R1-060884
`
`3GPP TSG RAN1#44-bis
`Athens, Greece
`March. 24 – March 26, 2006
`
`Agenda Item:
`Source:
`Title:
`Document for:
`
`
`
`
`
`
`10.2.3
`Motorola
` Random Access Sequence Design
`Discussion
`
`
`1. Introduction
`
`This paper summarizes preamble design of random access channel for E-UTRA, including preamble design
`for non-synchronized random access with code multiplexing approach, and synchronized preamble design
`with TDM/FDM approach. Detailed design examples are provided together with detection and timing
`estimation algorithms.
`
`
`
`2. Preamble Design for Non-synchronized Random Access with Code Multiplexing
`
`The preamble of non-synchronized random access can be transmitted with a long spreading factor,
`overlapped with the scheduled data channel. We call this approach as code division multiplexing (CDM)
`design for preamble. The preamble is separated from the scheduled channel with a long spreading code.
`The large spreading gain ensures low interference and good detection performance for preamble detection.
`
`The basic structure of the preamble for non-synchronized random access is illustrated in the Figure 1. The
`length of the preamble is 1ms over two 0.5ms sub-frames. Each 0.5ms sub-frame consists of several DFT-
`S-OFDM symbols with extended cyclic prefix (CP). The length of the extended CP should be not less than
`the maximum round-trip delay. In this case, the numerology of long CP frame structure specified for
`downlink transmission scheme in TR 25.814 is applied. The number of DFT-S-OFDM symbols per 0.5ms
`sub-frame is 6, and the extended CP duration is 16.67us, for all scalable bandwidth deployments.
`
`The random access channel sequence(s) gn to generate the transmitted random access preamble waveforms
`should have the following properties:
`
`
`1. Good detection probability while maintaining low false alarm rate e.g. by maximizing post-
`decoder Es/(Nt+Ne) for a occupied random access channel preamble where Ne is the residual
`interference due to other random access channel transmissions in a given random access channel
`and Nt is thermal noise.
`a. cross correlation of the sequences that occupy the same frequency and same cyclic shift
`value impacts achievable Es/(Nt+Ne) and false alarm rate
`2. Number of random access channel preamble waveforms should be defined to handle the maximum
`expected multiple access scenarios (traffic load) while guaranteeing low collision probability.
`a. Subsets of preambles could be defined such that performance is improved at lighter loads
`(e.g., first use cyclic shifts of a single CAZAC/GCL sequence before using additional
`sequences)
`3. Enable accurate timing estimation (e.g. good autocorrelation properties and sufficient occupied
`BW).
`4. Low power de-rating (low CM/PAPR).
`
` A
`
` good choice of the signature sequence is the GCL sequence, including Frank-Zadoff-Chu sequence.
`GCL sequence has optimal periodic autocorrelation performance and very good periodic cross-correlation
`property when designed properly. Besides, a Walsh orthogonal sequence can be used together with the
`GCL sequence to fit into the preamble frame structure.
`
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`As an example, with 5MHz bandwidth, there are 300 usable sub-carriers per symbol. A GCL sequence
`with length M=300 will occupy one symbol. The GCL sequence can be further spread with a Walsh
`sequence into several symbols. One example is to select the Walsh sequence with length W=4. The total
`spreading factor will be WM=1200, which corresponds to a spreading gain of 30.8dB. Figure 1 illustrates
`an example of the random access preamble with the Walsh sequence {+1, -1, +1, -1}. The parameters for
`this design are summarized in Table 1. Given one GCL sequence, there are 16 possible random access
`opportunities. When the bandwidth is large, more GCL sequences with good correlation properties can be
`used to increase the random access opportunities.
`
`
`Figure 1 Preamble Design with Code Multiplexing
`
`
`
`
`
`Table 1 Example CDM Design Parameters for Non-Synchronized Random Access
`RACH Parameters of CDM
`Bandwidth (MHz)
`5.0
`10.0
`15.0
`Design
`MHz
`MHz
`MHz
`300
`600
`900
`4
`4
`4
`4
`4
`4
`4
`8
`12
`64
`128
`192
`
`20.0
`MHz
`1200
`4
`4
`16
`256
`
`
`
`Chip Length/Sym (M )
`Length of Walsh Code (N W )
`# of Cyclic shifted (N SH )
`# of Sequences (N S )
`# RACH opportunities
`
`1.25
`MHz
`75
`4
`4
`1
`16
`
`2.5
`MHz
`150
`4
`4
`2
`32
`
`
`
`2
`
`pn
`
`e
`
`when
`
`M
`
` is even
`
`
`
`j
`
`pn n
`(
`
`1)
`
`
`
`
`
`
`g
`
`n
`
`
`
`Preamble Sequence Design
`
`General chirp-like (GCL) [5] or its special case, Chu-sequence [6] can be selected as the signature sequence.
