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Physical Random Access ChannelPRACH
Sebastian Wagner
EURECOM
18-02-2013
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Outline
Introduction
PRACHPRACH Sequence DesignPRACH TransmitterPRACH Receiver
Numerical Results
Summary and Future Work
Introduction 3/14
Timing for Uplink Transmission
eNBUE2
UE1δ1
δ2
eNBt [ms]0 1 2 3 4 5 6 7 8 9
UE1t [ms]
UE2t [ms]
I Transmission from eNB
I Signal received from eNB (e.g. frame synchronization, PBCH,...)
I Assume eNB allocates UL in SF 6 and 7 to UEs 2 and 1, respectively
I Propagation delay causes interference at eNB⇒ timing adjustment of 2δ1,2
Introduction 3/14
Timing for Uplink Transmission
eNBUE2
UE1δ1
δ2
eNBt [ms]0 1 2 3 4 5 6 7 8 9
UE1t [ms]
UE2t [ms]
I Transmission from eNB
I Signal received from eNB (e.g. frame synchronization, PBCH,...)
I Assume eNB allocates UL in SF 6 and 7 to UEs 2 and 1, respectively
I Propagation delay causes interference at eNB⇒ timing adjustment of 2δ1,2
Introduction 3/14
Timing for Uplink Transmission
eNBUE2
UE1δ1
δ2
eNBt [ms]0 1 2 3 4 5 6 7 8 9
UE1t [ms]0 1 2 3 4 5 6 7 8 9
UE2t [ms]0 1 2 3 4 5 6 7 8 9
I Transmission from eNB
I Signal received from eNB (e.g. frame synchronization, PBCH,...)
I Assume eNB allocates UL in SF 6 and 7 to UEs 2 and 1, respectively
I Propagation delay causes interference at eNB⇒ timing adjustment of 2δ1,2
Introduction 3/14
Timing for Uplink Transmission
eNBUE2
UE1δ1
δ2
eNBt [ms]0 1 2 3 4 5 6 7 8 9
UE1t [ms]0 1 2 3 4 5 6 7 8 9
UE2t [ms]0 1 2 3 4 5 6 7 8 9
I Transmission from eNB
I Signal received from eNB (e.g. frame synchronization, PBCH,...)
I Assume eNB allocates UL in SF 6 and 7 to UEs 2 and 1, respectively
I Propagation delay causes interference at eNB⇒ timing adjustment of 2δ1,2
Introduction 3/14
Timing for Uplink Transmission
eNBUE2
UE1δ1
δ2
eNBt [ms]0 1 2 3 4 5 6 7 8 9
UE1t [ms]0 1 2 3 4 5 6 7 8 9
UE2t [ms]0 1 2 3 4 5 6 7 8 9
2δ2
I Transmission from eNB
I Signal received from eNB (e.g. frame synchronization, PBCH,...)
I Assume eNB allocates UL in SF 6 and 7 to UEs 2 and 1, respectively
I Propagation delay causes interference at eNB⇒ timing adjustment of 2δ1,2
Introduction 4/14
Random Access Procedure
UE
eNB
t
t
1
1. Transmit PRACH preamble (64 possible preambles, randomly chosenby UE or assigned by eNB)
2a. Receive PRACH preamble and estimate delay
2b. Random access response (detected preamble, timing adjustment,C-RNTI, UL grant for L2/L3 message...)
3. L2/L3 message (RACH procedure message)
4. Contention resolution message (if any contention)
Introduction 4/14
Random Access Procedure
UE
eNB
t
t
1
2a
1. Transmit PRACH preamble (64 possible preambles, randomly chosenby UE or assigned by eNB)
2a. Receive PRACH preamble and estimate delay
2b. Random access response (detected preamble, timing adjustment,C-RNTI, UL grant for L2/L3 message...)
3. L2/L3 message (RACH procedure message)
4. Contention resolution message (if any contention)
Introduction 4/14
Random Access Procedure
UE
eNB
t
t
1
2a
2b
1. Transmit PRACH preamble (64 possible preambles, randomly chosenby UE or assigned by eNB)
2a. Receive PRACH preamble and estimate delay
2b. Random access response (detected preamble, timing adjustment,C-RNTI, UL grant for L2/L3 message...)
