R1- 060797
`
`
`
`
`3GPP TSG RAN WG1 Meeting #44bis
`Athens, Greece, March 27-31, 2006
`
`Agenda Item: 10.2.3
`Source:
`Huawei
`RACH design for E-UTRA
`Title:
`Document for: Discussion
`
` 1
`
` Introduction
`The random access channel (RACH) is used on the uplink of E-UTRA in order to notify the network that
`the UE has data to transmit, as well as to allow the Node B to estimate the timing of the UE. In WCDMA
`the RACH channel consists of a preamble and a message burst. There are multiple orthogonal preambles to
`allow simultaneous access of multiple UEs to the network. A message burst is transmitted after the Node B
`has acknowledged the successful reception of the RACH preamble.
`In order to achieve low latency in accessing the network in E-UTRA it is desirable that the UE transmits at
`high power at the first transmission and avoids power ramping. It implies that the RACH preambles should
`allow for small power back-off in the UE’s output power amplifier.
`Another important factor to achieve low latency is the ability of the Node B to correctly detect several
`simultaneous random access preambles and to correctly estimate their timings. For that purpose, the RACH
`preambles should have the following properties: a) Good autocorrelation properties to allow for accurate
`timing estimation; b) Good cross-correlation properties to allow for accurate timing estimation of different
`simultaneous and asynchronous RACH preambles; and c) Zero cross-correlation for synchronous and
`simultaneous RACH preambles.
`The RACH preambles in WCDMA satisfy to large extent all of the desired correlation properties.
`However, some of these properties, such as mutual cross-correlation, i.e. the detection probability of a
`single preamble in presence of a number of other simultaneous preambles still could be better at low SIR
`values.
`The range of delays on which both out-of-phase autocorrelation and cross-correlation of RACH preambles
`should have low values is primarily determined by the maximum round-trip delay from the Node B to the
`UE, because the UE synchronizes its RACH transmissions to the timing of the broadcast pilot signals from
`the Node B. Depending on the length (duration) of RACH preambles, such low-correlation zone (of delays)
`of interest might be less than the length of the preambles. If that is the case, the sets of RACH preambles
`can be designed to have improved correlation properties for the delays of interest.
`Thus in this contribution we deal with the design of the sets of RACH preambles for E-UTRA, with the
`major goal to reduce the latency of RACH procedure compared to the current UTRA system by improving
`preamble detection probability in presence of other simultaneous preambles. For certain applications it
`may be beneficial to transmit the RACH message immediately after the RACH preamble. This issue is
`investigated in [1].
`In Section 2, the multiplexing of the random access channel is discussed. In Section 3 the RACH preambles
`based on zero correlation zone GCL sequences are proposed. In Section 4 the simulation results, both of the
`evaluation of the probability of preamble detection in presence of other received preambles, as well as of
`the evaluation of transmit power back-off, are presented. Finally, Section 5 concludes the paper.
`2 Multiplexing of Random Access and Data Transmissions
`According to the TR [2], the random access transmissions and data transmissions are multiplexed in time
`and/or frequency. Such orthogonal multiplexing allows for random access transmissions at high initial
`transmission power and thus low latency. The drawback of the orthogonal multiplexing is that resources
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`are allocated to random access that may not be used. To reduce such waste of resources, the amount of
`resources allocated to RACH preambles can be semi-static and decided on the estimated need for random
`access transmissions.
`Code division multiplexing (CDM) has also been proposed [3]. With CDM, specific resources that may not
`be used by the random access channel are not allocated. However, there is interference between the random
`access transmissions and the data transmissions. In [3] the interference analysis is based on the
`pre-condition that the RACH preambles are sent with the appropriate power for good detection
`probabilities. To achieve that, an accurate power control like power ramping in WCDMA is needed. Such
`ramping increases latency and is not desirable.
`In order to minimize the latency we propose hybrid TDM/FDM for multiplexing of the RACH preamble
`and data in accordance with [2].
