3GPP/TSGR1#6(99)893
`
`TSG-RAN Working Group 1 meeting #6
`Espoo, Finland
`July 13-16, 1999
`
`TITLE:
`
`Proposal for RACH Preambles
`SOURCE:
`
`Motorola, Texas Instruments
`
`1.0 Introduction
`Several problems with the originally proposed RACH preambles based on Gold codes [1] were
`presented in [2]. These included 1) Large crosscorrelations between signature sequences at offsets
`greater than 255 chips, 2) Large crosscorrelations between signature sequences at all offsets
`when, due to Doppler shifts and differences between mobile TX and base RX oscillator frequen-
`cies, channel phase rotation is present, and 3) Poor estimation of the offset frequency due to this
`channel phase rotation caused by multiple access interference. Consequently, Nokia’s proposal of
`using a section of a real-valued version of the uplink scrambling code as the spreading code was,
`in principle, accepted. This eliminates the problem of large crosscorrelations at offsets greater
`than 255 chips. The resulting preambles therefore consist of length 16 signature sequences
`225 1–
`formed from a set of orthogonal Gold codes spread by a 4096 chip segment section of a
`length Gold code. The problem of large crosscorrelations in the presence of frequency offset is
`still however present. This is illustrated in Fig. 1 where, for one particular long spreading code, a
`histogram of the maximum absolute crosscorrelations over a 2048 chip window is shown for the
`
`case of a 400 Hz frequency offset. Each point in the histogram represents one of the
`
`16
`2
`correlations. This contribution presents a set of preambles which eliminates this problem and, in
`addition, facilitates simple and accurate estimation of offset frequency as required for AFC initial-
`ization. Accurate AFC initialization based only on the received preamble is important for reliable
`detection of the message.
`
`Ł ł(cid:231) (cid:247)(cid:230) (cid:246)
`
`cross-
`
`The proposed preambles have the following characteristics:
`
`1.
`
` Low crosscorrelations at all offsets with and without the presence of channel phase rotation
`
`2. Flexibility in detection schemes. Coherent accumulation, noncoherent accumulation, or dif-
`ferential detection can be used without increased crosscorrelation. Consequently, there is no
`need to include a second set of preambles in the standard to facilitate differential detection.
`Mobile and base station complexity as well as broadcast channel signaling is reduced.
`
`3. Detection schemes with complexity no greater that possible needed with the present pream-
`bles.
`
`1
`
`SAMSUNG 1008-0001
`
`

`
`Uplink scrambling codes with Gold codes, 400 Hz offset, [ −2048,2048 ] lags
`
`8
`
`7
`
`6
`
`5
`
`4
`
`3
`
`2
`
`1
`
`Number of Occurences
`
`0
`
`0
`
`200
`
`400
`
`1200
`1000
`800
`600
`Maximum Pairwise Crosscorrelation Magnitude
`Figure 1: Maximum absolute crosscorrelations for the present preambles when a channel
`phase rotation of 400 Hz is present.
`
`1400
`
`1600
`
`1800
`
`4.
`
`Improvement in detection performance relative to that possible with the present preambles
`
`5.
`
`Simple offset frequency estimation without susceptibility to multiple access interference.
`These characteristics are discussed in detail in the following sections.
`
`2.0 Proposed Preambles
`The proposed preambles are formed from 256 repetitions of length 16 Hadamard codes multiplied
`225 1–
`by a cell-specific scrambling code consisting of a 4096 chip segment of a
`length, real-val-
`ued Gold code. Each of the sixteen preambles associated with a cell-specific scrambling code uses
`a different Hadamard code. The scrambling codes are formed in the same manner as the in-phase
`dedicated channel uplink scrambling code. The 256 different codes correspond to different initial
`shift register contents of one of the shift registers.
`0 1 … 255
`0 1 … 15
`,
`,
`,
`,
`,
`,
`=
`=
`,is the
`,
`, is the set of length 16 Hadamard codes and
`,
`If
`cn n
`hm m
`, corresponding to the
`th
`set of 256 length 4096 scrambling codes, then the
`th preamble,
`m
`smn
`n
`scrambling code is
`
`2
`
`SAMSUNG 1008-0002
`
`

