Physical Random Access Channel - PRACH

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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


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





Introduction 3/14


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





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


UE

eNB

t

t

1

2a






Introduction 4/14


UE

eNB

t

t

1

2a

2b






Introduction 4/14


UE

eNB

t

t

1

2a

2b 3






Introduction 4/14


UE

eNB

t

t

1

2a

2b 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:


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 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


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

Physical Random Access Channel - PRACH

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