`3 Zero Correlation Zone GCL Sequences
`The starting point for the design of the new RACH preambles with improved correlation properties is the
`application of the sets of so-called Zero Correlation Zone (ZCZ) sequences. Namely, a set of ZCZ
`sequences consists of equal-length sequences whose periodic out-of-phase autocorrelation is zero over the
`range of delays |p|≤D, while the periodic cross-correlation between any two sequences from the set is zero
`in the same range of delays |p|≤D, which is referred to as a ZCZ. For given length of sequences, N, and
`given number of sequences in the set, M, the upper bound of the length D of the ZCZ is given by [4]
` D≤N/M-1.
`
` (1)
`Having in mind possible efficient implementation of the corresponding bank of matched filters for the new
`RACH preambles, as well as compatibility with the structure of RACH preambles in UTRA system, in the
`sequel we shall consider a new general ZCZ sequence sets that are defined as the orthogonal sets of
`Generalized Chirp-Like (GCL) sequences [5]. A GCL sequence {c(k)} is defined as
`
`
` ()( kbka
` )(kc
`k
`m
`N
`mod
`,1,0
`),
`.1
`,
`
`
`
` (2)
`
`
`where N=sm2, s and m are positive integers, {b(k)} is a “modulation” sequence of m arbitrary complex
`numbers of unit magnitude, while {a(k)} is a special “carrier” sequence, which has to be a Zadoff-Chu
`sequence defined as
` a(k) =
`
` Nkk(
`
`2/)2mod
`
`
`
`qk
`
`, k=0, 1, …, N-1,
`
`
`
`NW
`where WN=exp(-j2πr/N), r is relatively prime to N, and q is any integer.
`Any GCL sequence has an ideal periodic autocorrelation function. If the two GCL sequences cx(k) and cy(k)
`are defined by using the same Zadoff-Chu sequence {a(k)} but different, arbitrary modulation sequences
`{bx(k)} and {by(k)}, it can be shown (similar as in [6], see the Appendix) that the periodic cross-correlation
`θxy(cid:31)(p), defined as
`
`
`
` (3)
`
`
`
`
`
` )( (kckc
`*
`y
`x
`
`
`
`p
`
`)
`
`,
`
`1 0
`
`N k
`
`(
`
`
`
`p
`
`)
`
`
`
`
`
`xy
`
`(
`
`
`p 
`)
`yx
`
`
`
`is zero for all time shifts plsm, l=0,1,…,m-1, i.e.
`
`
`
` θxy(cid:31)(p) = 0, for 0<|p|<sm, sm<|p|<2sm, …,(m-1)sm<|p|< sm2. (4)
`
`Thus, if the above two modulation sequences are orthogonal, the resulting GCL sequences will be not just
`orthogonal, but also will have a Zero Correlation Zone (ZCZ) of length sm-1, i.e. the periodic
`cross-correlation between any two sequences from the set will be zero for all the delays between –sm and
`+sm. Based on this property, the set of m preambles is defined by the following construction:
`Construction: The set of orthogonal GCL sequences is obtained by modulating a common Zadoff-Chu
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`sequence {a(k)} of length N=sm2 with m different orthogonal modulation sequences {bi(k)},
`i=0,1,2,…,m-1, k=0,1,2,…,m-1.
`Although the matched filters for RACH preambles actually calculate the aperiodic auto/cross-correlations,
`it is expected that the ideal periodic cross-correlation properties will be to large extent preserved. The
`reason is that for delays between –sm and +sm, typically much smaller than the length of the sequences, the
`summations in the formulas for the aperiodic and periodic cross-correlation values only differ in a small
`number of terms. This expectation is confirmed by numerical evaluations, as it will be shown later.
`It can be seen that the above general construction produces the sets of ZCZ sequences with maximum
`length D=sm-1 of the ZCZ for given sequence length N=sm2 and given number of sequences in the set
`M=m, i.e. D satisfies the upper bound (1).