`
`smn k( )
`
`=
`
`cn k( )
`
`255(cid:229)
`
`i
`
`0=
`
`–(
`hm k
`
`16i
`
`)
`
`.
`
`(1)
`
`This is illustrated in Fig. 2.
`
`Long scrambling code
`cl
`
`4096 chips
`
`X
`
`256
`
`hi
`
`hi
`
`hi
`
`hi
`
`hi
`16
`chips
`
`Figure 2: Structure of proposed preambles.
`
`This structure can be viewed as a modification of the current preambles. The main difference is
`that in the proposed codes, the 256 chips corresponding to one symbol are interleaved at intervals
`of 16 across the preamble while in the current proposal all 256 chips are transmitted consecu-
`tively. In addition the 16 symbols are derived from Hadamard codes in the proposed structure
`instead of Orthogonal Gold codes.
`
`3.0 Advantages of the Proposed Preambles
`The proposed preambles offer three advantages over the current preambles.
`
`3.1 Flexibility
`The proposed structure allows a great deal of flexibility in the design of preamble detectors.
`Coherent accumulation over the entire 1ms, differential detection over some number of symbols,
`and noncoherent detection are all possible while specifying only one set of preambles. The latter
`two methods are possible without adding an additional set of preambles because the received pre-
`amble can be broken into segments without loss of orthogonality. For example, with the present
`preambles if two preambles arrive at the base within a chip and the received preamble is broken
`into four segments and correlations are performed over these segments, the resulting correlator
`outputs will contain signal energy from both users since the preambles are not orthogonal over
`0.25ms segments. The noncoherent addition over the correlator outputs for the four segments will
`therefore contain signal energy from both users and thus a strong preamble could bias the decision
`statistics of weaker users. The proposed preambles however are orthogonal over 16 chip segments
`and therefore the correlator outputs will contain signal energy from only one user.
`
`3
`
`SAMSUNG 1008-0003
`
`

`
`This flexibility has several advantages. First, because it is not necessary to have two sets of pream-
`ble codes, mobile station complexity is reduced and less signaling is required on the broadcast
`channel. Second, multiple detection schemes can be applied in the same sector. Noncoherent or
`differential detection could be used to detect high speed users while coherent detection could be
`used for slow speed users.
`
`The following notation will be used in describing three possible detection schemes. Let the
`r k( )
`received preamble be denoted by
`which is assumed to be sampled at the chip rate. This sig-
`nal is multiplied by the scrambling code of the
`th sector and matched filtered against the
`th
`n
`m
`user’s Hadamard code:
`
`ym l( )
`
`15(cid:229)=
`
`k
`
`0=
`
`+(
`cn k
`
`16l
`
`
`
`)r k +(
`
`16l
`
`)hm k( )
`
`,
`
`l
`
`=
`
`0 1 … 255
`,
`,
`,
`
`(2)
`
`to yield a sequence of 256 matched filtered outputs.
`
`Coherent Accumulation
`
`Detection by coherent accumulation can be performed by summing the matched filter outputs and
`squaring the result to give the decision statistic:
`
`(3)
`
`2
`
`.
`
`ym l( )
`
`255(cid:229)
`
`l
`
`0=
`
`=
`
`mc
`
`Noncoherent Accumulation
`
`Alternatively, matched filter outputs can be accumulated within some number of segments of the
`preamble, the results squared and then accumulated. For example if the 1ms preamble is divided
`into four segments, the decision statistic would be:
`
`(4)
`
`+(
`ym l
`
`)
`
`64i
`
`2
`
`.
`
`63(cid:229)
`
`3(cid:229)=
`
`mn
`
`i
`
`0=
`
`l
`
`0=
`
`Differential
`
`Differential detection may be performed by accumulating within a segment and then taking the
`conjugate product of consecutive sums. With four segments the decision statistic would be
`
`.
`
`(5)
`
`63(cid:229)Ł ł(cid:231) (cid:247)(cid:230) (cid:246) *
`
`+(
`ym k
`
`64 i 1–(
`
`)
`
`)
`
`k
`
`0=
`
`63(cid:229)Ł ł(cid:231) (cid:247)(cid:230) (cid:246)
`+(
`ym l
`
`)
`
`64i
`
`l
`
`0=
`
`3(cid:229)=
`
`md
`
`i
`
`1=
`
`Note that this statistic is somewhat different from what is usually considered with differential
`detection. Namely, the absolute value of the consecutive products is taken instead of the real part.
`As will be discussed shortly this was found to give better performance when large frequency off-
`sets are present.
`
`4
`
`SAMSUNG 1008-0004
`
`g
`g
`g
`

