AN2254, Scrambling Code Generation for WCDMA on the StarCore

Freescale Semiconductor
Application Note
AN2254
Rev. 1, 11/2004
Scrambling Code Generation for
WCDMA on the StarCore™
SC140/SC1400 Cores
By Imran Ahmed
In a Wideband Code Division Multiple Access (WCDMA)
environment, each user is assigned a unique complex
scrambling sequence to encode its information-bearing signal.
The receiver has the scrambling code of the user, unscrambles
the received signal, and recovers the original data [1]. This
application note presents a method for complex pseudo-random
sequence (PN code) generation and complex scrambling of an
I/Q code multiplexed signal on a StarCore® SC140 digital
signal processor (DSP). The PN codes in this application note
are generated for a WCDMA Universal Mobile
Telecommunications Systems (UMTS) uplink (signal from
handset to base station) according to the third-generation
partnership project (3GPP) specifications.
This application note provides practical information to help
users understand PN code generation and complex scrambling,
which are required in the WCDMA standards. Typically, these
operations are performed on Architecture-Specific Integrated
Circuits (ASICs), but here we explore the use of the Freescale
StarCore™-based DSPs to accomplish the same task.
© Freescale Semiconductor, Inc., 2002, 2004. All rights reserved.
CONTENTS
1
1.1
1.2
2
2.1
2.2
3
3.1
3.2
3.3
3.4
4
5
Pseudo-Random Sequences ....................................2
Randomness Properties ........................................... 2
Generating Pseudo-Random Sequences ..................2
Scrambling Codes for WCDMA .............................2
Generating Long Complex Scrambling Codes ....... 3
Scrambling an I-Q/Code Multiplexed Sign ......... al 6
Software Implementation on the StarCore
SC140/SC1400 Cores ............................................. 6
Allocating Memory Space ...................................... 6
Binary PN Code and Complex Scrambling
Sequences................................................................ 7
Forming the Complex Scrambling Sequences ........9
Complex Scrambling of an IQ/Code
Multiplexed Signal ................................................ 13
Results ...................................................................16
References .............................................................19
Pseudo-Random Sequences
1
Pseudo-Random Sequences
Pseudo-random sequences or PN codes are sequences of 1s and 0s generated by an algorithm so that the resulting
numbers look statistically independent and uniformly distributed. A random signal differs from a pseudo-random
signal in that a random signal cannot be predicted. A pseudo-random signal is not random at all; it is a
deterministic, periodic signal that is known to both the transmitter and the receiver. Even though the signal is
deterministic, it appears to have the statistical properties of sampled white noise. To an unauthorized listener, it
appears to be a truly random signal.
1.1 Randomness Properties
CDMA systems achieve their multiple access capability using large sets of sequences with three basic properties
that are applied to a periodic binary sequence as a test for the appearance of randomness [2]:
•
Balance Property. In each period of the sequence, the number of binary 1s must differ from the
number of binary 0s by at most one digit. In other words, the sequences are balanced so that each
element of the sequence alphabet occurs with equal frequency.
•
Run Property. A run is defined as a sequence of the same binary digit. The appearance of a different
binary digit marks the start of a new run. The length of the run is the number of digits in the run. For
the randomness run property, in each period, about one-half the runs of each binary digit should be of
length 1, about one-fourth of length 2, one-eighth of length 3, and so on.
•
Correlation Property. Random sequences are often described in terms of their correlation properties.
A scrambling sequence in a CDMA system must have small off-peak autocorrelation values to allow
for rapid sequence acquisition at the receiver and to minimize self interference due to multipath
acquisitions. Furthermore, the cross correlations are small enough among such sequences at all delays
to minimize multiple-access interference.
1.2 Generating Pseudo-Random Sequences
Pseudo-random binary codes are typically generated using a system of linear feedback shift registers (LFSRs). The
LFSR generators produce a sequence that depends on the number of stages, the feedback tap connections, and the
initial conditions. The output sequences can be classified as either maximal length (m-sequence) or nonmaximal
length. The m-sequences have the property that for an n-stage LFSR the sequence repetition period in clock pulses,
p, is as shown in Equation 1.
Equation 1
P = 2n–1
Thus, if the sequence length is less than the maximum period of (2n–1), the sequence is classified as a nonmaximal
length sequence. In fact, all the m-sequences are generated by primitive polynomials of degree n over Galois Field
2 (GF(2)).
2
Scrambling Codes for WCDMA
In a CDMA scheme, all users transmit on the same frequency and are differentiated by their unique scrambling
codes. The receiver correlates the received signal with a synchronously generated replica of the scrambling code to
recover the original information-bearing signal. The third-generation partnership project (3GPP) specifications
define how these uplink complex scrambling codes are generated. Part of the process in the transmitter, in addition
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
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Scrambling Codes for WCDMA
to spreading, is the scrambling operation. Because scrambling is used on top of spreading as shown Figure 1, it
does not change the bandwidth of the signal, but only makes the signals from different users separable from each
other [3].
