorrelationZoneConfig INTEGER(0..15),
   preambleReceivedTargetPower INTEGER (-202..-60),
   preambleTransMax ENUMERATED {n3, n4, n5, n6, n7, n8, n10, n20, n50, n100, n200},
   powerRampingStep ENUMERATED {dB0, dB2, dB4, dB6},
   ra-ResponseWindow ENUMERATED {sl1, sl2, sl4, sl8, sl10, sl20, sl40, sl80},
}
NCS and number of preamble sequences per PRACH root sequence for long formats with ΔfRA = 1.25 kHz
zeroCorrelationZoneConfig NCS Number of
preamble sequences
LRA = 839 / NCS		 Number of
consecutive
root sequence
indices needed		 PRACH
reuse factor		 Cell radius
[meters]
0 0 1 64 13 5000
1 13 64 1 838 78
2 15 55 2 419 90
3 18 46 2 419 108
4 22 38 2 419 132
5 26 32 2 419 155
6 32 26 3 279 191
7 38 22 3 279 227
8 46 18 4 209 275
9 59 14 5 167 352
10 76 11 6 139 453
11 93 9 8 104 555
12 119 7 10 83 710
13 167 5 13 64 996
14 279 3 22 38 1663
15 419 2 32 26 2498

NCS and number of preamble sequences per PRACH root sequence for short formats with ΔfRA = 15 . 2μ kHz
zeroCorrelationZoneConfig NCS Number of
preamble sequences
LRA = 139 / NCS		 Number of
consecutive
root sequence
indices needed		 PRACH
reuse factor		 Cell radius
[meters]
0 0 1 64 2 5000
1 2 69 1 138 72
2 4 34 2 69 144
3 6 23 3 46 216
4 8 17 4 34 288
5 10 13 5 27 360
6 12 11 6 23 432
7 13 10 7 19 468
8 15 9 8 17 540
9 17 8 8 17 612
10 19 7 10 13 684
11 23 6 11 12 828
12 27 5 13 10 972
13 34 4 16 8 1224
14 46 3 22 6 1655
15 69 2 32 4 2483

Example of scattered PRACH
PRACH Initial TA

Random access configurations

38.211 §6.3.3 : For the purpose of slot numbering in the tables, the following subcarrier spacing shall be assumed

FR1 and unpaired spectrum (TDD)