`
`3.2 Reduction in Crosscorrelation
`As illustrated in Fig. 1, the current preamble codes can have large crosscorrelations when a fre-
`quency offset is present. With coherent accumulation detection, crosscorrelation causes the deci-
`sion statistics of preamble codes which are not present to take nonzero values. When the
`transmitted preamble is received with large signal power, these decision statistics could cross the
`detection threshold and cause false detections. This may occur for example when the power con-
`trol error is such that the mobile overestimates the amount of power required to reach the base. A
`distribution of power control error which is log-normal with standard deviation of 9 dB and lim-
`ited at 12 dB is suggested in [3]. To insure a low rate of false detections, a large degree of “isola-
`tion” between the decision statistics of the transmitted and non-transmitted preambles is required.
`This false detection phenomenon is described in more detail in Section 6 for a case where the
`undesired decision statistics are only 9 dB down from the desired.
`
`The large crosscorrelations seen in Fig. 1 were found to occur at zero lag. and are investigated fur-
`ther in the following section.
`
`3.2.1 Zero Lag Crosscorrelations
`
`The decision statistics for the three detection methods discussed above are presented in Figs. 3
`through 5 for frequency offsets from 0 to 1200 Hz. These plots show the 16 decision statistics
`when the first preamble is transmitted and the correct timing offset is being processed. In Fig. 3
`the 16 decision statistics for coherent detection of the present and proposed preambles are plotted.
`From Fig. 3a we see that for the current preambles the decision statistic corresponding to the 14th
`preamble is less than 10 dB below that of the transmitted preamble at an offset of only 400 Hz. On
`the other hand, the decision statistics are greater than 40 dB below that of the transmitted pream-
`ble for the proposed codes for offsets up to 1200 Hz. In either case however, the decision statistic
`of the transmitted preamble drops off rapidly between 400 and 800 Hz. This reduction does not
`occur when noncoherent accumulation is used as shown in Fig. 4 where the noncoherent decision
`statistics of (4) are plotted. From Fig. 4a we see that noncoherent accumulation over four seg-
`ments is not viable with the current preamble codes due to the low isolation between decision sta-
`tistics at even 0 Hz. This is expected in that the present preamble codes are not orthogonal
`over.25ms. Greater than 40 dB of isolation between decision statistics is however seen with the
`proposed codes, Fig. 4b. Note that the decision statistic of the transmitted preamble does not drop
`with large frequency offsets. The case of differential detection is shown in Fig. 5. A uniform isola-
`tion of approximately 12 dB is seen for the current preambles and more than 40 dB with the pro-
`posed preambles.
`
`3.2.2 Crosscorrelation of Proposed Signatures at Nonzero Lags
`The above section described the crosscorrelation properties of the proposed codes at zero-lag. At
`other lags, the random property of the long code keeps the crosscorrelations small. Figure 6
`shows a histogram of the maximum absolute crosscorrelations over a 2048 chip window with a
`400 Hz frequency offset for the proposed preambles. Crosscorrelations are seen to be clustered at
`about -26 dB relative to the main peak. Comparison with the corresponding plot for the present
`
`5
`
`SAMSUNG 1008-0005
`
`

`
`Uplink scrambling code with Gold codes, Coherent Detection
`
`0Hz
`
`0
`
`0
`
`0
`
`0
`
`2
`
`2
`
`2
`
`2
`
`4
`
`4
`
`4
`
`4
`
`6
`
`6
`
`6
`
`6
`
`8
`n
`
`8
`n
`
`8
`n
`
`8
`n
`
`a)
`
`10
`
`12
`
`14
`
`16
`
`400Hz
`
`10
`
`12
`
`14
`
`16
`
`800Hz
`
`10
`
`12
`
`14
`
`16
`
`1200Hz
`
`10
`
`12
`
`14
`
`16
`
`Uplink scrambling code with Hadamard codes, Coherent Detection
`
`80
`60
`40
`20
`0
`
`)
`
`80
`60
`mc
`40
`20
`0
`
`Correlation output squared (dB) 10log10(g
`
`80
`60
`40
`20
`0
`
`80
`60
`40
`20
`0
`
`0Hz
`
`10
`
`12
`
`14
`
`16
`
`400Hz
`
`10
`
`12
`
`14
`
`16
`
`800Hz
`
`10
`
`12
`
`14
`
`16
`
`1200Hz
`
`10
`
`12
`
`14
`
`16
`
`2
`
`2
`
`2
`
`2
`
`4
`
`4
`
`4
`
`4
`
`6
`
`6
`
`6
`
`6
`
`8
`m
`
`8
`m
`
`8
`m
`
`8
`m
`
`50
`
`0
`0
`
`)
`
`mc
`50
`
`(g
`
`10
`
`0
`0
`
`50
`
`0
`0
`
`50
`
`0
`0
`
`Correlation output squared (dB) 10log
`
`b)
`Figure 3: Decision statistics for coherent detection with a) present preamble and b)
`proposed preambles.
`
`6
`
`SAMSUNG 1008-0006
`
`

`
`Uplink scrambling code with Gold codes, Noncoherent Detection
`
`0Hz
`
`10
`
`12
`
`14
`
`16
`
`400Hz
`
`10
`
`12
`
`14
`
`16
`
`800Hz
`
`10
`
`12
`
`14
`
`16
`
`1200Hz
`
`10
`
`12
`
`14
`
`16
`
`2
`
`2
`
`2
`
`2
`
`4
`
`4
`
`4
`
`4
`
`6
`
`6
`
`6
`
`6
`
`8
`n
`
`8
`n
`
`8
`n
`
`8
`n
`
`a)
`
`Uplink scrambling code with Hadamard codes, Noncoherent Detection
`
`60
`
`40
`
`20
`
`0
`
`0
`
`60
`
`)
`
`40
`mn
`
`Correlation output squared (dB) 10log10(g
`
`0
`
`0
`
`60
`
`40
`
`20
`
`0
`
`0
`
`20
`
`0
`
`0
`
`60
`
`40
`
`20
`
`0Hz
`
`10
`
`12
`
`14
`
`16
`
`400Hz
`
`10
`
`12
`
`14
`
`16
`
`800Hz
`
`10
`
`12
`
`14
`
`16
`
`1200Hz
`
`10
`
`12
`
`14
`
`16
`
`2
`
`2
`
`2
`
`2
`
`4
`
`4
`
`4
`
`4
`
`6
`
`6
`
`6
`
`6
`
`8
`n
`
`8
`n
`
`8
`n
`
`8
`n
`
`60
`
`40
`
`20
`
`0
`
`0
`
`60
`
`)
`
`40
`mn
`
`Correlation output squared (dB) 10log10(g
`
`0
`
`0
`
`60
`
`40
`
`20
`
`0
`
`0
`
`20
`
`0
`
`0
`
`60
`
`40
`
`20
`
`b)
`Figure 4: Decision statistics for noncoherent detection with a) present non-differentially
`encoded preambles and b) proposed preambles.
`
`7
`
`SAMSUNG 1008-0007
`
`