3. L2/L3 message (RACH procedure message)
4. Contention resolution message (if any contention)
Introduction 4/14
Random Access Procedure
UE
eNB
t
t
1
2a
2b 3
1. Transmit PRACH preamble (64 possible preambles, randomly chosenby UE or assigned by eNB)
2a. Receive PRACH preamble and estimate delay
2b. Random access response (detected preamble, timing adjustment,C-RNTI, UL grant for L2/L3 message...)
3. L2/L3 message (RACH procedure message)
4. Contention resolution message (if any contention)
Introduction 4/14
Random Access Procedure
UE
eNB
t
t
1
2a
2b 3 4
1. Transmit PRACH preamble (64 possible preambles, randomly chosenby UE or assigned by eNB)
2a. Receive PRACH preamble and estimate delay
2b. Random access response (detected preamble, timing adjustment,C-RNTI, UL grant for L2/L3 message...)
3. L2/L3 message (RACH procedure message)
4. Contention resolution message (if any contention)
PRACH 5/14
PRACH FormatsSequence length TSEQ criteria:
I Fit into one subframe (1ms) but be as long as possible
I Account for maximum round-trip delay (RTD) ∆max
I Compatibility with PUSCH ⇒ sub-carrier spacing is 1.25 kHz
I Coverage performance
TSEQ = 800µs∆max ∆max
d= max. delay spreadCP GT
PRACH Formats (broadcasted in SI)
0 CP=103.13µs, TSEQ = 800µs, d ≈ 5.2µs → ∆max = 97.4µs⇒ rmax = ∆maxc
2 ≈ 14km max. cell radius
1 CP=684.38µs, TSEQ = 800µs, 2ms burst → ∆max = 515.62µs⇒ rmax = ∆maxc
2 ≈ 77km
2,3,4 ...
PRACH 5/14
PRACH FormatsSequence length TSEQ criteria:
I Fit into one subframe (1ms) but be as long as possible
I Account for maximum round-trip delay (RTD) ∆max
I Compatibility with PUSCH ⇒ sub-carrier spacing is 1.25 kHz
I Coverage performance
TSEQ = 800µs∆max ∆max
d= max. delay spreadCP GT
PRACH Formats (broadcasted in SI)
0 CP=103.13µs, TSEQ = 800µs, d ≈ 5.2µs → ∆max = 97.4µs⇒ rmax = ∆maxc
2 ≈ 14km max. cell radius
1 CP=684.38µs, TSEQ = 800µs, 2ms burst → ∆max = 515.62µs⇒ rmax = ∆maxc
2 ≈ 77km
2,3,4 ...
PRACH 5/14
PRACH FormatsSequence length TSEQ criteria:
I Fit into one subframe (1ms) but be as long as possible
I Account for maximum round-trip delay (RTD) ∆max
I Compatibility with PUSCH ⇒ sub-carrier spacing is 1.25 kHz
I Coverage performance
TSEQ = 800µs∆max ∆max
d= max. delay spreadCP GT
PRACH Formats (broadcasted in SI)
0 CP=103.13µs, TSEQ = 800µs, d ≈ 5.2µs → ∆max = 97.4µs⇒ rmax = ∆maxc
2 ≈ 14km max. cell radius
1 CP=684.38µs, TSEQ = 800µs, 2ms burst → ∆max = 515.62µs⇒ rmax = ∆maxc
2 ≈ 77km
2,3,4 ...
PRACH 6/14
Preamble Sequence Design
Prime-length NZC Zadoff-Chu (ZC) sequences xu(n) of root u:
xu(n) = exp(−j πun(n+1)
NZC
), 0 6 n 6 NZC − 1, NZC = 839
I Constant amplitude: limits PAPR, flat bounded interference,...