Symbol Rate
Chip Rate
Chip Rate
Data
Channelization
Code
Scrambling
Code
Figure 1. Relation Between Spreading and Scrambling
With I-Q/code multiplexing, also called dual-channel quaternary phase shift keying (QPSK) modulation, the power
levels of the dedicated physical data channel (DPDCH) and the dedicated physical control channel (DPCCH)
typically differ. This is especially true as data rates increase and can lead in extreme cases to binary phase shift
keying (BPSK) type transmission when the branches are independently transmitted. This situation is avoided by
using a scrambling operation after the spreading with channelization codes. The transmission of two parallel
channels, DPDCH and DPCCH, leads to multicode transmission, which increases the peak-to-average power ratio
[3]. The spreading modulation solution shown in Figure 2 keeps the transmitter power amplifier efficiency the
same as for normal balanced QPSK transmission in general.
CD
CSCRAMB
I
DPDCH
IQ
Multiplex
I+jQ
Q
DPCCH
To QPSK
Modulation
CC
Figure 2. I-Q/Code Multiplexing With Complex Scrambling.
2.1 Generating Long Complex Scrambling Codes
All uplink physical channels are subjected to scrambling with a complex-valued scrambling code. In WCDMA
uplink transmissions, the scrambling code can either be short or long. There are 224 long uplink scrambling codes,
and these codes are assigned by higher layers. The long codes are essentially Gold codes. Large sets of Gold codes
have low cross-correlation properties so that as many users as possible can use the channel with minimum mutual
interference. According to 3GPP specifications, Gold codes are generated with a system of 25-stage linear
feedback shift registers, as shown in Figure 3 [4].
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
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3
Scrambling Codes for WCDMA
MSB
LSB
C1,n
C2,n
Figure 3. Uplink Long Scrambling Code Generator
These 25-degree generator polynomials are truncated to the 10 ms frame length that results in 38400 chips at the
rate of 3.84 Mcps. The long scrambling sequences, c1,n and c2,n, are constructed from a position-wise modulo 2
sum of 38400 chip segments of the two binary m-sequences. The two binary m-sequences are constructed using the
following primitive polynomial over GF(2), as show in Figure 3. Furthermore, sequence c2,n is a 16,777,232 chip
delayed version of sequence c1,n.
Equation 2
X25 + X3 + 1
Equation 3
X25 + X3 + X2 + X + 1
Let x, and y be the two m-sequences that are constructed from primitive polynomials of Equation 2 and Equation
3, respectively. The resulting sequences constitute segments of a set of Gold sequences. Now, let n23 ... n0 be the
24-bit binary representation of the scrambling sequence number n with n0 as the least significant bit. The x
sequence depends on the chosen scrambling sequence number n and is denoted as xn in the sequel. Furthermore, let
xn(i) and y(i) denote the i:th symbol of the sequences xn and y, respectively. The m-sequences xn and y are
constructed as follows:
1.
Initial conditions:
Equation 4
xn(0) = n0, xn(1) = n1, ..., xn(22) = n22, xn(23) = n23, xn(24) = 1
Equation 5
y(0) = y(1) = ... = y(23) = y(24) = 1
2.
Recursive definition of subsequent symbols:
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
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Scrambling Codes for WCDMA
Equation 6
xn(i+25) = xn(i+3) + xn(i) modulo 2, i=0, ..., 225-27
.
Equation 7
y(i+25) = y(i+3) + y(i+2) + y(i+1) + y(i) modulo 2, i=0, ..., 225-27
3.
Binary Gold sequence zn:
Equation 8
zn(i) = xn(i) + y(i) modulo 2, i=0, ..., 225-2
4.
Real-valued Gold sequence:
Equation 9
+1 if zn(i) = 0
for i = 0, 1, 2, ..., 225-2.
Zn(i) =
-1 if zn(i) = 1
a. The real-valued long scrambling sequences c1,n and c2,n are defined as follows:
Equation 10
c1,n(i) = Zn(i), i=0, ..., 225-2
Equation 11
c2,n(i) = Zn(i+16777232) modulo (225–1), i=0, ..., 2 25–2
b. The complex-valued long scrambling sequence Cn, is defined as follows, where i = 0, 1, ..., 225-2
and denotes rounding to the nearest lower integer:
Equation 12
i
Cn(i) = c1,n(i) ( 1 + j( -1 ) c2,n( 2 * FLOOR(i/2) ) )
A more intuitive way of forming the complex-valued scrambling code from two real-valued codes,
c1,n and c2,n, with the decimation principle is:
Equation 13
Cscrambling = c1,n( w0 + jc2,n (2k) w1 ), k = 0, 1, 2, ...
with sequences w0 and w1 given as chip rate sequences:
Equation 14
w0 = {1 1}, w1 = {1 -1}
The decimation factor for the second sequence is 2. Ultimately this way of creating the scrambling
sequence reduces the zero crossings in the constellation and further reduces the amplitude
violations in the modulation process. In conclusion, Equation 13 and Equation 14 give the same
complex scrambling code as is achieved through Equation 12.