`
`Uplink scrambling code with Gold codes, Differential Detection
`
`0Hz
`
`0
`
`0
`
`0
`
`0
`
`2
`
`2
`
`2
`
`2
`
`4
`
`4
`
`4
`
`4
`
`6
`
`6
`
`6
`
`6
`
`8
`n
`
`8
`n
`
`8
`n
`
`8
`n
`
`a)
`
`10
`
`12
`
`14
`
`16
`
`400Hz
`
`10
`
`12
`
`14
`
`16
`
`800Hz
`
`10
`
`12
`
`14
`
`16
`
`1200Hz
`
`10
`
`12
`
`14
`
`16
`
`Uplink scrambling code with Hadamard codes, Differential Detection
`
`0Hz
`
`80
`60
`40
`20
`0
`
`)
`
`80
`60
`md
`40
`20
`0
`
`Correlation output squared (dB) 10log10(g
`
`80
`60
`40
`20
`0
`
`80
`60
`40
`20
`0
`
`0
`
`0
`
`0
`
`0
`
`2
`
`2
`
`2
`
`2
`
`4
`
`4
`
`4
`
`4
`
`6
`
`6
`
`6
`
`6
`
`8
`n
`
`8
`n
`
`8
`n
`
`8
`n
`
`10
`
`12
`
`14
`
`16
`
`400Hz
`
`10
`
`12
`
`14
`
`16
`
`800Hz
`
`10
`
`12
`
`14
`
`16
`
`1200Hz
`
`10
`
`12
`
`14
`
`16
`
`80
`60
`40
`20
`0
`
`)
`
`80
`60
`md
`40
`20
`0
`
`Correlation output squared (dB) 10log10(g
`
`80
`60
`40
`20
`0
`
`80
`60
`40
`20
`0
`
`b)
`Figure 5: Decision statistics for differential detection with a) present differentially encoded
`preambles and b) proposed preambles.
`
`8
`
`SAMSUNG 1008-0008
`
`

`
`preambles, Fig. 1, shows a dramatic reduction in crosscorrelation.
`
`Uplink scrambling code with Hadamard codes, 400 Hz offset, [ −2048,2048 ] lags
`
`16
`
`14
`
`12
`
`10
`
`8
`
`6
`
`4
`
`2
`
`Number of Occurences
`
`0
`
`0
`
`50
`
`150
`100
`Maximum Pairwise Crosscorrelation Magnitude
`Figure 6: Maximum absolute crosscorrelations for the proposed preambles when a channel
`phase rotation of 400 Hz is present.
`
`200
`
`250
`
`3.3 Offset Frequency Estimation
`
`Besides increasing correlation between signature sequences, a frequency offset between the
`received preamble and the base station oscillator can degrade coherent demodulation of the mes-
`sage frame. By estimating this offset from the preamble, the receiver oscillator’s frequency may
`be adjusted prior to message detection or the offset may be used as an initial condition for an auto-
`matic frequency control circuit. A simple method which is relatively easy to implement is based
`on calculating phase differences between consecutive samples [4]. Filtering or phase unwrapping
`can then be applied to yield the offset frequency estimate.
`
`The structure of the present non-differentially encoded preambles however makes this relatively
`simple approach vulnerable to multiple-access interference from other RACH preambles. As an
`example consider the case of an interfering preamble with no offset which arrives with the same
`offset as the preamble whose offset frequency is to be estimated. Let
`and
`be the desired and
`yk
`yk
`interfering symbols respectively at time
`and let
`be the change in phase between symbols cor-
`k
`responding to the desired offset frequency. Neglecting additive noise, the received signal is then
`yke jkq
`
`rk
`
`=
`
`yk+
`
`.
`
`(6)
`
`The phase can be estimated by taking the argument of the filtered differences over
`
`N
`
`16=
`
`sym-
`
`9
`
`SAMSUNG 1008-0009
`
`q
`

