channelization cbjkode and uses

8/13/2019 Channelization Cbjkode and Uses

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Nonblocking OVSF Codes and Enhancing Network

Capacity for 3G Wireless and Beyond Systems

Hasan CamComputer Science and Engineering Department

Arizona State UniversityTempe, AZ 85287

[email protected]

Abstract

Orthogonal variable spreading factor (OVSF) codes are employed as channelization codesin WCDMA. Any two OVSF codes are orthogonal if and only if one of them is not a parentcode of the other. Therefore, when an OVSF code is assigned, it blocks all of its ancestorand descendant codes from assignment because they are not orthogonal to each other. Un-fortunately, this code blocking problem of OVSF codes can cause a substantial spectral ef-ciency loss of up to 25%. This paper presents nonblocking OVSF (NOVSF) codes to increasesubstantially the utilization of channelization codes without having the overhead of code reas-signments. In addition, an encoding algorithm is presented to increase network capacity andsupport higher data rates when NOVSF codes are employed. Index Terms nonblocking, OVSF, WCDMA, capacity, time multiplexing, encoding.

1 Introduction

The third generation (3G) wireless standards UMTS/IMT-2000 use the wideband CDMA (WCDMA)

to support high data rate and variable bit rate services with different quality of service (QoS) re-quirements. In WCDMA, all users share the same carrier under the direct sequence CDMA (DS-CDMA) principle [1]. In the 3GPP specications [2], orthogonal variable spreading factor (OVSF)codes [3] are used as channelization codes for data spreading on both downlink and uplink. OVSFcodes also determine the data rates allocated to calls. Because OVSF codes require a single RAKEcombiner at the receiver, they are preferable to multiples of orthogonal constant spreading factorcodes which need multiple RAKE combiners at the receiver.

1


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When a particular code is used in OVSF, its descendant and ancestor codes cannot be usedsimultaneously because their encoded sequences become indistinguishable. Therefore, the OVSFcode tree has a limited number of available codes. Because one OVSF code tree, along with onescrambling code, is used for transmissions from a single source that may be a base station or mobilestation, the same OVSF code tree is used for the downlink transmissions and therefore the base

station must carefully assign the OVSF codes to the downlink transmissions. The asynchronousuplink transmissions do not suffer from this limitation since each mobile station as a single sourceuses a unique scrambling code with the spreading codes of its OVSF code tree, where scramblingcode makes signals from different mobile stations separable from each other. But, if the uplink issynchronous, the OVSF code limitations of the downlink are also valid for the uplink. The use of OVSF codes in downlink and synchronous uplink guarantees that there is no intra-cell interferencein a at fading channel. Since the maximum number of OVSF codes is hard-limited, the efcientassignment of OVSF codes has a signicant impact on resource utilization.

Any two OVSF codes are orthogonal if and only if one of them is not a parent code of the other.

Therefore, when an OVSF code is assigned, it blocks all of its ancestor and descendant codes fromassignment because they are not orthogonal. This results in a major drawback of OVSF codes,called blocking property [4]: a new call cannot be supported because there is no available freecode with the requested spreading factor (SF), even if the network has excess capacity to supportit. To alleviate the effects of the blocking property of OVSF codes, various schemes such as codereassignment schemes [4, 5, 6, 7], time sharing of channels, statistical multiplexing of bursty datatrafc [8] are proposed in the literature.

This paper presents three types of nonblocking OVSF (NOVSF) codes, the preliminary versionof which appeared in [9]. NOVSF codes are nonblocking in the sense that no code assignmentblocks the assignment of any other code. All NOVSF codes are orthogonal to each other and,therefore, can be assigned simultaneously as far as orthogonality is concerned. Three differenttechniques are discussed to obtain the proposed three types of NOVSF codes. The rst techniqueproposes eight OVSF codes with SF 8 that are shared in time. The second technique is involvedwith the rearrangement of OVSF code trees as follows. Initially, there are X orthogonal codes withthe spreading factor of X , where X is either four or eight. Each of these X orthogonal codes rstgenerates Y orthogonal codes with the SF Y and then the generated Y codes are placed on a distinctlayer of NOVSF code tree. If the SF ranges from 4 to 32, this type of code tree may be a verydesirable for broadband xed wireless networks, where highest spreading factor is not expectedto exceed 32. The third technique introduces a very structured way of generating NOVSF codes

starting with spreading factor of 4, if there is no upper bound for SF.3G systems including WCDMA are designed to be service-independent in order to accom-

modate a exible introduction of new services. The capacity and QoS requirements increase asmore support is needed to support end-user services such as multimedia and high-speed packetdata services. However, the total aggregate data rate in downlink of 3G systems is still few Mbps.Therefore, this paper proposes an encoding technique that rst determines the patterns in the inputdata. If some patterns are repeated much more frequently than the others, then each of the most


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frequently used patterns is mapped to more than one time slot in the rst type of NOVSF codes,so that a chip sequence can represent more than one bit. When this mapping is done properly, thenetwork capacity can be increased.