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
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Software Implementation on the StarCore SC140/SC1400 Cores
2.2 Scrambling an I-Q/Code Multiplexed Signal
Figure 2 shows that before the data signal is QPSK modulated, the I-Q/code multiplexed data signal is multiplied
with the complex scrambling code. In this step, the two complex signals are multiplied together as shown in the
following equations, where DI = the real part of the incoming data:
Equation 15
( DIi + jDQi ) x ( SIi + jSQi )
Where:
•
DI = real part of the incoming data
•
DQ = complex part of the incoming data
•
SI = real part of the scrambling code
•
SQ = complex part of the scrambling code
•
I = 0, 1, 2, . . . , 38399
Equation 15 implies the final result, as follows:
Equation 16
(( DIi*SIi ) – ( DQi*SQi )) + j(( DIi*SQ i ) + ( DQi*SIi ))
3
Software Implementation on the StarCore
SC140/SC1400 Cores
This section describes how the algorithms in Section 2, Scrambling Codes for WCDMA, are implemented on the
StarCore SC140/SC1400 DSP cores. For ease of implementation, the algorithms slightly differ from the theory
presented in Section 2. The first part of the program generates the PN code, and the second part performs the actual
scrambling of the incoming signal. First, the memory space required for these calculations is specified.
3.1 Allocating Memory Space
The assembly code assumes that required memory space has been allocated before the assembly routine is called.
This memory space is 16-bit aligned. Table 1 lists the exact amount of space required for different global variables.
Table 1. Memory Allocation
Global Variable Name
Description
Number of Bytes
REG1
Holds the starting phase value for PN code generation. As
shown in Equation 3, the PN code generated depends on
the initial value of the 25-stage LFSR. The most significant
bit of the upper 25-stage LFSR is always one (1), and the
initial value for this register is passed to the assembly code.
The lower 25-stage LFSR does not require initialization
because all of its 25 bits are always configured to a value of
one (1) at the start of a new sequence.
4
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Table 1. Memory Allocation
Global Variable Name
Description
Number of Bytes
CODE_IQ
Points to the interleaved complex scrambling code. This
scrambling code is stored as a real-valued code scaled
down by a factor of 2 (+1 as +0.5 or -1 as -0.5). Since the
code length for a frame is 38400 chip segments, each
sample is stored as a 16 bit sample, and each chip segment
contains an I and Q part, a buffer of 38400*2*2 bytes is
assigned.
38400 × 2 × 2
INPUT_IQ
Points to the buffer in the memory where the interleaved
input data to be scrambled is stored. This assembly code
assumes that the data samples are 16-bits wide and are
held in the memory buffer as I/Q interleaved samples.
38400 × 2 × 2
Points to the memory buffer where the interleaved
scrambled data is stored for one frame.
38400 × 2 × 2
OUTPUT_IQ
3.2 Binary PN Code and Complex Scrambling Sequences
For optimal implementation of the algorithm to generate the complex binary PN code, 16 stacked-bit samples are
generated in one iteration rather than generating the PN code one bit at a time. Since a PN code is essentially a
system of LFSRs, the last 16 bits are processed in one operation to give 16 samples of PN code. Example 1 shows
the pseudo code for this implementation.
Example 1. Pseudo Code for 16-Bit Vector Processing
X= Upper LFSR
Y= Lower LFSR
for (i = 0; i < 2400; i++)
X0
X3
=
=
(X >> 0)
(X >> 3)
;//(38400/16) = 2400
{
;//X0 holds the lower 16 bits of X non-shifted, reqd for c1 & X25 feedback
;//X3 holds the lower 16 bits of X shifted by 3,reqd for X25 feedback
poly.
X4 =
X7 =
X25 =
(X >> 4)
(X >> 7)
(X3 ^ X0)
;//X4 holds the lower 16 bits of X shifted by 4, reqd for c2
;//X7 holds the lower 16 bits of X shifted by 7, reqd for c2
;//feedback polynomial, accodring to eqn. 6, most significant 16 bits
;//for next iteration, 9 from previous iteration, as old 16 shifted out
X = (X >> 16)
;//lower 16 bits shifted out
X = (X | (X25 << 9)) ;//most sig. 9 bits from prev iteration & 16 sig bits from this iteration
;//X is ready for next
X18 = (X >> 2)
;//X18 holds the lower 16 bits of X shifted by 18, reqd for c2
Y0
Y1
= (Y >> 0)
= (Y >> 1)
;//Y0 holds the lower 16 bits of Y non-shifted, reqd for c1 & Y25 feedback
;//Y1 holds the lower 16 bits of Y shifted by 1, reqd for Y25 feedback
Y2
= (Y >> 2)
;//Y2 holds the lower 16 bits of Y shifted by 2, reqd for Y25 feedback
Y3
= (Y >> 3)
;//Y3 holds the lower 16 bits of Y shifted by 3, reqd for Y25 feedback
poly.
poly.
poly.
Y4 = (Y >> 4)
;//Y4 holds the lower 16 bits of Y shifted by 4, reqd for c2
Y6 = (Y >> 6)
;//Y5 holds the lower 16 bits of Y shifted by 6, reqd for c2
Y25 = (Y3 ^ Y2 ^ Y1 ^ Y0) ;//feedback polynomial, accodring to eqn. 7, most significant 16 bits
;//for next iteration, 9 from previous iteration, as old 16 shifted out
Y = (Y >> 16)
;//lower 16 bits shifted out
Y = (Y | (Y25 << 9)) ;//most sig. 9 bits from prev iteration & 16 sig bits from this iteration
;//Y is ready for next
Y17 = (Y >> 1)
;//X17 holds the lower 16 bits of Y shifted by 17, reqd for c2
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
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Software Implementation on the StarCore SC140/SC1400 Cores
c1 = (X0 ^ Y0)
;//16-stacked bit c1 according to figure 3 configuration
c2 = (X4 ^ X7 ^ X18 ^ Y4 ^ Y6 ^ Y17) ;//16-stacked bit c2 according to figure 3 configuration
}
Now, the formation of the complex scrambling codes begins. In this part of the code, the C/Assembly calling
function enters the assembly code, and the data variables and pointers are put into the appropriate registers for the
assembly function to use. The pn_generation subroutine includes the pn_generation_param.asm parameter file,
which defines the local constants used by this subroutine:
•
REG2_INIT holds the value 0x01FFFFFF for initializing the lower 25-stage LFSR, as shown in
Figure 3.