I Ideal cyclic auto-correlation:∑NZC−1
n=0 xu(n)x∗u (n + Cν) = δ(Cν)
I Ideal cyclic cross-correlation:∑NZC−1
n=0 xu(n)x∗u ′(n) = 1√NZC
I Efficient DFT1:
Xu(k)=x∗u (u−1k)Xu(0)=Xu(0) exp(
jπu(u−1k)(u−1k+1)NZC
)
64 Preamble sequences xu,ν(n) are cyclic shifts of ZC
xu,ν(n) = xu((n + Cν)%NZC)
1S. Beyme and C. Leung, “Efficient computation of DFT of Zadoff-Chu sequences”
PRACH 6/14
Preamble Sequence Design
Prime-length NZC Zadoff-Chu (ZC) sequences xu(n) of root u:
xu(n) = exp(−j πun(n+1)
NZC
), 0 6 n 6 NZC − 1, NZC = 839
I Constant amplitude: limits PAPR, flat bounded interference,...
I Ideal cyclic auto-correlation:∑NZC−1
n=0 xu(n)x∗u (n + Cν) = δ(Cν)
I Ideal cyclic cross-correlation:∑NZC−1
n=0 xu(n)x∗u ′(n) = 1√NZC
I Efficient DFT1:
Xu(k)=x∗u (u−1k)Xu(0)=Xu(0) exp(
jπu(u−1k)(u−1k+1)NZC
)64 Preamble sequences xu,ν(n) are cyclic shifts of ZC
xu,ν(n) = xu((n + Cν)%NZC)
1S. Beyme and C. Leung, “Efficient computation of DFT of Zadoff-Chu sequences”
PRACH 7/14
Zero-Correlation ZoneI xu,ν(n) and xu ′,ν′(n) are not orthogonal if u 6= u ′
⇒ shift a ZC sequence as often as possible from single root uI But Cν determines max. RTD estimation ∆max and hence cell size
Shifts for unrestricted set (low-speed cells)
Cν =
{νNCS ν = 0, 1, . . . , bNZC
NCS− 1c, NCS 6= 0
0 NCS = 0
I NCS quantized to 4 bit, NCS = 0, 13, 15, 18, . . . , 279, 419
Example:
1. NCS = 13 ⇒ Cν = 0, 13, 26, . . . , 806, 819, ν = 0, 1, . . . , 63⇒ all preambles orthogonal but ∆max ≈ 11µs, rmax ≈ 1.6 km
2. NCS = 0 ⇒ Cν = 0, ∀ν⇒ all preambles non-orthogonal, computational expensive,∆max ≈ 5ms, rmax > 100 km (preamble format 3)
PRACH 7/14
Zero-Correlation ZoneI xu,ν(n) and xu ′,ν′(n) are not orthogonal if u 6= u ′
⇒ shift a ZC sequence as often as possible from single root uI But Cν determines max. RTD estimation ∆max and hence cell size
Shifts for unrestricted set (low-speed cells)
Cν =
{νNCS ν = 0, 1, . . . , bNZC
NCS− 1c, NCS 6= 0
0 NCS = 0
I NCS quantized to 4 bit, NCS = 0, 13, 15, 18, . . . , 279, 419
Example:
1. NCS = 13 ⇒ Cν = 0, 13, 26, . . . , 806, 819, ν = 0, 1, . . . , 63⇒ all preambles orthogonal but ∆max ≈ 11µs, rmax ≈ 1.6 km
2. NCS = 0 ⇒ Cν = 0, ∀ν⇒ all preambles non-orthogonal, computational expensive,∆max ≈ 5ms, rmax > 100 km (preamble format 3)
PRACH 7/14
Zero-Correlation ZoneI xu,ν(n) and xu ′,ν′(n) are not orthogonal if u 6= u ′
⇒ shift a ZC sequence as often as possible from single root uI But Cν determines max. RTD estimation ∆max and hence cell size
Shifts for unrestricted set (low-speed cells)
Cν =
{νNCS ν = 0, 1, . . . , bNZC
NCS− 1c, NCS 6= 0
0 NCS = 0
I NCS quantized to 4 bit, NCS = 0, 13, 15, 18, . . . , 279, 419
Example:
1. NCS = 13 ⇒ Cν = 0, 13, 26, . . . , 806, 819, ν = 0, 1, . . . , 63⇒ all preambles orthogonal but ∆max ≈ 11µs, rmax ≈ 1.6 km
2. NCS = 0 ⇒ Cν = 0, ∀ν⇒ all preambles non-orthogonal, computational expensive,∆max ≈ 5ms, rmax > 100 km (preamble format 3)