The remainder of this paper is organized as follows. In Section 2, the tree-structured generationand blocking properties of OVSF codes are described. Section 3 presents the proposed NOVSFcodes. In Section 4, an encoding technique for binary patterns in input data is introduced to enhancenetwork capacity when the rst type of NOVSF codes is used. Concluding remarks are made inSection 5.

2 OVSF Code Generation and Blocking Property

In WCDMA, all users share the same carrier under the direct sequence code division multipleaccess (DS-CDMA) principle [1]. In the 3GPP specications [2], orthogonal variable spreadingfactor (OVSF) codes [3] are used as channelization codes for data spreading on both downlink anduplink. Because OVSF codes require a single RAKE combiner at the receiver, they are preferableto multiples of orthogonal constant spreading factor codes which need multiple RAKE combinersat the receiver. WCDMA supports data rates up to 2.048 Mbps in 5 MHz bandwidth using vari-able spreading factors. Table 1 summarizes the spreading factors, symbol rates, and bit rates forWCDMA physical channels.

Spreading Factor Symbol rate (ksps) Bit rate (kbps)4 960 19208 480 960

16 240 48032 120 24064 60 120

128 30 60256 15 30512 7.5 15

Table 1: The spreading factors, symbol rates, and bit rates for WCDMA physical channels. Thespreading factor 512 is used on the downlink only. The chip rate for all spreading factors is 3.84Mcps.

OVSF codes can be generated recursively in a binary tree structure using Walsh matrices orapplying the following rule recursively: code C n , i of length n generates the following two orthog-onal codes of length 2 n: C 2 n , i = [C n , i, C n , i] and C 2 n , i+ 1 = [C n , i, C n , i], where C n , i denotes theinverted sequence (or binary complement) of C n , i, n equals SF that is a power of 2, and i is an index


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[3]. An OVSF code tree is a binary tree with ten layers, labeled from 0 to 9 starting with the rootnode, such that SF of codes at layer k is equal to 2 k . As stated earlier, any two OVSF codes areorthogonal if and only if one of them is not a parent code of the other. Therefore, when an OVSFcode is assigned to a channel, it blocks all of its ancestor and descendant codes from assignmentbecause they are not orthogonal to each other. For instance, the assignment of code C 4

,1 shown

in Fig. 1 blocks the assignment of its ancestor codes (i.e., C 2 , 1 and C 1 , 1 ) and descendant codes(i.e., C 8

,1 and C 8

,2 ). Since Fig. 1 shows only the rst four layers of the OVSF code tree, not all

the descendant codes blocked by the assignment of C 4,1 are shown in the gure. This results in

a major drawback of OVSF codes, called code blocking property: a new call is blocked becausethere is no free OVSF code corresponding to the requested data rate, even though the system stillhas sufcient capacity to support the new call. Because of code blocking problem, the loss inspectral efciency of WCDMA can be as high as 25% of total system throughput [8]. Therefore,it is highly desirable to to eliminate or at least alleviate code blocking problem.

1,1C = (1)

2,1C = (1, 1)

4,3C = (1,1,1,1)

8,2C = (1,1,1,1,1,1,1,1)

8,4C = (1,1,1,1,1,1,1,1)

8,6C = (1,1,1,1,1,1,1,1)

8,3C = (1,1,1,1,1,1,1,1)

8,5C = (1,1,1,1,1,1,1,1)

8,7C = (1,1,1,1,1,1,1,1)

8,8C = (1,1,1,1,1,1,1,1)

8,1C = (1, 1, 1, 1, 1, 1, 1, 1)4,1C = (1,1,1,1)

2,2C = (1, 1)

4,2C = (1,1,1,1)

4,4C = (1,1,1,1)

SF = 8SF = 4SF = 2SF = 1

layer 0 layer 1 layer 2 layer 3

assigned code

Figure 1: Code blocking and and reassignment in OVSF code tree. The circle and cross signs onthe links indicate the assigned and blocked codes, respectively. For instance, the assignment of code C 4

,1 blocks the assignments of C 2

,1 , C 1

,1 , C 8

,1 , and C 8

,2 because they are either ancestors or

descendants of C 4,1 . Code C 4

,4 can be prevented from being blocked by freeing C 8

,8 and reassigning

code C 8,6 to the channel of C 8

,8 .