•
MASK16 holds the value 0x000000FFFF for masking the lower 16-bits of a data register.
•
NUM_ITER specifies the number of times the main loop in the function iterates. It is initialized to
2400.
Data registers D6 and D7 are the two 25-stage LFSRs. Since the LFSRs are only 25-stage, only the lower 25 bits of
the data registers are used for this purpose. The most significant 15-bits are set to zero (data registers are 40 bits
wide). The first three instructions initialize the lower LFSR and the upper LFSR as shown in Figure 3 according to
the initialization value that is stored in global variable REG1 for the upper LFSR (see Example 2). The last
instruction loads address register R0 to point to the memory buffers to store the interleaved scrambling code
samples I and Q.
Example 2. Setting Data and Address Registers
move.l
move.l
move.l
move.l
will be
#REG1,r0
#REG2_INIT,d7
(r0),d6
#CODE_IQ,r0
stored
;//R0
;//D7
;//D6
;//R0
points
is the
is the
points
to initial value of upper LFSR
lower LFSR
upper LFSR
to where IQ scrambling code
The program can be divided into two main parts:
1.
Generating the binary PN code.
2.
Forming the complex scrambling sequence.
3.2.1 Generating the Binary PN Code
Generating the binary PN codes as stacked bits is accomplished following the algorithm shown in Example 1. The
mainloop in the program generates the PN codes. The mainloop produces 16-bit stacked c1 and c2 PN code
samples, as shown in Figure 3. As the routine starts, it executes instructions to set up the address and data registers
before the code jumps into mainloop. The code sets up mainloop and the loop counter for the loop to perform 2400
iterations, as described in Example 3 (which shows a complete assembly code listing for generating the PN codes
and the function for forming complex scrambling sequences, pn_generation.asm). Following is a step-by-step
description of one iteration of the StarCore DSP code to demonstrate how it executes:
1.
To determine c1and c2 for the PN code, we must determine the polynomials that are required. The c1
part of the PN code is a modulo 2 sum of the least significant bits of the X and Y registers.
a. The first 16-bit c1 sample is determined in instruction set ‘b’ of Example 3.
b. Inside the mainloop, it is calculated in instruction set ‘j’ and stored into the memory buffer in
instruction set ‘d’.
2.
Determining c2 requires a modulo 2 sum of several shifted polynomials:
— 4-bit shifted D6 (X4-instruction set ‘c’ and ‘k’)
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
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Software Implementation on the StarCore SC140/SC1400 Cores
— 7-bit shifted D6 (X7-instruction set ‘d’)
— 18-bit shifted D6 (X18-instruction set ‘h’)
— 4-bit shifted D7 (Y4-instruction set ‘d’)
— 6-bit shifted D7 (Y6-instruction set ‘e’)
— 17-bit shifted D7 (Y17-instruction set ‘i’)
The first 16-bit sample for c2 is determined in instruction set ‘j’ of code listing 3 and then stored in the
memory buffer in the very next instruction set ‘k’.
3.
Since the algorithm determines 16-bit samples and then shifts out the lower 16 bits from data registers
D6 and D7, the determination of the feedback polynomials, X25 and Y25, is required:
a. The feedback polynomial X25 is a modulo 2 sum of the non-shifted lower 16 bits of D6 (X0
instruction set ‘a’ and ‘h’) and a 3-bit shifted version of D6 (X3 instruction set ‘b’ and ‘i’).
b. The first feedback X25 polynomial is determined in instruction set ‘c’ and then in instruction set
‘k’ in mainloop and is stored in register D1 in the same instruction set ‘k.’
c. The feedback polynomial Y25 is a modulo 2 sum of the non-shifted lower 16 bits of D7 (Y0
instruction set ‘a’ and ‘i’), 1-bit shifted D7 (Y1 instruction set ‘a’ and ‘i’), 2-bit shifted D7 (Y2
instruction set ‘b’ and ‘j’), and a 3-bit shifted D7 (Y3 instruction set ‘c’ and ‘k’).
d. The first feedback Y25 polynomial is determined in instruction set ‘d’ and stored in register D9 in
the same cycle.
4.
After the feedback polynomials (X25 and Y25) have been determined and the original registers (D6
and D7) are shifted by 16 bits, we put the significant 16 bits of the 25-stage LFSRs into place. This
occurs in cycles ‘e,’ ‘f,’ ‘g,’ and ‘h:’
a. In instruction set ‘e,’ the lower 16 bits of the feedback polynomials (X25 and Y25) are extracted
and stored in D1 and D9.
b. In instruction set ‘f,’ the lower 16 bits of D1 and D9 are shifted to the left by 9, so that they
become the higher 16 bits of a 25-stage LFSR.
c. In instruction set ‘g,’ D6, which by now has shifted out its lower 16 bits and has only 9 bits located
in its least significant part, gets the higher 16 bits from D1.
d. Similarly, in instruction set ‘h,’ D7 gets its higher 16 bits from D9 for its 25-stage LFSR without
affecting its lower 9 bits.