`The Chu-sequence is defined [6] as
`2 1
`
`j
`
`M
`2
`
`,
`
`n
`
`
`
`0,1,
`
`,
`
`M
`
`
`
`1
`
`
`
`
`
`2 1
`
`when M
`e
`
` is odd
`M
`2
`where p is relatively prime to M. For a fixed p, the Chu-sequence is orthogonal to its time-shift. For
`different p, Chu-sequences are not orthogonal. Note that all GCL sequences (including the Chu-sequence)
`have optimal autocorrelation properties.
`
`There is an extra benefit of selecting GCL sequence with a prime number length [4]. From [5], GCL
`sequence with a prime number length will yield “optimal” cross-correlation performance. However, the
`optimal sequence can be truncated to obtain a signature sequence with arbitrary length. This approach may
`yield some increase in PAPR/CM. Careful selection of sequence may make this side effect marginal,
`particularly for a large M.
`
`Different GCL sequences can be used to increase random access opportunities and to mitigate inter-cell
`interference for random access channel. Note that for Chu-sequence, different p can yield different group
`of signature sequences. For M = 300, p = {1,7,11,13,17,19,23,29,31,37,…}. Given a fixed p, the
`corresponding Chu-sequence is orthogonal when it is shifted circularly. However, the sequences are not
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`orthogonal for different p and behave as random sequences. Thus, by assigning different p to different
`sector/cell, inter-cell interference can be mitigated. For M=300, one can select at least 20 sequences as
`listed in Table 2.
`
`Table 2 p Values of Chu-Signature Sequences for Sectors/Cells
`
`10 11 12 13 14 15 16 17 18 19 20
`9
`8
`7
`6
`5
`4
`Index 1 2 3
`p
`1 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79
`
`
`
`Preamble Detection and Timing Estimation
`
`When an UE randomly selects a preamble with a GCL sequence gn and a Walsh sequence wn, the preamble
`is a repetition of the sequence with length WM, where W is the length of the Walsh sequence. For one
`DFT-S-OFDM symbol, the transmit sequence is xn=w(i)gn, where i is the index of DFT-S-OFDM symbol
`and i=0, …, W-1.
`
`At the receiver, the received signal i-th symbol can be represented as
`
`
`( )i
`( )i
`
`( )i
`y
`x
`h
`z
`,
`
` 
`n
`n
`n d
`n
`
`where  indicates circular convolution, hn is channel impulse response, and d is the delay between the
`transmit xn and node-B perceived uplink timing. Note that the delay d should be less than the extended CP
`length, which is 16.68us in this example. It is assumed that the channel does not change or changes very
`slowly over W number of symbols. Combining with Walsh code
`1
`W
`1
`
`
`( )i
`y
`w i y
`W g
`h
`( )
`
` 
`n
`n
`W
`i
`0
`
`
`
`
`n
`
`
`
`n d
`
`
`1
`W
`
`W
`1
`
`
`i
`0
`
`
`w i z
`( )
`
`( )i
`
`
`n
`
`.
`
`
`The periodic correlation of sequence gn and yn is
`1 M
`1
`
`c
`y g
`
`
`m
`n
`n m
`M
`) mod
`
`M
`n
`0
`
`The correlation can be performed either in time or frequency domain. Through some manipulations, we
`obtain
`
`
`
`*(
`
`
`
`WM h
`m d
`
`
`
`
`z
`
`'
`m
`
`,
`
`c
`m
`where zm’ is the equivalent channel noise.
`
`When the channel information is not available to the receiver at the Node-B, energy of cm is used for
`preamble detection and timing estimation.
`
`The detection algorithm consists of three steps. The average power of correlation sequence is first
`computed.
`
`|
`
`c
`m
`
`2
`|
`
`.
`
`M
`1
`
`m
`0
`
` 
`
`1
`WM
`
`Next, the following is computed
`
`P
`
`
`
`1 max |
`arg max
`c
`c
` 
`d
`m
`m
`P
`m
`m
`where d is the maximum power and d is the estimated timing delay of the channel path with maximum
`power. The final step is to check whether the maximum power is greater than a pre-defined power
`threshold TH . Thus,
`
`|
`
`2
`|
`
`,
`
`
`2
`d
`| , and
`
`
`d
`random access request with delay
`random access is absent
`
` is present
`
`.
`
`
`
` 
`d
`TH
`
` 
`
`d
`TH
`
`
`
`
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`Performance
`
`The detection and false alarm performance of the CDM scheme over a TU 3km/hr channel is illustrated in
`Figure 2. When the SNR is -18dB, the detection error rate is 1% with a falsm alarm rate of 0.1%. This
`indicates that the effective SNR for the preamble detection at the Node-B can be as low as -18dB for
`effective detection.