To alleviate code blocking problem and improve the utilization of OVSF codes, some codereassignment algorithms [4] are proposed in the literature. These heuristic algorithms often leadto chain of code reassignments that result in a lot of overhead because many receivers need to beinformed of new code reassignments. As an example for code reassignments, assume that a newcall requests an OVSF code with SF 4 at layer 2 in Fig. 1, where two codes of layer 2 are assigned,and the other 2 codes, namely, C 4

,3 and C 4

,4 , are blocked. So, although the wireless system has

excess capacity to support a new call requesting an OVSF code of SF 4, there is no available code


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of SF 4 unless some of the existing channels are assigned new codes and their current codes arefreed. For instance, one approach to remove the blocking of C 4

,4 is to free C 8

,8 by assigning C 8

,6 to

its channel. Indeed, in addition to C 8,8 , there may be many other descendant codes of C 4

,4 at layers

4 through 9 that need to be freed in order to prevent C 4,4 from being blocked. Hence, a chain of

code reassignments are usually required to be able to remove the blocking of a code.

3 Nonblocking OVSF Codes

The proposed three types of NOVSF codes are presented in this section.

3.1 Type 1: NOVSF Codes Employing Time Multiplexing

The main objective of these codes is to improve the utilization of OVSF codes without the overheadof code reassignments. To achieve this, only a single layer of OVSF codes with SF is taken intoconsideration and time multiplexing is applied to share them among channels. This implies thatboth time and code multiplexing are used in NOVSF codes. Note that all OVSF codes of the samelayer are orthogonal to each other and, therefore, do not block each other. Each code may be sharedin time among more than one channel. The number of time slots in an OVSF code with SF 8 canbe variable or xed. If it is variable, then we need to introduce a variable, say cycle length, toindicate the number of time slots, which requires that receiver be informed about the cycle lengthduring transmission.

We assume that the number of time slots is xed and equal to 64. In this case, assigning onetime slot of an OVSF code with SF 8 would be equivalent to assigning an OVSF code with SF 512to a channel without any time multiplexing. Similarly, when all 64 time slots of an OVSF codeare assigned to the same channel, the supported data rate becomes the same as the one that wouldbe obtained in case of assigning an OVSF code with SF 8 without any time multiplexing. Thus,if all 64 time slots of a code are not assigned to the same channel, the data over the channel aretransmitted intermittently.

Figure 2 illustrates 8 OVSF codes with SF 8, namely, A, B, C , D , E , F , G , and H . Each codehas 64 time slots, each corresponding to a sequence of 8 chips. Hence, there are 64 chip sequencesin all 64 time slots, resulting in a total of 512 = 64 8 chips. The date rate supported by each timeslot is equivalent to the data rate that an OVSF code with SF 512 can support. Each time slot of the WCDMA standard frame can carry 2560 chips, which implies that there are 5 transmissionsof 64 time slots in a frame. If the date rate supported by a time slot is denoted by R, then datarate supported by K time slots equals R K . The time slots that are assigned to a channel do nothave to be consecutive. Fig. 3 illustrates how the rst 8 time slots of two NOVSF codes, namely, A and B, may be shared in time among ve different channels at some point of time. The datarates corresponding to the OVSF codes with SF 512, 256, 128, 64, 32, 16, and 8 are obtained by


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assigning 1, 2, 4, 8, 16, 32, or 64 time slots, respectively, that are a power of 2. Indeed, since anynumber of time slots may be assigned to a channel, many intermediate data rates can be supportedin channels when NOVSF codes are employed. Moreover, the way that NOVSF codes are shared intime is somewhat similar to how an OVSF code is shared in time among more than one interactiveand/or background trafc users in Downlink Shared Channel (DSCH).