`
`bols:
`
`qˆ
`
`=
`
`arg
`
`z
`
`N 1–(cid:229)=
`
`z
`
`
`
`yk* yk
`
`1– rk
`
`rk
`
`1–
`
`k
`
`1=
`
`N 1–(cid:229)=
`
`e jq
`
`k
`
`1=
`
`+
`
`1–(
`* e j k
`ykyk
`
`)q
`
`+
`
`yk
`
`1– yk
`
`1–
`
`e jkq
`
`+
`
`
`
`yk* ykyk
`
`1– yk
`
`1–
`
`(7)
`
`(8)
`
`The term
`
`in the above is a correlation between the new sequence,
`
`
`yk* yk
`, which
`1– ykyk
`ykyk
`1–
`1–
`,
`comes from taking consecutive products of the desired preamble and the new sequence,
`ykyk
`1–
`which comes from consecutive products of the interfering preamble. The problem comes from the
`fact that while cross correlations between signatures are designed to be zero, the crosscorrelations
`between these new sequences are generally not zero. Consequently, the last term in (8) could
`cause a significant bias in the estimate.
`
`This is indeed the case for the desired and interfering signatures corresponding to signatures 0
`and 2 respectively from [5]. In this case, the last interfering term has equal magnitude to the term
`containing the phase information. Figure 7 plots offset frequency error standard deviation vs.
`interfering power for this example for both the present and proposed preambles. With the present
`preambles degradation begins at -3 dB reaching over 1 kHz when the interfering and desired sig-
`nal power are equal. With the proposed preambles however, the symbols of the interfering pream-
`bles are orthogonal to those of the desired and therefore no degradation in frequency estimation is
`observed with increasing interference power. Note that this does not occur if the present differen-
`tially encoded preambles are used.
`
`. 4
`
`.0 Complexity comparison
`In this section we compare the complexity of receiving the RACH preamble for the current Gold
`codes based preambles to the proposed Walsh Hadamard codes based preambles. We show that
`the complexity of the proposed sequences under all cases, that is whether are they received coher-
`ently, differentially or by segmenting is about the same as the corresponding complexity for
`receiving the current Gold codes based sequences. Thus, the improved performance and receiver
`implementation flexibility for the proposed codes is achieved without any increase in receiver
`complexity.
`Figures 8 and 9 give the coherent receiver block diagrams for the current and proposed sequences
`.
`
`We can now do the complexity comparison for the coherent receiver for the current Gold code
`based scheme and the proposed Walsh Hadamard code based scheme. In our calculations we
`assume that the correlation outputs have to be generated over a total lag of L= 1024 chips corre-
`sponding to a cell radius of a maximum 75 Km. at an oversampling ratio of n = 2 as given in fig-
`
`10
`
`SAMSUNG 1008-0010
`
`*
`*
`*
`*
`*
`

`
`Offset Frequency = 400 Hz, SNR = 10 dB, Preambles 0 and 2
`
`Present Preambles
`Proposed Preambles
`
`1600
`
`1400
`
`1200
`
`1000
`
`800
`
`600
`
`400
`
`200
`
`Offset Frequency Estimate Standard Deviation (Hz)
`
`0
`−12
`
`−10
`
`−4
`−6
`−8
`Interfering/Desired Power (dB)
`
`−2
`
`0
`
`Figure 7: Effect of interfering preamble on offset frequency estimation
`
`ure (1) and (2).
`Complexity calculation for the coherent demodulation for the current Gold code based approach:
`Number of complex adds per correlation output = 16*255+16*15 = 4320
`Number of complex adds for L lags at n samples per chip = 4320*L*n
`For L = 1024, n = 2 the total number of complex adds is = 8.9 Million complex adds
`
`Complexity calculation for the coherent demodulation for the proposed Walsh Hadamard code
`based approach:
`Number of complex adds per correlation output = 16*255+16*4 = 4144
`Number of complex adds for L lags at n samples per chip = 4144*L*n
`For L = 1024, n = 2 the total number of complex adds is equal = 8.5 Million complex adds
`
`We can thus see that for the coherent demodulation the proposed Walsh Hadamard based codes
`have a lower complexity as compared to the current Gold code based approach.
`
`Instead of doing the complexity calculation in detail for all the other cases, Table 1 enumerates
`the complexity comparison for the current Gold code based approach and the proposed Walsh
`Hadamard based codes for the different detection techniques:
`
`11
`
`SAMSUNG 1008-0011
`
`

`
`4096*n delays
`
`256*n
`
`256*n
`
`D D
`
`D D
`
`D D
`
`D D
`
`D D
`
`D D
`
`D D
`
`D D
`
`n
`
`n
`
` despreader
`Length 256
`
` despreader
`Length 256
`
`n = over sampling
`(assumed 2 for this report)
`
`Length 16 adder corresponding to Gold code 1
`
`Length 16 adder corresponding to Gold code 16
`
`Figure 8: Block diagram of the preamble coherent receiver for the current Gold code based
`preamble. Due to the presence of a length 4096 long code on the top, a length 4096*n matched
`filter is required, n being the amount of over sampling and is assumed to be 2 in the complexity
`calculations for this report.
`
`12
`
`SAMSUNG 1008-0012
`
`