These are the overall steps performed to generate the binary PN code in mainloop. The mainloop iterates 2400
times, producing 16-bit samples of c1 and c2 in each iteration. As a result, 38400 chip segments are produced.
3.3 Forming the Complex Scrambling Sequences
Once the binary PN code is generated, the next step is the formation of complex scrambling sequences from the
binary PN code. Complex scrambling code is formed according to Equation 12 or Equation 13 and Equation 14.
According to these equations, every other sample of c2 binary PN code is selected before the formation of complex
scrambling code. After a 16-bit binary scrambling sequence is formed, it is mapped into a real-valued code
according to Equation 9 on page 5, one bit at a time. This occurs in the mappingloop section of the program. This
part of the code takes the 16-bit c1 and c2 samples and forms complex scrambling codes, 16 bits at a time.
According to Equation 12, the real part of the scrambling sequence is c1 itself, and no change is required for
calculating the real part of the scrambling sequence. The complex part of the scrambling sequence is a
multiplicative result of the real valued code of c1,c2 and +1 or -1, depending on whether it is an even or odd
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
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Software Implementation on the StarCore SC140/SC1400 Cores
sample. Moreover, before the multiplication to calculate the complex part of the scrambling sequence, the c2 used
is a decimated version of the original c2 by 2. Decimation of c2 by a factor of 2 is accomplished by ANDing c2
with 0x5555, shifting the result to the left by one bit and then ORing the shifted result with itself.
The next step is the multiplication of c1 and decimated c2 using an exclusive-or (EOR) operation.
The final step is the multiplication by +1 or -1, depending on whether it is an even or odd sample. This step is also
performed using an EOR operation with 0xAAAA. Thus, for each 16-bit sample of PN code, 16 chip segments of
complex scrambling code are formed. Finally, the complex scrambling code is mapped into real values and stored
into the memory buffer as interleaved IQ samples. To prevent overflow, a scaled-down version of the real-valued
code (+1 or –1 to +0.5 or –0.5) is stored in memory. The mappingloop program iterates 15 times for one iteration of
the mainloop program because one iteration of the code is performed while mappingloop is being set up.
Example 3. Generating PN Codes
;*******************************************************************************
;* File:
pn_generation.asm
;* Function:
binary pn code generation for WCDMA
;* Author:
Imran Ahmed
;* Version/Date:
1.0 Oct 10 2001
;*
;* Target Processor: Star*Core 140
;*
;* Description:
;* Module Details:
;* Registers Used:
;* d0,d1,d2,d3,d4,d5,d6,d7,d8,d9,d10,d11,d12,d13,d14,d15
;* r0
;* entry : jsr
;*******************************************************************************
;*
;* Revision History:
Date
Change Details
Initials
;*
-----------------------;*
;*******************************************************************************
;----------------------------pn_generation_param.asm---------------------------;*******************************************************************************
;
;MASK16
EQU $000000FFFF
;REG2_INIT EQU $0001FFFFFF
;NUM_ITER
EQU #2400
;MASKONE EQU $0000000001
;MASK_DECM2 EQU $0000005555
;MASK_PN1 EQU $000000AAAA
;
;*******************************************************************************
;------------------------------WCDMA PN GENERATION-----------------------------;*******************************************************************************
section .data local
include ’pn_generation_param.asm’
endsec
section .text local
global main_pn_generation
main_pn_generation type func
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
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Software Implementation on the StarCore SC140/SC1400 Cores
[
push d6
push d7
]
[
push r6
push r7
]
move.l #REG1,r0
move.l #REG2_INIT,d7
move.l (r0),d6
move.l #CODE_IQ,r0
[
move.f #0.5,d13
move.f #-0.5,d14
;//R0
;//D7
;//D6
;//R0
points
is the
is the
points
to initial value of upper LFSR
lower LFSR
upper LFSR
to where IQ scrambling code will be stored
;//1 scaled down by a factor of 2 to 0.5 to avoid overflow
;//-1 scaled down by a factor of 2 to -0.5 to avoid
;//overflow
;//used to keep track for decimation of c2 code
clr d4
]
dosetup0 mainloop
doen0 #NUM_ITER
;-------------------------generation of binary PN codes (c1 & c2) starts here-----------------a
[
move.w #9,d15