`
`3.1
` Some Interesting Special Cases of Orthogonal GCL Sequence Sets
`The most obvious choices for the selection of orthogonal modulation sequences would be either the sets of
`Hadamard sequences or Discrete Fourier Transform (DFT) sequences. The set of DFT sequences is defined
`as
`
`
`,ki
`m
`
`
` )( Wkb
`ik
`,
`,1,0
`,
`1
`
`
`i
`m
`The set of Hadamard sequences is defined as the rows in an mxm Hadamard matrix, which is defined as
`T=mI
`follows: A Hadamard matrix Hm of order m consists of only 1s and -1s and has the property HmHm
`where I is the identity matrix and T denotes transpose. For m=2n, where n is a positive integer, Hadamard
`sequences can be defined as
`
`
`
`
`
`. (5)
`
`l ki
`
`
`l
`
`, (6)
`
`m l
`
`
`
` )(kb
`,ki
`m
`
`
`)1(
`,
`,1,0
`,
`1
`
`
`
`
`i
`where il, kl are the bits of the m-bits long binary representations of integers i and k.
`
`
`1 0
`
`
`
`
`
`
`
`3.2 Design of Numerical Parameters of the Proposed RACH Preambles
`The question is now how to select the actual numbers m and N to fit into the requirements of E-UTRA. The
`access slot, i.e. the time-frequency resource allocated for RACH, has a duration TA and can be confined to a
`sub-band of the total available spectrum. In order to distinguish which cell a transmitted RACH preamble is
`intended for, the access slots in adjacent cells should as much as possible be separated in time and
`frequency.
`The duration of the preamble is denoted by TS and is given as the quotient of the sequence length N and the
`bandwidth B of the RACH preamble: TS =N/B. The maximum round-trip time, τd =2R/c, where R is the cell
`range (radius) and c is the speed of light. The performance targets for E-UTRA are required to be met for
`cell ranges up to 5 km and to be met with slight degradation for cells ranges up to 30 km. The specifications
`should not preclude cell ranges up to 100 km [7].
`The maximum delay spread, τs, depends on the environment. TS should be shorter than TA to avoid that the
`received signal extends after the access slot. Let τm be the sum of the maximum round-trip time and the
`maximum delay spread: τm =τd+ τs. Then TS < TA - τm , so it follows
` N < (TA - τm )B. (7)
`The duration of the ZCZ is equal to D/B, and should be greater than the total maximum delay τm.
`Since D=sm-1 and N=sm2, D can be expressed as D=N/m-1. Hence,
` N/m-1 > τmB. (8)
`Replacing N with the right-hand side of (7), it follows that
` m < (TA - τm ) /( τm+1/B). (9)
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`The bandwidth B has to be larger than the inverse of the required accuracy of the time-of-arrival estimation,
`which is much smaller than the shortest duration of the cyclic prefix, 3.65 μs [2]. τm is typically of the order
`of several microseconds and hence is much greater than 1/B. It can be seen from (9) that the number of
`sequences in the set is then almost independent of B. Therefore, in order to use the spectrum efficiently, B
`should be as small as possible. The total number of preambles in a cell can then be increased by allocating
`several sub-bands for RACH. The number of preambles can also be increased by using several sets of
`GCL-sequences with different values of r. We select B to be 1.024 MHz, which gives a time-of-arrival
`estimation resolution of close to 1 μs. It also gives a margin to the minimum uplink nominal bandwidth,
`which is 1.25 MHz.
`In the numerical design, TA is first selected to give a large enough number of signatures as given by (9).
`Then, m and s should be selected such that (7) and (8) are satisfied. In order to fulfill the different
`requirements for various cell ranges we propose four different parameter sets, as shown in Table 1.