`
`16*n
`
`16*n
`
`16*n
`
`D D
`
`D D
`
`D D
`
`D D
`
`D D
`
`D D
`
`D D
`
`D D
`
`D D
`
`n
`
`n
`
`n
`
`Length 256
`despreader
`
`Length 256
`despreader
`
`Length 256
`despreader
`
`Length 256
`despreader
`
`Length 16 Walsh Hadamard transform
`
`Correlation outputs with respect to the 16 preamble codes
`
`n = over sampling
`(
`d 2 f
`thi
`t)
`Figure 9: Figure 2: Block diagram of the preamble coherent receiver for the proposed Walsh
`Hadamard code based preamble. Due to the presence of a length 4096 long code on the top, a
`length 4096*n matched filter is required, n being the amount of over sampling and is assumed
`to be 2 in the complexity calculations for this report.
`
`Current Gold code based
`preambles
`
`Proposed Walsh code based
`preambles
`
`Coherent reception
`
`8.9 M complex adds
`
`8.5 M complex adds
`
`Differential decoding
`(16 for current codes and 4
`for proposed)
`
`4 segment decoding
`
`8.9 M complex adds +
`0.03 M complex multiply
`
`9.0 M complex adds + 0.098 M
`complex multiply
`
`8.9 M complex adds +.131 M
`complex multiply
`
`Table 1: Complexity comparison for the different reception techniques for the current and
`proposed preamble codes. We can see that in all the cases, the complexity for the proposed
`Walsh Hadamard codes is almost the same as the corresponding complexity for the current
`Gold code based approach.
`
`5.0 Detection Performance
`The performance of the three detectors presented in Section 3.1 was evaluated for the present and
`
`13
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`SAMSUNG 1008-0013
`
`

`
`proposed preambles in channels with frequency offset and fading. Two sets of simulations corre-
`sponding to two RACH detection scenarios were simulated. Similar results were obtained in both
`scenarios.
`
`5.1 Comparison of Decision Statistic with a Fixed Threshold
`In the first set of simulations the received signal at the base consisted of a single preamble plus
`additive noise. For each detector the decision statistic corresponding to the transmitted preamble
`was calculated as described in Section 3.1 and compared with a threshold to give a detection prob-
`ability. The threshold was set so that when no signal was present, the probability of the statistic
`being greater than the threshold was equal to a false alarm probability of 0.001. In each channel
`four configurations are evaluated: 1) Coherent accumulation detection (identical results would be
`obtained in these simulations with either the present or proposed preambles) 2) Differential detec-
`tion with current preambles 3) Noncoherent detection with proposed preambles and 4) Differen-
`tial detection with proposed preambles.
`
`Frequency Offset
`
`Figures 10 through 14 show results in a nonfading channel which has a linearly increasing chan-
`nel phase, i.e., a frequency offset. At 0 Hz coherent detection performs approximately 1.75 dB
`better than both noncoherent accumulation and differential detection with the proposed preambles
`and 2.5 dB better than differential detection with the current preambles. At higher offsets, coher-
`ent accumulation detection degrades significantly while the noncoherent and differential schemes’
`performance stays relatively fixed. At all offset frequencies, noncoherent and differential detec-
`tion with the proposed preambles either outperforms or equals the performance of differential
`detection with the current preambles. At 400 Hz this difference is 1 dB
`
`. F
`
`ading
`
`Figures 15 through 19 show results in fading channels assuming a 2 GHz carrier frequency. At
`speeds up to 120 km/h, coherent detection is superior by approximately 2 dB while noncoherent
`and differential detection with the proposed preambles is about.5 dB better than differential detec-
`tion with the present preambles. At 300 km/h and 500 km/h coherent detection degrades rapidly
`while noncoherent detection with the proposed preambles has the best performance.
`
`Overall, using noncoherent detection over four.25ms segments with the proposed preambles gives
`detection performance which is robust over both frequency offsets and rapid fading. In addition,
`depending on the channel type, detection with the current preambles is either equal to or inferior
`to that with the proposed preambles.
`
`5.2 Maximum of Decision Statistics
`
`Previous contributions, [6][7], have evaluated RACH detection performance in terms of the prob-
`ability of the maximum decision statistic corresponding to the transmitted preamble. To cross
`
`14
`
`SAMSUNG 1008-0014
`
`

`
`15
`
`static channel, 0 Hz offset frequency, 0 km/h
`0.001 false alarm probability,
`
`Coherent Accumulation
`Gold Codes, 16 Symbol Differential
`Proposed, Noncoherent Accumulation, 4 Segments
`Proposed, 4 Symbol Differential
`
`100
`
`10−1
`
`Probability of Detection
`
`10−2
`−32
`
`−30
`
`−28
`
`−24
`
`−22
`
`−20
`
`−26
`Ec/No (dB)
`Figure 10: Static channel detection performance. No frequency offset.
`
`static channel, 200 Hz offset frequency, 0 km/h
`0.001 false alarm probability,
`
`Coherent Accumulation
`Gold Codes, 16 Symbol Differential
`Proposed, Noncoherent Accumulation, 4 Segments
`Proposed, 4 Symbol Differential
`
`100
`
`10−1
`
`Probability of Detection
`
`10−2
`−32
`
`−30
`
`−28
`
`−24
`
`−22
`
`−20
`
`−26
`Ec/No (dB)
`Figure 11: Static channel detection performance. 200 Hz frequency offset.
`
`SAMSUNG 1008-0015
`
`