;used for offset purposes in shifting registers
tfr d6,d0
;//c1 = x0
tfr d7,d9
;//y25 = y0
lsr d7
;//y1
tfr d6,d1
;//x25 = x0
]
b
[
eor d7,d9
;//y25 = yo^y1
eor d9,d0
;//c2 = x0^y0
lsr d7
;//y2
lsrr #3,d6
;//x3 = x >> 3
]
c
[
lsr d7
;//y3
eor d7,d9
;//y25 = y0^y1^y2
eor d6,d1
;//x25 = x0^x3
lsr d6
;//x4
]
;---------------------------mainloop main kernel-------------------------------------falign:
loopstart0
mainloop
d
[
eor d7,d9
lsr d7
lsrr #3,d6
tfr d6,d8
move.w #9,d15
]
;//y25 = y0^y1^y2^y3
;//y4
;//x7
;//c2 = x4
;//used as offset in shifting
[
eor d7,d8
lsrr #2,d7
and #MASK16,d1,d1
and #MASK16,d9,d9
]
;//c2 = x4^y4
;//y6
;//get lower 16 bits of x25, zero high bits
;//get lower 16 bits of y25, zero high bits
e
f
[
eor d6,d8
lsll d15,d1
lsll d15,d9
lsrr #9,d6
;//c2 = y4^x4^x7
;//x25 =<<9
;//y25 =<<9
;//x >> 16
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
Freescale Semiconductor
11
Software Implementation on the StarCore SC140/SC1400 Cores
]
g
[
or d1,d6
lsrr #10,d7
eor d7,d8
]
;//x |= x25
;//y >> 16, was at y6
;//c2 = y4^x4^x7 ^y6
[
tfr d6,d1
tfr d6,d0
or d9,d7
lsrr #2,d6
]
;//x25 = x0
;//c1 = x0
;//y |= y25
;//x18
[
eor
lsr
tfr
lsr
]
d6,d8
d6
d7,d9
d7
;//c2 = y4^x4^y6^x7^x18
;//x3
;//y25 = y0
;//y17 = y16 >> 1 (y1)
[
eor
eor
eor
lsr
]
d7,d8
d7,d9
d9,d0
d7
;//c2 = y4^x4^y6^x7^x18^y17
;//y25 = y0^y1
;//c2 = x0^y0
;//y2
[
eor
lsr
eor
lsr
]
d6,d1
d6
d7,d9
d7
;//x25 = x0^x3
;//x4
;//y25 = y0^y1^y2
;//y3
h
i
j
k
;--------------------mapping into real values sarts here------------------------[
and #MASK_DECM2,d8.l
;//decimation of every other sample of c2
dosetup1 mappingloop
;//setup mappingloop
]
asl d8,d4
;//left shift decimated version of c2
or d4,d8
;//or with itself, repeats one sample twice
[
eor d12,d8
;//Q part of scrambling = c1(i)*c2(i) -- eqn. 12
doen1 #15
;//set mappingloop counter to 15
and #MASKONE,d12,d2
;//extract c1’s least sig. bit
asr d12,d12
;//shift out the c1 bit already checked
]
[
eor #MASK_PN1,d8.l
;//Q part of scrambling [c1(i)*c2(i)] * +1 and -1
respecively
tsteq d2
tfr d13,d10
;//-- eqn. 12
;//test c1’s bit for 0 or 1
;//I part of scram. code, assume c1==0, map into real
value 1,
and #MASKONE,d8,d3
]
[
asr d8,d8
tfrf d14,d10
;//i.e. put 0.5
;//extracts c2’s least sig. bit
;//extracts c2’s least sig. bit
;//I part of scram. code, if c1==1, map into real value -
1,
tsteq d3
tfr d13,d11
;//i.e. put -0.5
;//test c2’s bit for 0 or 1
;//assume c2==0, map into real value 1, i.e. put 0.5
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
12
Freescale Semiconductor
Software Implementation on the StarCore SC140/SC1400 Cores
]
loopstart1
mappingloop
[
tfrf d14,d11
and #MASKONE,d12,d2
asr d12,d12
]
[
moves.2f d10:d11,(r0)+
;//if c2==1, map into real value -1, i.e. put 0.5
;//extract c1’s least sig. bit
;//shift out the c1 bit already checked
;//move I and Q scrambling code into memory buffer,
increment
tsteq d2
tfr d13,d10
;//buffer
;//test c1’s bit for 0 or 1
;//I part of scram. code, assume c1==0, map into real
value 1,
and #MASKONE,d8,d3
asr d8,d8
]
[
tfrf d14,d10
;//i.e. put 0.5
;//extracts c2’s least sig. bit
;//extracts c2’s least sig. bit
;//I part of scram. code, if c1==1, map into real value -
1,
tsteq d3
tfr d13,d11
]
loopend1
tfrf d14,d11
moves.2f d10:d11,(r0)+
;//i.e. put -0.5
;//test c2’s bit for 0 or 1
;//assume c2==0, map into real value 1, i.e. put 0.5
;//if c2==1, map into real value -1, i.e. put 0.5
;//move I and Q scrambling code into memory buffer,
increment
;//buffer
loopend0
[
pop r6
pop r7
]
[
pop d6
pop d7
]
rts
endsec
3.4 Complex Scrambling of an IQ/Code Multiplexed Signal
This section describes in detail how complex scrambling code is formed on the SC140 DSP core, and also
describes the process of actual complex scrambling of an I/Q code multiplexed signal. With its four ALUs, the
SC140 core can compute complex numbers and perform several different operations very efficiently. Imposing one
constraint on the incoming complex signal is required to ensure that all entries of the incoming I-Q/code
multiplexed signal are less than one to help prevent overflow. After complex scrambling, the final output signal is
scaled down by a factor of 2 and stored in memory.
After the complex signal has been formed, it is time for scrambling the received data. This function carries out the
complex scrambling operation according to Equation 16. The received I-Q/code multiplexed signal is multiplied
by the complex scrambling code, and the Output_IQ is stored in memory. Following is the flow of the assembly
code in Example 4 for generating the complex scrambling sequence from previously-generated binary PN code
and scrambling the received data:
1.