`
`Table 1 Numerical parameters of RACH preambles
`R (km) TA(ms)
`N
`τd(μs)
`τs (μs) m
`5
`0.5
`33
`5
`10
`400
`13
`0.5
`87
`5
`4
`400
`30
`1.0
`200
`20
`3
`792
`100
`3.0
`667
`20
`3
`2367
`
`As an example of extending the set of preambles consider the case of R=13 km. From Table 1, N=400 and
`there are 160 valid choices of r for which r and N are relatively prime. As a bandwidth of 5 MHz
`accommodates four 1.25 MHz wide subbands, there are then 4·4·160=2560 possible preambles.
`
`4 Simulation results
`Three kinds of evaluations are performed. First, the aperiodic cross-correlation functions of the GCL
`sequences are investigated, to confirm that the properties are similar to the ideal periodic cross-correlation
`functions. Then, the detection performance, in particular in the presence of interfering preambles, of the
`GCL sequences is compared to the performance of truncated WCDMA RACH preambles. Finally, the
`impact of the proposed sequences on the transmit power back-off is evaluated. The parameters of the GCL
`sequences are N=400 (s=25 and m=4), q=0, and r=1 throughout the section.
`4.1 Aperiodic cross-correlation properties
`
`
`
`p
`
`)
`
`, p≥0,
`
`p
`
`*
`y
`x
`
`
`
` kckc )( (
`
`N
`
`1
`
`
`
`
`k
`0
`
`where p is the delay and “*” denotes complex conjugate, is shown in Figure 1, for the GCL-DFT sequence.
`The set of GCL-Hadamard sequences has similar autocorrelation and cross-correlation functions.
`The peaks of the cross-correlation functions are located near multiples of sm=100. However, for the given
`parameters, the cross-correlation functions do not exceed 20 for delays less than 96.
`4.2 Detection probability
`The detection performances of the proposed preambles have been evaluated by link-level simulations. The
`truncated WCDMA RACH preamble has been used as a reference with modulating Hadamard sequences
`that are 4 bits long, instead of 16 bit long sequences, to keep the same number of signature sequences as for
`the proposed sequences.
`The number of receive antennas is two and correlations from the two antennas at the same delay are
`combined non-coherently, i.e. the absolute values of the squared matched filter outputs from the two
`antennas at the same delay are added. The propagation channels simulated are AWGN and Typical Urban
`(TU) at 3 km/h.
`
`
`The amplitude of the aperiodic cross-correlation function
`xy
`
`(
`
`p
`
`)
`
`
`
`*
`
`yx
`
`(
`
`
`
`p
`
`)
`
`
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`Figure 1 Absolute values of the autocorrelation and cross-correlation functions of the GCL-DFT sequences.
`
`
`The detector correlates the received signal with all possible preambles in the search window. A threshold is
`set to give a false alarm probability of 0.0001 at a single delay. Missed detection is declared if the
`transmitted preamble is not detected within the true range of delays of received signal replicas. The number
`of concurrently transmitted preambles ranges from 1 to 4. All preambles are transmitted with independent
`random delays within the search window, corresponding to randomly distributed mobiles in the cell. If two
`or more different preambles are transmitted using the same time-frequency resources, the signal-to-noise
`ratio (SNR) of the observed preamble (whose probability of missed detection is evaluated) is fixed (SNR =
`-15 dB) and the other interfering preambles are transmitted with various power offsets to the observed
`preamble. However, all interfering preambles are transmitted with the same power.
`As it is not yet decided whether a message will be transmitted in conjunction with the RACH preamble, we
`also consider RACH bursts with the preamble immediately followed by a message. The message is
`modelled as a random sequence of QPSK symbols; the sequence has the same length and is transmitted
`with the same power as the preamble. Simulation results with a message are only shown for the worst case
`of four transmitted RACH bursts.
`The probabilities of missed detection of the observed preamble as functions of SNR are shown in Figure 2,
`for the case of a single transmitted preamble without message, both on AWGN and TU channels. The
`probabilities of missed detection of the observed preamble as functions of signal-to-interference ratio
`(SIR), in presence of interferers, are shown in Figures 3 and 4 for AWGN and TU channels respectively.