`
`Figure 2. Detection Error and False Alarm Performance over TU-3km/h Channel
`
`
`
`Can be used for other random- access
`channels or data transmission.
`
`Data transmission
`
`BWRA
`
`0.5 ms subframe
`
`1 DFT-SOFDM Symbol
`
`(Scheduled) Data transmission
`
`Random Access Preamble (Scheduling Request)
`Figure 3 Synchronized Random Access Design
`
`
`
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`3. Preamble Design for Synchronized Random Access
`
` A
`
` TDM/FDM region corresponding to one or several DFT-S-OFDM symbol is reserved for synchronized
`random access. A random access symbol can be reserved every x frames (e.g. x = 1 … 10.) as shown in
`Figure 3. In the localized mode the sub-carriers are divided into NRB resource blocks with each resource
`blocks uses a fixed number of contiguous sub-carriers. Next, for each of the NRB resource blocks, a number
`of signature sequence groups are pre-defined so that every group consists of NS signature sequence and
`different groups can be assigned to different neighboring sectors. Each group may also consist of several
`cyclically shifted version of the signature sequences (NSH ). As such, the total number of RACH
`opportunities per DFT-SOFDM symbol is given by NRB*NS.* NSH .
`
`There are different design options for E-UTRA based on this structure. One design example is summarized
`in Table 3. In this example, which corresponds to 5MHz bandwidth, 300 subcarriers are divided into 4
`resource blocks with NRB =4. A RACH signature sequence occupies 75 subcarriers corresponding to
`1.25MHz bandwidth. The number of RACH opportunities varies with bandwidth (e.g. 64 for 5MHz).
`
`
`Table 3 Example RACH Parameters for the TDM/FDM Structure
`RACH Parameters in
`Bandwidth (MHz)
`5.0
`10.0
`Localized mode
`1125
`1125
`min. RB BW (kHz)
`4
`8
`# RB (N RB )
`# of Occupied Subcarriers
`75
`75
`# of Sequences (N S )
`8
`8
`# of Cyclic shifted(N SH )
`2
`2
`64
`128
`# RACH opportunities
`
`15.0
`1125
`12
`75
`8
`2
`192
`
`20.0
`1125
`16
`75
`8
`2
`256
`
`
`
`1.25
`1125
`1
`75
`8
`2
`16
`
`2.5
`1125
`2
`75
`8
`2
`32
`
`
`Figure 4 Detection Error Rate and False Alarm Rate for Synchronized Random Access Channel
`
`
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`The signature sequence are obtained from different “classes” of generalized chirp like (GCL) or Chu-
`sequences which are complex valued and have unit amplitude. The GCL/Chu sequence have low cross
`correlation at all time lags which improves the detection performance.
`
`The detection algorithm for signature sequence is similar to that of non-synchronized random access. The
`detection and false alarm performance for 5MHz bandwidth is illustrated in Figure 4. The length of
`signature sequence is specified in Table 3. Figure 4 indicates that the random access has good performance
`at SNR=-2dB, where the detection error rate is about 1%, and the false alarm rate is about 0.5%.
`
`
`
` A
`
`4. Conclusion
`
` preliminary design for non-synchronized random access with code multiplexing approach is proposed in
`this contribution. Also a synchronized random access with TDM/FDM allocation is discussed. Detection
`and timing estimation algorithm for non-synchronized random access is presented. It has shown that good
`detection performance with low false alarm probability can be achieved with the code multiplexing random
`access design. The interference to scheduled channel is expected to be insignificant due to the large
`spreading factor.
`
`
`
`5. References
`
`1. R1-051058, “RACH Preamble Design,” Texas Instruments, RAN1#42bis, San Diego, USA, Oct. 2005.
`2. R1-051033, “Further Topics on Uplink DFT-SOFDM for EUTRA,” Motorola, RAN1#42bis, San
`Diego, USA, Oct. 2005.
`3. R1-051173, “Link Comparison of Localized vs. Distributed Pilot and Localized vs. Distributed Data,”
`Texas Instruments, RAN1#42bis, San Diego, USA, Oct. 2005.
`4.
`IEEE C802.16e-04/143r1, “Ranging Improvement for 802.16e OFDMA Phy”, Motorola
`5. B. M. Popovic, “Generalized Chip-Like Polyphase Sequences with Optimum Correlation Properties,”
`IEEE Trans Inform. Theory, vol. 38, no. 4, pp1406-1490, July 1992.
`6. D. C. Chu, “Polyphase codes with good periodic correlation properties,” IEEE Trans. Inform. Theory,
`vol. 18, pp531-532, July 1972.
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