PRACH Config
Index		 Preamble
format		 nSFN
mod x = y		 Subframe
number		 Starting
symbol		 Number of
PRACH slots
within a subframe		 number of
time-domain
PRACH occasions
within a PRACH slot		 PRACH duration
x y
0 0 16 1 9 0 - - 0
1 0 8 1 9 0 - - 0
2 0 4 1 9 0 - - 0
3 0 2 0 9 0 - - 0
4 0 2 1 9 0 - - 0
5 0 2 0 4 0 - - 0
6 0 2 1 4 0 - - 0
7 0 1 0 9 0 - - 0
8 0 1 0 8 0 - - 0
9 0 1 0 7 0 - - 0
10 0 1 0 6 0 - - 0
11 0 1 0 5 0 - - 0
12 0 1 0 4 0 - - 0
13 0 1 0 3 0 - - 0
14 0 1 0 2 0 - - 0
15 0 1 0 1,6 0 - - 0
16 0 1 0 1,6 7 - - 0
17 0 1 0 4,9 0 - - 0
18 0 1 0 3,8 0 - - 0
19 0 1 0 2,7 0 - - 0
20 0 1 0 8,9 0 - - 0
21 0 1 0 4,8,9 0 - - 0
22 0 1 0 3,4,9 0 - - 0
23 0 1 0 7,8,9 0 - - 0
24 0 1 0 3,4,8,9 0 - - 0
25 0 1 0 6,7,8,9 0 - - 0
26 0 1 0 1,4,6,9 0 - - 0
27 0 1 0 1,3,5,7,9 0 - - 0
28 1 16 1 7 0 - - 0
29 1 8 1 7 0 - - 0
30 1 4 1 7 0 - - 0
31 1 2 0 7 0 - - 0
32 1 2 1 7 0 - - 0
33 1 1 0 7 0 - - 0
34 2 16 1 6 0 - - 0
35 2 8 1 6 0 - - 0
36 2 4 1 6 0 - - 0
37 2 2 0 6 7 - - 0
38 2 2 1 6 7 - - 0
39 2 1 0 6 7 - - 0
40 3 16 1 9 0 - - 0
41 3 8 1 9 0 - - 0
42 3 4 1 9 0 - - 0
43 3 2 0 9 0 - - 0
44 3 2 1 9 0 - - 0
45 3 2 0 4 0 - - 0
46 3 2 1 4 0 - - 0
47 3 1 0 9 0 - - 0
48 3 1 0 8 0 - - 0
49 3 1 0 7 0 - - 0
50 3 1 0 6 0 - - 0
51 3 1 0 5 0 - - 0
52 3 1 0 4 0 - - 0
53 3 1 0 3 0 - - 0
54 3 1 0 2 0 - - 0
55 3 1 0 1,6 0 - - 0
56 3 1 0 1,6 7 - - 0
57 3 1 0 4,9 0 - - 0
58 3 1 0 3,8 0 - - 0
59 3 1 0 2,7 0 - - 0
60 3 1 0 8,9 0 - - 0
61 3 1 0 4,8,9 0 - - 0
62 3 1 0 3,4,9 0 - - 0
63 3 1 0 7,8,9 0 - - 0
64 3 1 0 3,4,8,9 0 - - 0
65 3 1 0 1,4,6,9 0 - - 0
66 3 1 0 1,3,5,7,9 0 - - 0
67 A1 16 1 9 0 2 6 2
68 A1 8 1 9 0 2 6 2
69 A1 4 1 9 0 1 6 2
70 A1 2 1 9 0 1 6 2
71 A1 2 1 4,9 7 1 3 2
72 A1 2 1 7,9 7 1 3 2
73 A1 2 1 7,9 0 1 6 2
74 A1 2 1 8,9 0 2 6 2
75 A1 2 1 4,9 0 2 6 2
76 A1 2 1 2,3,4,7,8,9 0 1 6 2
77 A1 1 0 9 0 2 6 2
78 A1 1 0 9 7 1 3 2
79 A1 1 0 9 0 1 6 2
80 A1 1 0 8,9 0 2 6 2
81 A1 1 0 4,9 0 1 6 2
82 A1 1 0 7,9 7 1 3 2
83 A1 1 0 3,4,8,9 0 1 6 2
84 A1 1 0 3,4,8,9 0 2 6 2
85 A1 1 0 1,3,5,7,9 0 1 6 2
86 A1 1 0 0,1,2,3,4,5,6,7,8,9 7 1 3 2
87 A2 16 1 9 0 2 3 4
88 A2 8 1 9 0 2 3 4
89 A2 4 1 9 0 1 3 4
90 A2 2 1 7,9 0 1 3 4
91 A2 2 1 8,9 0 2 3 4
92 A2 2 1 7,9 9 1 1 4
93 A2 2 1 4,9 9 1 1 4
94 A2 2 1 4,9 0 2 3 4