`
`16
`
`static channel, 400 Hz offset frequency, 0 km/h
`0.001 false alarm probability,
`
`Coherent Accumulation
`Gold Codes, 16 Symbol Differential
`Proposed, Noncoherent Accumulation, 4 Segments
`Proposed, 4 Symbol Differential
`
`100
`
`10−1
`
`Probability of Detection
`
`10−2
`−32
`
`−30
`
`−28
`
`−24
`
`−22
`
`−20
`
`−26
`Ec/No (dB)
`Figure 12: Static channel detection performance. 400 Hz frequency offset.
`
`static channel, 800 Hz offset frequency, 0 km/h
`0.001 false alarm probability,
`
`Coherent Accumulation
`Gold Codes, 16 Symbol Differential
`Proposed, Noncoherent Accumulation, 4 Segments
`Proposed, 4 Symbol Differential
`
`100
`
`10−1
`
`10−2
`
`Probability of Detection
`
`10−3
`−32
`
`−30
`
`−28
`
`−24
`
`−22
`
`−20
`
`−26
`Ec/No (dB)
`Figure 13: Static channel detection performance. 800 Hz frequency offset.
`
`SAMSUNG 1008-0016
`
`

`
`static channel, 1200 Hz offset frequency, 0 km/h
`0.001 false alarm probability,
`
`Coherent Accumulation
`Gold Codes, 16 Symbol Differential
`Proposed, Noncoherent Accumulation, 4 Segments
`Proposed, 4 Symbol Differential
`
`100
`
`10−1
`
`10−2
`
`Probability of Detection
`
`10−3
`−32
`
`−26
`Ec/No (dB)
`Figure 14: Static channel detection performance. 1200 Hz frequency offset.
`
`−30
`
`−28
`
`−24
`
`−22
`
`−20
`
`fading channel, 0 Hz offset frequency, 0 km/h
`0.001 false alarm probability,
`
`Coherent Accumulation
`Gold Codes, 16 Symbol Differential
`Proposed, Noncoherent Accumulation, 4 Segments
`Proposed, 4 Symbol Differential
`
`100
`
`10−1
`
`Probability of Detection
`
`10−2
`−32
`
`−26
`Ec/No (dB)
`Figure 15: Fading channel detection performance. Fading is constant across preamble.
`
`−30
`
`−28
`
`−24
`
`−22
`
`−20
`
`17
`
`SAMSUNG 1008-0017
`
`

`
`fading channel, 0 Hz offset frequency, 30 km/h
`0.001 false alarm probability,
`
`Coherent Accumulation
`Gold Codes, 16 Symbol Differential
`Proposed, Noncoherent Accumulation, 4 Segments
`Proposed, 4 Symbol Differential
`
`100
`
`10−1
`
`Probability of Detection
`
`10−2
`−32
`
`−30
`
`−28
`
`−24
`
`−22
`
`−20
`
`−26
`Ec/No (dB)
`Figure 16: Fading channel detection performance. 30 km/h
`
`18
`
`fading channel, 0 Hz offset frequency, 120 km/h
`0.001 false alarm probability,
`
`Coherent Accumulation
`Gold Codes, 16 Symbol Differential
`Proposed, Noncoherent Accumulation, 4 Segments
`Proposed, 4 Symbol Differential
`
`100
`
`10−1
`
`Probability of Detection
`
`10−2
`−32
`
`−30
`
`−28
`
`−24
`
`−22
`
`−20
`
`−26
`Ec/No (dB)
`Figure 17: Fading channel detection performance. 120 km/h
`
`SAMSUNG 1008-0018
`
`