START mainloop #38400.
2.
Read the I and Q, complex scrambling code from memory, 1-word sample at a time.
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
Freescale Semiconductor
13
Software Implementation on the StarCore SC140/SC1400 Cores
3.
Read the I and Q, input signal data from memory, 1-word sample at a time.
4.
Perform the scrambling of the input data signal, according to Equation 16.
5.
Store the I-Q/code interleaved complex scrambled signal into memory.
6.
END mainloop.
Example 4. Complex Scrambling of an I-Q/code Multiplexed Signal
;*******************************************************************************
;*
;* File:
cmplx_scrambling.asm
;* Function:
formation of complex scrambling code and scrambling of
;* received I-Q/code multiplexed signal for WCDMA
;* Author:
Imran Ahmed
;* Version/Date:
1.0 Oct 10 2001
;*
;* Target Processor: Star*Core 140
;*
;* Description:
;* Module Details:
;* Registers Used:
;* d0,d1,d2,d3,d4,d5,d6,d7,d8,d9,d10,d11,d15
;* r0,r2,r4
;* entry : jsr
;*******************************************************************************
;*
;* Revision History:
Date
Change Details
Initials
;*
-----------------------;*
;*******************************************************************************
;--------------------------cmplx_scrambling_param.asm--------------------------;*******************************************************************************
;
;NUM_ITEREQU19199
;//(38400-2)/2
;INV_SQRT2 EQU #0.70710678;//1/sqrt(2)
;
;*******************************************************************************
;---------------------------WCDMA COMPLEX SCRAMBLING---------------------------;*******************************************************************************
section .data local
include ’cmplx_scrambling_param.asm’
endsec
section .text local
global main_cmplx_scrambling
main_cmplx_scrambling type func
[
push d6
push d7
]
[
push r6
push r7
]
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
14
Freescale Semiconductor
Software Implementation on the StarCore SC140/SC1400 Cores
move.l
move.l
move.l
move.f
#INPUT_IQ,r0
#CODE_IQ,r4
#OUTPUT_IQ,r2
#INV_SQRT2,d15
;//R0 -> received input signal
;//R4 -> complex scrambling signal
;//R2 -> IQ complex scrambled signal to be stored
;//(1/sqrt(2)), required for scrambling to keep
the
dosetup1 mainloop
[
move.4f (r0)+,d0:d1:d2:d3
move.4f (r4)+,d4:d5:d6:d7
;//energy of the srambled signal constant
doen1 #NUM_ITER
;//move 2 input IQ samples from memory to data
;//registers
;//move 2 scrambling IQ code samples from memory
to
;//data registers
]
[
mpy
mpy
mpy
mpy
]
[
mac
mac
mac
mac
]
d0,d4,d8
d0,d5,d9
d2,d6,d10
d2,d7,d11
;//(DI*SI)
;//(DI*SQ)
;//(DI*SI)
;//(DI*SQ)
part
part
part
part
from
from
from
from
eqn.
eqn.
eqn.
eqn.
16,
16,
16,
16,
1st
1st
2nd
2nd
sample
sample
sample
sample
-d1,d5,d8
d1,d4,d9
-d3,d7,d10
d3,d6,d11
;//(-(DQ*SQ)) part from eqn. 16, 1st sample
;//(DQ*SI) part from eqn. 16, 1st sample
;//(-(DQ*SQ)) part from eqn. 16, 2nd sample
;//(DQ*SI) part from eqn. 16, 2nd sample
;-------------------code and scaling to preserve the energy of the constellation---------------------[
;-------------------code and scaling to preserve the energy of the constellation-------mpy d15,d8,d8
;//(1/sqrt(2)) x (scrambled output I), 1st sample
mpy d15,d9,d9
;//(1/sqrt(2)) x (scrambled output Q), 1st sample
mpy d15,d10,d10
;//(1/sqrt(2)) x (scrambled output I), 2nd sample
mpy d15,d11,d11
;//(1/sqrt(2)) x (scrambled output Q), 2nd sample
]
[
asl d8,d8
;//output I scaling factor change from 4 to 2, 1st
;//sample
asl d9,d9
;//output Q scaling factor change from 4 to 2, 1st
;//sample
asl d10,d10
;//output I scaling factor change from 4 to 2, 2nd
;//sample
asl d11,d11
;//output Q scaling factor change from 4 to 2, 2nd
sample
]
;----------------------------end of code to preserve energy of constellation------------------[
move.4f (r0)+,d0:d1:d2:d3
move.4f (r4)+,d4:d5:d6:d7
;//move 2 input IQ samples from memory to data
;//registers
;//move 2 scrambling IQ code samples from memory
to
;//data registers
]
falign
loopstart1
mainloop
[
moves.4f d8:d9:d10:d11,(r2)+
;//move 2 complex scrambled IQ samples into
memory
;//buffer
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
Freescale Semiconductor
15
Results
mpy d0,d4,d8
mpy d0,d5,d9
mpy d2,d6,d10
mpy d2,d7,d11
]
[
mac -d1,d5,d8
mac d1,d4,d9
mac -d3,d7,d10
mac d3,d6,d11
move.4f (r0)+,d0:d1:d2:d3
move.4f (r4)+,d4:d5:d6:d7
;//(DI*SI)
;//(DI*SQ)
;//(DI*SI)
;//(DI*SQ)
part
part
part
part
from
from
from
from
eqn.
eqn.
eqn.
eqn.