`The SIR is defined as the ratio of the power of the observed preamble to the power of any of the interfering
`preambles.
`From Figure 2 it is clear that there is no difference in the probability of missed detection in the absence of
`interfering sequences between WCDMA RACH preambles and the proposed preambles. The probability of
`missed detection does not change when the message is sent immediately after the preamble (not shown).
`However, the results shown in Figures 3 and 4 clearly demonstrate significantly improved detection
`performance of the proposed preambles in the presence of one or several interfering sequences. For the
`proposed set of RACH preambles, the detection performance does not change with an increased number of
`interferers, whereas for the WCDMA preambles the performance deteriorates as the number of interferers
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`increases. The lower probability of missed detection for the proposed set of preambles is due to the good
`cross-correlation properties of the zero-correlation zone sequences. When a message is sent together with
`the preamble, there is some degradation in the detection performance, in particular for the GCL sequences.
`However, there is still a large gain compared to the WCDMA preamble.
`
`Figure 2 Missed detection probability for one transmitted sequence
`
`
`
`
`
`Figure 3 Missed detection probability of a transmitted sequence in presence of interferers.
`
`
`
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`Figure 4 Missed detection probability of a transmitted sequence in presence of interferers.
`
`
`
`
`
`4.3 Transmit Power Back-Off
`Two measures related to the power back-off are the peak-to-average power ratio (PAPR) and the cubic
`metric (CM).
`Let z(t) be the normalized baseband signal, such that its expectation value E(|z(t)|2) = 1. The PAPR at the
`99.9th percentile is defined as the value x such that the probability that 10log10(|z(t)| 2)< x equals 0.999.
`The CM is defined in [8].
`Table 2 lists the PAPR values at the 99.9th percentile for a reference WCDMA RACH preamble truncated
`to 400 samples with 4-bit Hadamard modulating sequences, and for the GCL sequences with DFT and
`Hadamard modulating sequences. Table 3 lists the corresponding CM values.
`
`Table 2 PAPR (99.9th percentile) values
`Pulse-shaping filter
`WCDMA GCL-DFT GCL-Hadamard
`Sinc
`3.9–5.9 dB
`2.8 dB
`4.5 dB
`Root-raised cosine ,
`2.6–3.4 dB
`3.0 dB
`3.6 dB
`roll-off factor=0.15
`
`Pulse-shaping filter
`Sinc
`Root-raised cosine,
`roll-off factor=0.15
`
`Table 3 Cubic metric values
`WCDMA
`GCL-DFT GCL-Hadamard
`0.1–0.5 dB
`-0.6 dB
`1.4 dB
`−0.3 to −0.1 dB
`-0.6 dB
`1.1 dB
`
`
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`In all cases the maximum PAPR value is given over all modulating sequences. The range of values given
`for the WCDMA RACH preamble is over all scrambling codes. For the GCL sequences, the Zadoff-Chu
`sequence with r=1 has been used. Two different pulse-shaping filters are applied, a simple sinc filter and a
`root-raised cosine filter with roll-off factor 0.15 (as in [9]).
`From the tables, it is clear that the DFT-modulated sequence has both lower PAPR and lower cubic metric
`than the Hadamard-modulated GCL sequence. Furthermore, applying a root-raised cosine filter improves
`neither PAPR nor the cubic metric of the DFT-modulated sequence.
`Finally, the PAPR of the DFT-modulated GCL sequence is as good as for the WCDMA sequences with a
`root-raised cosine filter, while the cubic metric is somewhat better than for the WCDMA sequences.
`Apparently, it is possible to find sets of GCL sequences that allow for a low power amplifier back-off.
`
` 5
`
` Conclusion
`The proposed RACH preambles based on ZCZ-GCL sequences allow for detection of several simultaneous
`preambles with a high detection probability even when the powers of the received signals are very
`different. The probability of detection of each proposed preamble is independent of the number of
`interfering signals, quite opposite to the RACH preambles in WCDMA. This property, along with a
`reduced power amplifier back-off in the case of DFT modulated GCL sequences, can help to reduce the
`latency in E-UTRA.