`
`fading channel, 0 Hz offset frequency, 300 km/h
`0.001 false alarm probability,
`
`Coherent Accumulation
`Gold Codes, 16 Symbol Differential
`Proposed, Noncoherent Accumulation, 4 Segments
`Proposed, 4 Symbol Differential
`
`100
`
`10−1
`
`Probability of Detection
`
`10−2
`−32
`
`−30
`
`−28
`
`−26
`Ec/No (dB)
`Figure 18: Fading channel detection performance. 300 km/h
`
`−24
`
`−22
`
`−20
`
`check our results we ran a second set of simulation with this scenario.
`
`Frequency Offset
`
`Figures 20 through 24 give results in a channel with a frequency offset. Results are similar to
`those presented above. The coherent and differential 16 curves in Fig. 20 match those presented in
`Fig. 3 of [6]. Overall the relative performance of differential detection with the current preambles
`is seen to be worse in these scenarios than in the above. This is because of the poor isolation
`between decision statistics discussed in Section 3.2. Because the decision statistics of non trans-
`mitted preambles have some energy, they will tend to be detected in favor of the actual transmitted
`preamble. This effect is not revealed in the simulations of the previous section since only a single
`preamble is transmitted. Detection based on the proposed preambles is seen to be superior by
`about 1.5 dB over differential detection with the current preambles. The performance of coherent
`detection refers to coherent detection of the proposed preambles.
`
`Fading
`
`Figures 24 through 27 give results in fading channels. Differential detection with the current pre-
`ambles is seen to be inferior to noncoherent and differential detection with the proposed pream-
`bles by 1.5 to 2.0 dB over a range of Doppler spreads. Again, the performance of coherent
`detection refers to coherent detection of the proposed preambles.
`
`19
`
`SAMSUNG 1008-0019
`
`

`
`fading channel, 0 Hz offset frequency, 500 km/h
`0.001 false alarm probability,
`
`Coherent Accumulation
`Gold Codes, 16 Symbol Differential
`Proposed, Noncoherent Accumulation, 4 Segments
`Proposed, 4 Symbol Differential
`
`100
`
`10−1
`
`Probability of Detection
`
`10−2
`−32
`
`−30
`
`−28
`
`−24
`
`−22
`
`−20
`
`−26
`Ec/No (dB)
`Figure 19: Fading channel detection performance. 500 km/h
`
`Doppler = 0 Hz.
`
`Coherent
`Gold codes, 16 symb. diff.
`Proposed, 4 symb. diff.
`Proposed, 4 segmented
`
`100
`
`10−1
`
`10−2
`
`10−3
`
`Probability of error
`
`10−4
`−32
`
`−31
`
`−30
`
`−29
`
`−28
`
`−26
`
`−25
`
`−24
`
`−23
`
`−22
`
`−27
`Ec/N0 (dB)
`Figure 20: Probability of maximum decision statistic not corresponding to transmitted
`preamble. Static channel, no frequency offset.
`
`20
`
`SAMSUNG 1008-0020
`
`

`
`Doppler = 400 Hz.
`
`Coherent
`Gold codes, 16 symb. diff.
`Proposed, 4 symb. diff.
`Proposed, 4 segmented
`
`100
`
`10−1
`
`10−2
`
`10−3
`
`Probability of error
`
`10−4
`−32
`
`−31
`
`−30
`
`−29
`
`−28
`
`−26
`
`−25
`
`−24
`
`−23
`
`−22
`
`−27
`Ec/N0 (dB)
`Figure 21: Probability of maximum decision statistic not corresponding to transmitted
`preamble. Static channel, 400 Hz offset
`
`Doppler = 800 Hz.
`
`Coherent
`Gold codes, 16 symb. diff.
`Proposed, 4 symb. diff.
`Proposed, 4 segmented
`
`100
`
`10−1
`
`10−2
`
`10−3
`
`Probability of error
`
`10−4
`−32
`
`−31
`
`−30
`
`−29
`
`−28
`
`−26
`
`−25
`
`−24
`
`−23
`
`−22
`
`−27
`Ec/N0 (dB)
`Figure 22: Probability of maximum decision statistic not corresponding to transmitted
`preamble. Static channel, 800 Hz offset.
`
`21
`
`SAMSUNG 1008-0021
`
`

`
`22
`
`Doppler = 1200 Hz.
`
`Coherent
`Gold codes, 16 symb. diff.
`Proposed, 4 symb. diff.
`Proposed, 4 segmented
`
`100
`
`10−1
`
`10−2
`
`10−3
`
`Probability of error
`
`10−4
`−32
`
`−31
`
`−30
`
`−29
`
`−28
`
`−26
`
`−25
`
`−24
`
`−23
`
`−22
`
`−27
`Ec/N0 (dB)
`Figure 23: Probability of maximum decision statistic not corresponding to transmitted
`preamble. Static channel, 1200 Hz offset.
`
`Doppler = 0 Hz.
`
`Coherent
`Gold codes, 16 symb. diff.
`Proposed, 4 symb. diff.
`Proposed, 4 segmented
`
`100
`
`10−1
`
`10−2
`
`10−3
`
`Probability of error
`
`−27
`Ec/N0 (dB)
`Figure 24: Probability of maximum decision statistic not corresponding to transmitted
`preamble. Fading channel, fading constant across preamble.
`
`10−4
`−32
`
`−31
`
`−30
`
`−29
`
`−28
`
`−26
`
`−25
`
`−24
`
`−23
`
`−22
`
`SAMSUNG 1008-0022
`
`

`
`Doppler = 460 Hz.
`
`Coherent
`Gold codes, 16 symb. diff.
`Proposed, 4 symb. diff.
`Proposed, 4 segmented
`
`100
`
`10−1
`
`10−2
`
`Probability of error
`
`10−3
`−30
`
`−28
`
`−26
`