A SF = 8

numberlayer

SF = 1

SF = 2

SF = 4

B C D E G HF

Slot 1 Slot 3Slot 2 Slot 4 Slot 64

[X]=(1)

[X X]=(1, 1)[X X]=(1, 1)

B =( 1, 1, 1, 1,1,1,1,1)

Orthogonal Codes: A, B, C, D, E, F, G, H

C =( 1, 1,1,1, 1, 1,1,1)

D =( 1, 1,1,1,1,1, 1, 1)

A =( 1, 1, 1, 1, 1, 1, 1, 1) E =( 1,1, 1,1, 1, 1, 1, 1)

F =( 1,1, 1,1,1, 1,1, 1)

G =( 1,1,1, 1, 1,1,1, 1)

H =( 1,1,1, 1,1, 1, 1,1)

3

2

0

1

Figure 2: The NOVSF code-tree containing eight orthogonal OVSF codes with SF=8 each. Eachof these eight codes has 64 time slots.

3.1.1 Performance of Code Assignment Algorithms for OVSF and NOVSF CodesDynamic code assignment schemes have the ability to enhance statistical multiplexing and spec-tral efciency of WCDMA systems. Code assignment schemes determine how to allocate codes todifferent channels. Because OVSF codes are very valuable resources in WCDMA, they should bemanaged properly to support as many users with different QoS requirements as possible. A numberof code assignment algorithms for OVSF codes are introduced in the literature [4, 8, 10, 11, 12].The code assignment algorithm in [10] assigns codes to low data rate users in a manner that max-imizes the available number of low SF codes corresponding to high data rate codes. They assumethat a user can be assigned multiple OVSF codes, requiring multiple RAKE receivers. In [4],code blocking problem is mitigated by reassigning existing users to new codes in a manner tomaximize the available number of low SF codes, without addressing to support different types of trafc. This algorithm may lead to a chain of code reassignments, resulting in a lot of overheadfor informing receivers about the change of code assignments. The code assignment algorithmin [11] supports both real-time and non-real-time trafc, without addressing the problem of ef-ciently sharing OVSF codes between a number of bursty trafc users. Another code assignmentalgorithm [12] shares bandwidth between bursty trafc sources with different QoS requirementsby dynamically changing the spreading code and bandwidth at the cost of increased complexity.


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Two NOVSF Codes : A =(1,1,1,1,1,1,1,1) B =(1,1,1,1,1,1,1,1)

A A

A Achannel 2

channel 1

channel 4

channel 5

A A

A A

channel 3 B B

B B

B

B B

B

Figure 3: Two NOVSF codes are shared in time among at least ve different channels. Due tolimited space, only few time slots of each codes 64 time slots are shown. The rst time slots of codes A and B are shared by two and three, respectively, channels.

Code reassignments have substantial overhead, and there may not be sufcient network re-sources to accomplish code reassignments. First of all, code reassignments require all those re-ceivers whose channels are involved with code reassignments have to be informed about the as-signments of new OVSF codes. In [13], signaling radio bearers (SRBs) are proposed to minimizethe signaling overhead that occur while receivers are informed about new code assignments. Ac-cording to [14], the radio resource control (RRC) messages are sent on four particular radio bearerscalled signaling radio bearers (SRBs) whose total data rate equals 3.4 kbps and the transmissiontime interval (TTI) is 40 ms. But, SRBs are also used in handover, negotiation and renegotiation of

QoS parameters. This implies that SRBs may not be available at the time of code reassignments.In addition, more than one call may need chains of code reassignments at the same time. Hence,code reassignments may not be accomplished even if the network has excess capacity to support anew call. If SRBs are available at the time of code reassignments, code reassignments may take asmuch as 1,600 msec [13]. As the code reassignments are performed for one call, those new callsrequiring code reassignments are queued or dropped.

Our proposed NOVSF codes enhance the utilization of codes by improving spectral efciencyup to 25% in WCDMA without doing any code or time-slot reassignments. In [15], we haverecently compared the performance of OVSF code reassignment techniques with a preliminary

code allocation technique for NOVSF codes. Figure 4 illustrates the throughput plots of bothNOVSF and OVSF codes with various probabilities that signaling radio bearers are free or notwhen code reassignments are needed in OVSF codes. Fig. 5 illustrates the number of new callrejects in NOVSF and OVSF codes [15], where the number of new call rejects determines the callblocking probability.

Since CDMA based systems is interference limited, we have also carried out simulations to


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0 5 10 15 20 250

1

2

3

4

5

6

7

8

9x 10

4

Offered Load (in Erlangs)

T h

r o u g

h p u t

( b y t e s

/ s e c

)

NOVSFOVSF (K = 0.90)OVSF (K = 0.75)OVSF (K = 0.50)OVSF (K = 0.25)K = SRB free prob.

Figure 4: Comparison of throughputs between NOVSF and OVSF codes with various probabilitiesthat signaling radio bearers (SRBs) are free or not. K denotes the probability that SRBs are freewhen code reassignments are needed.