`In case that it is needed to increase the number of preambles in a cell or in the system, ZCZ-GCL preambles
`can be combined with random selection of transmission sub-bands and/or multiple “carrier” (Zadoff-Chu)
`sequences.
`
`References:
`[1] R1-060541,” Some Considerations for Random Access Frame Design,” Huawei, February 2006.
`[2] TR 25.814 v1.0.1, “Physical layer aspects for Evolved UTRA,” December 2005.
`[3] R1-060387, “RACH Design for EUTRA,” Motorola, February 2006.
`[4] H.Torii et al., “A New Class of Zero-Correlation Zone Sequences”, IEEE Transaction on Information Theory,
`Vol. 50, No.3, pp. 559-565, Mar. 2004.
`
`[5] B. M. Popovic, ”Generalized chirp-like polyphase sequences with optimum correlation properties,” IEEE
`Transactions on Information Theory, vol. 38, no. 4, pp 1406-1409, July 1992.
`[6] B. M. Popovic, “New Complex Space-Time Block Codes for Efficient Transmit Diversity,” IEEE 6th Int. Symp.
`on Spread-Spectrum Tech. & Appl (ISSSTA 2000)., NJ, USA, pp. 132-136, Sep. 2000.
`[7] TR 25.913 v7.2.0, “Requirements for Evolved UTRA (E-UTRA) and Evolved UTRAN (E-UTRAN),”
`December 2005.
`[8] TS 25.101 v6.8.0, “User Equipment (UE) radio transmission and reception (FDD),” June 2005.
`[9] R1-051058, “RACH Preamble Design,” Texas Instruments, October 2005.
`
`
`Appendix: Periodic Cross-Correlation of GCL Sequences
`The periodic cross-correlation xy(cid:31)(p) of two GCL sequences cx(k) = bx(k mod m)·a(k) and
`k(k+N mod 2)/2 +qk, k=0,1,2…,N-1, N=sm2, is defined as
`cy(k)=by(k mod m)·a(k), a(k)= WN
`yx(cid:31)(-p) = 
`xy(cid:31)(p) =
`
`where “*” denotes complex conjugation. It follows
`
`1 0
`
`N k
`
`*
` )( (kckc
`
`
`y
`x
`
`
`
`p
`
`)
`
`, (A.1)
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`
`kp
`
`
`N
`
`
` (kb
`x
`
`mod
`
`
`
`) bm
`
`
`*
`y
`
`((
`
`k
`
`
`
`p
`
`)
`
`mod
`
`m
`
`)
`
`, (A.2)
`
`1 0
`
`W
`
`N k
`
`
`
`where C(p)=
`
`22mod
`
`
`2/
`
`. By introducing a change of variables
`
`xy(cid:31)(p) = C(p) 
`
`
`Np
`pq
`
`NW
` k=im+j, i=0,1,..,sm-1, j=0,1,…,m-1, (A.3)
`into (A.2), it follows that
`
`xy(cid:31)(p) =
`
`
`
`( pC
`
`)
`
`sm
`
`1
`ip
`
`smW
`
`
`
`i
`0
`
`
`If plsm, l=0,1,…,m-1, the first summation in (A.4) is zero, hence xy(cid:31)(p)=0 for arbitrary modulation
`sequences {bx(j)} and {by(j)}. In this way we have completed the proof of (4).
`
`W
`
`
`N
`
`jp
`
`b
`
`x
`
`(
`
`j
`
`mod
`
`
`
`) bm
`
`
`((
`
`j
`
`
`
`p
`
`)
`
`mod
`
`m
`
`)
`
`, (A.4)
`
`*
`y
`
`m j
`
` 
`
`1 0
`
`SAMSUNG 1006-0009