95 A2 2 1 2,3,4,7,8,9 0 1 3 4
96 A2 1 0 2 0 1 3 4
97 A2 1 0 7 0 1 3 4
98 A2 2 1 9 0 1 3 4
99 A2 1 0 9 0 2 3 4
100 A2 1 0 9 9 1 1 4
101 A2 1 0 9 0 1 3 4
102 A2 1 0 2,7 0 1 3 4
103 A2 1 0 8,9 0 2 3 4
104 A2 1 0 4,9 0 1 3 4
105 A2 1 0 7,9 9 1 1 4
106 A2 1 0 3,4,8,9 0 1 3 4
107 A2 1 0 3,4,8,9 0 2 3 4
108 A2 1 0 1,3,5,7,9 0 1 3 4
109 A2 1 0 0,1,2,3,4,5,6,7,8,9 9 1 1 4
110 A3 16 1 9 0 2 2 6
111 A3 8 1 9 0 2 2 6
112 A3 4 1 9 0 1 2 6
113 A3 2 1 4,9 7 1 1 6
114 A3 2 1 7,9 7 1 1 6
115 A3 2 1 7,9 0 1 2 6
116 A3 2 1 4,9 0 2 2 6
117 A3 2 1 8,9 0 2 2 6
118 A3 2 1 2,3,4,7,8,9 0 1 2 6
119 A3 1 0 2 0 1 2 6
120 A3 1 0 7 0 1 2 6
121 A3 2 1 9 0 1 2 6
122 A3 1 0 9 0 2 2 6
123 A3 1 0 9 7 1 1 6
124 A3 1 0 9 0 1 2 6
125 A3 1 0 2,7 0 1 2 6
126 A3 1 0 8,9 0 2 2 6
127 A3 1 0 4,9 0 1 2 6
128 A3 1 0 7,9 7 1 1 6
129 A3 1 0 3,4,8,9 0 1 2 6
130 A3 1 0 3,4,8,9 0 2 2 6
131 A3 1 0 1,3,5,7,9 0 1 2 6
132 A3 1 0 0,1,2,3,4,5,6,7,8,9 7 1 1 6
133 B1 4 1 9 2 1 6 2
134 B1 2 1 9 2 1 6 2
135 B1 2 1 7,9 2 1 6 2
136 B1 2 1 4,9 8 1 3 2
137 B1 2 1 4,9 2 2 6 2
138 B1 1 0 9 2 2 6 2
139 B1 1 0 9 8 1 3 2
140 B1 1 0 9 2 1 6 2
141 B1 1 0 8,9 2 2 6 2
142 B1 1 0 4,9 2 1 6 2
143 B1 1 0 7,9 8 1 3 2
144 B1 1 0 1,3,5,7,9 2 1 6 2
145 B4 16 1 9 0 2 1 12
146 B4 8 1 9 0 2 1 12
147 B4 4 1 9 2 1 1 12
148 B4 2 1 9 0 1 1 12
149 B4 2 1 9 2 1 1 12
150 B4 2 1 7,9 2 1 1 12
151 B4 2 1 4,9 2 1 1 12
152 B4 2 1 4,9 0 2 1 12
153 B4 2 1 8,9 0 2 1 12
154 B4 2 1 2,3,4,7,8,9 0 1 1 12
155 B4 1 0 1 0 1 1 12
156 B4 1 0 2 0 1 1 12
157 B4 1 0 4 0 1 1 12
158 B4 1 0 7 0 1 1 12
159 B4 1 0 9 0 1 1 12
160 B4 1 0 9 2 1 1 12
161 B4 1 0 9 0 2 1 12
162 B4 1 0 4,9 2 1 1 12
163 B4 1 0 7,9 2 1 1 12
164 B4 1 0 8,9 0 2 1 12
165 B4 1 0 3,4,8,9 2 1 1 12
166 B4 1 0 1,3,5,7,9 2 1 1 12
167 B4 1 0 0,1,2,3,4,5,6,7,8,9 0 2 1 12
168 B4 1 0 0,1,2,3,4,5,6,7,8,9 2 1 1 12
169 C0 16 1 9 2 2 6 2
170 C0 8 1 9 2 2 6 2
171 C0 4 1 9 2 1 6 2
172 C0 2 1 9 2 1 6 2
173 C0 2 1 8,9 2 2 6 2
174 C0 2 1 7,9 2 1 6 2
175 C0 2 1 7,9 8 1 3 2
176 C0 2 1 4,9 8 1 3 2
177 C0 2 1 4,9 2 2 6 2
178 C0 2 1 2,3,4,7,8,9 2 1 6 2
179 C0 1 0 9 2 2 6 2
180 C0 1 0 9 8 1 3 2
181 C0 1 0 9 2 1 6 2
182 C0 1 0 8,9 2 2 6 2
183 C0 1 0 4,9 2 1 6 2
184 C0 1 0 7,9 8 1 3 2
185 C0 1 0 3,4,8,9 2 1 6 2
186 C0 1 0 3,4,8,9 2 2 6 2