16,
16,
16,
16,
1st
1st
2nd
2nd
sample
sample
sample
sample
;//(-(DQ*SQ)) part from eqn. 16, 1st sample
;//(DQ*SI) part from eqn. 16, 1st sample
;//(-(DQ*SQ)) part from eqn. 16, 2nd sample
;//(DQ*SI) part from eqn. 16, 2nd sample
;//move 2 input IQ samples from memory to data
;//registers
;//move 2 scrambling IQ code samples from memory
to
;//data registers
]
;-------------------code and scaling to preserve the energy of the constellation--------------[
mpy d15,d8,d8
;//(1/sqrt(2)) x (scrambled output I), 1st sample
mpy d15,d9,d9
;//(1/sqrt(2)) x (scrambled output Q), 1st sample
mpy d15,d10,d10
;//(1/sqrt(2)) x (scrambled output I), 2nd sample
mpy d15,d11,d11
;//(1/sqrt(2)) x (scrambled output Q), 2nd sample
]
[
asl d8,d8
;//output I scaling factor change from 4 to 2, 1st
;//sample
asl d9,d9
;//output Q scaling factor change from 4 to 2, 1st
;//sample
asl d10,d10
;//output I scaling factor change from 4 to 2, 2nd
;//sample
asl d11,d11
;//output Q scaling factor change from 4 to 2, 2nd
sample
]
;----------------------------end of code to preserve energy of constellation------------------loopend1
moves.4f d8:d9:d10:d11,(r2)+
;//move 2 complex scrambled IQ samples into
memory
;//buffer
[
pop
pop
]
[
pop
pop
]
rts
r6
r7
d6
d7
endsec
4
Results
The plots in Figure 4 and Figure 5 show the corresponding Matlab and StarCore DSP results for the complex
scrambled signal. As these figures indicate, the StarCore DSP and the Matlab results agree.
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
16
Freescale Semiconductor
Results
Real part of Scrambled Signal
2
Green − DSP output
Blue −− Matlab output
1.5
value of chip in constellation
1
0.5
0
−0.5
−1
−1.5
−2
1.915
1.916
1.917
1.918
1.919
1.92
1.921
chip segment number
1.922
1.923
1.924
1.925
4
x 10
Figure 4. Real Part of the Complex Scrambled Signal (Chips 19150–19250)
Imaginary part of Scrambled Signal
2
Green − DSP output
Blue −− Matlab output
1.5
value of chip in constellation
1
0.5
0
−0.5
−1
−1.5
−2
1.915
1.916
1.917
1.918
1.919
1.92
1.921
chip segment number
1.922
1.923
1.924
1.925
4
x 10
Figure 5. Imaginary Part of Complex Scrambled Signal (Chips 19150–19250)
In Figure 4 and Figure 5, the x-axis represents the number of the chip, and the y-axis represents the magnitude of
each of the chips. The StarCore DSP output is scaled up by a factor of 2 to account for the scaling factors used by
the DSP in an implementation of complex scrambling code. The complex scrambled signal obtained from the DSP
implementation matches the Matlab result. Figure 6 shows the signal constellation for the I-Q/code multiplexed
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
Freescale Semiconductor
17
Results
signal before complex scrambling, and Figure 7 shows the signal constellation after the complex scrambling
operations. The I-Q/code multiplexed signal with complex scrambling results in a rotated QPSK constellation.
Figure 7 shows the resulting constellation achieved by both the Matlab and the StarCore DSP implementations.
2
1.5
1
0.5
0
−0.5
−1
−1.5
−2
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Figure 6. QPSK Constellation Before Complex Scrambling
2
X (Blue) − DSP output
1.5
O (Green) − Matlab output
1
0.5
0
−0.5
−1
−1.5
−2
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Figure 7. QPSK Constellation Map after Complex Scrambling
Table 2 shows the assembly code results for PN code generation and formation of the pn_generation complex
scrambling sequence function for one frame. The second row of the table shows the results for scrambling of an IQ/code multiplexed signal in the cmplx_scrambling function for one frame.
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
18
Freescale Semiconductor
References
Table 2. Assembly Code Results
Function
pn_generation
cmplx_scrambling
1
Code Size (Bytes)
Cycles per Frame
MIPS
330
153618
15.36
124
38411
3.84
NOTES: 1. If scaling to preserve the energy of the constellation before and after
complex scrambling is included, it requires 7.6 MIPS with a code size of
180 bytes.
5
References
[1]
R. Prasad, “An Overview of CDMA Evolution Toward Wideband CDMA,” IEEE Communications
Surveys, vol. 1, no. 1, Fourth Quarter 1998.
[2]
B. Sklar, DIGITAL COMMUNICATIONS Fundamentals and Applications. New Jersey: Prentice-Hall, Inc.,
1988.
[3]
H Holma and A. Toskala, WCDMA for UMTS-Radio Access For Third Generation Mobile
Communications. New York: John Wiley & Sons, Ltd., 2001.
[4]
3GPP, “TS 25.213 V3.40 (2000-12): Spreading and Modulation (FDD),” Release 1999.
Scrambling Code Generation for WCDMA on the StarCore™ SC140/SC1400 Cores, Rev. 1
Freescale Semiconductor
19
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