PRACH 8/14
High-Speed Cells
I For cells with high Doppler shifts
I Creates correlation peaks in different search windows (depending onroot u) ⇒ false detection
I Solution: restrict the set of possible search windows, i.e., don’t usewindows (shifts of root sequence) that would contain false peaks
I Drawback: requires computation of numerous different roots toobtain 64 preambles ⇒ increased complexity in PRACHtransmitter/receiver
PRACH 9/14
PRACH Transmitter
compute prach seq generate prach
xu(n) FFT IFFT Repeat CP RF
exp(j 2πkCν
NZC
)Xu(k) Xu,ν(k)
Mapping
I Xu(k) = x∗u (u−1k)Xu(0) with
xu(n) = exp(−j πun(n+1)
NZC
), 0 6 n 6 NZC − 1,
where u−1 is the multiplicative inverse of u modulo NZC, i.e.,u−1u = 1 mod NZC (e.g. u = 129 → u−1 = 826, NZC = 839)
I Phase shift for preamble ν ⇒ cyclic shift Cν in time domain, i.e.,xu,ν(n) = xu((n + Cν) mod NZC)
I Sub-carrier mapping and N-IFFT (e.g. N = 6144 for 5MHz BW)
I Sequence repetition for PRACH formats > 1
I CP insertion
PRACH 10/14
PRACH Receiver
CP/FFT IFFT Detection
X ∗u (k)
rxdata
yu,ν(t, τ) Yu,ν(k , τ) ∀u yu,ν(t, τ) u,ν
τ
I Received signal yu,ν(t, τ) = xu,ν(t) ∗ h(t − τ) + w(t)
I CP removal and N-FFT (e.g. N = 6144 for 25 RBs)
I Dot-product with sequence X ∗u (k) (for all configured roots u)
Yu,ν(k , τ)X ∗u (k) = H(k , τ)Xu,ν(k)X ∗u (k) + W (k)
= H(k , τ)ej 2πkCν
NZC + W (k)
I N-IFFT (e.g. N = 1024 for NZC = 839)
yu,ν(t, τ) = F−1{Yu,ν(k , τ)X ∗u (k)} = h (t − (τ− Cν)) + w(t)
I Detection of peak of |yu,ν(t, τ)|2 at τ− Cν corresponding topreamble u,ν and channel delay τ
PRACH 11/14
Timing-Advance estimation
I Accuracy of 61441024 = 6 samples (, 0.78µs)
I Resolvable delay-spread depends on zero-correlation zone NCS
I Example: NCS = 13 with upsampling factor 1024839 ⇒ N ′CS = 15 ⇒
τmax = 6(N ′CS − 1) = 84 samples (, 10.94µs)
Numerical Results 12/14
False Detection Rate vs. UE Speed
0 100 200 300 400 500 600 700 800 9001,0000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
UE Speed [km/h]
fals
ed
etec
tion
rate
SNR=10dB, preamble=60, NCS = 15, root seq. num. = 0, 2Rx eNB
Low-Speed CellsHigh-Speed Cells
Summary and Future Work 13/14
Summary
I PRACH allows for efficient UL timing estimation in a wide-range ofenvironments (ZC properties, flexible ZCZ, formats)
I PRACH transmitter/receiver can be complex (large FFT-sizes,multiple FFTs for large cells or high mobility)
I Good performance up to 700 km/h
Summary and Future Work 14/14
Future Work
I Only PRACH configuration indexes 0-11 in 36.211 Table 5.7.1-4 areimplemented
I Possible algorithm optimization in PRACH sequence transmitter andPRACH receiver (e.g. computation of multiplicative inverse,...)
I PRACH receiver computation seems to take too long on hardwareleading to missed slots
I More testing required with signal generator and channel emulator
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