187 C0 1 0 1,3,5,7,9 2 1 6 2
188 C0 1 0 0,1,2,3,4,5,6,7,8,9 8 1 3 2
189 C2 16 1 9 2 2 2 6
190 C2 8 1 9 2 2 2 6
191 C2 4 1 9 2 1 2 6
192 C2 2 1 9 2 1 2 6
193 C2 2 1 8,9 2 2 2 6
194 C2 2 1 7,9 2 1 2 6
195 C2 2 1 7,9 8 1 1 6
196 C2 2 1 4,9 8 1 1 6
197 C2 2 1 4,9 2 2 2 6
198 C2 2 1 2,3,4,7,8,9 2 1 2 6
199 C2 8 1 9 8 2 1 6
200 C2 4 1 9 8 1 1 6
201 C2 1 0 9 2 2 2 6
202 C2 1 0 9 8 1 1 6
203 C2 1 0 9 2 1 2 6
204 C2 1 0 8,9 2 2 2 6
205 C2 1 0 4,9 2 1 2 6
206 C2 1 0 7,9 8 1 1 6
207 C2 1 0 3,4,8,9 2 1 2 6
208 C2 1 0 3,4,8,9 2 2 2 6
209 C2 1 0 1,3,5,7,9 2 1 2 6
210 C2 1 0 0,1,2,3,4,5,6,7,8,9 8 1 1 6
211 A1/B1 2 1 9 2 1 6 2
212 A1/B1 2 1 4,9 8 1 3 2
213 A1/B1 2 1 7,9 8 1 3 2
214 A1/B1 2 1 7,9 2 1 6 2
215 A1/B1 2 1 4,9 2 2 6 2
216 A1/B1 2 1 8,9 2 2 6 2
217 A1/B1 1 0 9 2 2 6 2
218 A1/B1 1 0 9 8 1 3 2
219 A1/B1 1 0 9 2 1 6 2
220 A1/B1 1 0 8,9 2 2 6 2
221 A1/B1 1 0 4,9 2 1 6 2
222 A1/B1 1 0 7,9 8 1 3 2
223 A1/B1 1 0 3,4,8,9 2 2 6 2
224 A1/B1 1 0 1,3,5,7,9 2 1 6 2
225 A1/B1 1 0 0,1,2,3,4,5,6,7,8,9 8 1 3 2
226 A2/B2 2 1 9 0 1 3 4
227 A2/B2 2 1 4,9 6 1 2 4
228 A2/B2 2 1 7,9 6 1 2 4
229 A2/B2 2 1 4,9 0 2 3 4
230 A2/B2 2 1 8,9 0 2 3 4
231 A2/B2 1 0 9 0 2 3 4
232 A2/B2 1 0 9 6 1 2 4
233 A2/B2 1 0 9 0 1 3 4
234 A2/B2 1 0 8,9 0 2 3 4
235 A2/B2 1 0 4,9 0 1 3 4
236 A2/B2 1 0 7,9 6 1 2 4
237 A2/B2 1 0 3,4,8,9 0 1 3 4
238 A2/B2 1 0 3,4,8,9 0 2 3 4
239 A2/B2 1 0 1,3,5,7,9 0 1 3 4
240 A2/B2 1 0 0,1,2,3,4,5,6,7,8,9 6 1 2 4
241 A3/B3 2 1 9 0 1 2 6
242 A3/B3 2 1 4,9 2 1 2 6
243 A3/B3 2 1 7,9 0 1 2 6
244 A3/B3 2 1 7,9 2 1 2 6
245 A3/B3 2 1 4,9 0 2 2 6
246 A3/B3 2 1 8,9 0 2 2 6
247 A3/B3 1 0 9 0 2 2 6
248 A3/B3 1 0 9 2 1 2 6
249 A3/B3 1 0 9 0 1 2 6
250 A3/B3 1 0 8,9 0 2 2 6
251 A3/B3 1 0 4,9 0 1 2 6
252 A3/B3 1 0 7,9 2 1 2 6
253 A3/B3 1 0 3,4,8,9 0 2 2 6
254 A3/B3 1 0 1,3,5,7,9 0 1 2 6
255 A3/B3 1 0 0,1,2,3,4,5,6,7,8,9 2 1 2 6

Beam sweeping

32 beams sweeping
Polarization 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Polarization 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

8 beams and 32 refinement beams sweeping
Polarization 1 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 6 7 32 33 34 35 36 37 38 39 Polarization 2 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 6 7 32 33 34 35 36 37 38 39