0 5 10 15 20 250

500

1000

1500

2000

2500

Offered Load (in Erlangs)

N u m

b e r o

f c a

l l r e

j e c t s

NOVSFOVSF (K = 0.90)OVSF (K = 0.75)OVSF (K = 0.50)OVSF (K = 0.25)

K = SRB free prob.

Figure 5: Comparison of number of call rejects indicating blocking probabilities between NOVSFand OVSF codes.


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check whether there is any increase on the total cell interference when NOVSF codes with timemultiplexing are employed. The simulation results indicate that the aggregate cell interference inNOVSF codes with time multiplexing is not more than that in OVSF codes, assuming that the sameamount of trafc is supported in both cases. Note that there are normally at most eight users at anypoint of time in case of NOVSF codes with time multiplexing.

3.2 Type 2 of NOVSF Codes

This type of NOVSF codes can be described in three different cases. In all cases, OVSF codesare reorganized in code trees such that all the codes of code tree are orthogonal to each other.The reason why the codes in the rst two cases are orthogonal is as follows. There are initially X 1 , X 2 , . . ., X i orthogonal codes with the same spreading factor (SF) that is equal to i, where eitheri = 4 or i = 8. Let code X j, j i, generate n j orthogonal codes with the same SF , where n j isa power of 2. All of these n j orthogonal codes with the same SF are placed on the same distinctlayer of a code tree. Therefore, all the codes of the resulting code tree are still orthogonal to eachother. Case 3 starts with four codes as in Case 1, but the descendants of a code can be assigned tomore than one tree layer.

Case 1: NOVSF codes with four initial orthogonal codes .In this case, as shown in Figure 6, there are initially four orthogonal codes, namely, A, B, C , and D. Using these four orthogonal codes, a binary code tree is constructed as follows. Code A ismade the root code with SF = 4 in the layer 1 of the tree. For the tree layer 2, the following twoorthogonal codes with SF = 8 are generated from code B: ( B, B) and ( B, B). Similarly, fourcodes are generated from code C and are placed on layer 3 of the tree. Finally, eight generated

codes from D are placed on layer 4 of the tree. All the codes of the tree are orthogonal to eachother and, they can be very desirable codes for broadband xed wireless networks where maximumSF should not exceed 32. Indeed, what is required is to have a code tree of four layers in this case,but the SF of codes at any one of these four layers can be equal to any power of 2 ranging between4 to 512, depending on the requested data rates of users. For instance, the SFs of the code treecould be 16, 4, 32, and 64 at some instant of time.

Case 2: NOVSF codes with eight initial orthogonal codes with SF from 8 to 512 .In this case, as shown in Figure 7, there are initially eight orthogonal codes, namely, A, B, C , D, E , F , G, and H . Using the rst seven orthogonal codes, a binary code tree is constructed as

follows. Code A is made the root code with SF = 8 in the layer 1 of the tree. For the tree layer 2,the following two orthogonal codes with SF = 16 are generated from code B: ( B, B) and ( B, B).Similarly, four codes are generated from code C and are placed on layer 3 of the tree. As illustratedin Figure 7, codes D, E , F , and G generate 8, 16, 32, and 64 codes, respectively, and are placed onlayers 4, 5, 6, and 7, respectively. Code H can be used as a standby code in any tree layer whenevermore codes are needed. Indeed, each one of the eight codes A, B, C , D , E , F , G , and H . can haveany spreading factor depending on the requested data rates. For instance, if there are eight users


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4,1C = (A)

8,1C = (B,B)

8,2C = (B,B)

16,1C = (C,C,C,C)

16,2C = (C,C,C,C)

16,4C = (C,C,C,C)

16,3C = (C,C,C,C)

32,2C = (D,D,D,D,D,D,D,D)

32,1C = (D,D,D,D,D,D,D,D)

32,3C = (D,D,D,D,D,D,D,D)

32,4C = (D,D,D,D,D,D,D,D)

32,5C = (D,D,D,D,D,D,D,D)

32,6C = (D,D,D,D,D,D,D,D)

32,7C = (D,D,D,D,D,D,D,D)

32,8C = (D,D,D,D,D,D,D,D)

SF = 8

D =(1,1,1,1)

C =(1,1,1,1)

B =(1,1,1,1)

A =( 1, 1, 1, 1)

Orthogonal Codes: A, B, C, D

SF = 32SF = 16SF = 4

Figure 6: NOVSF codes with four initial orthogonal codes. In this gure, it is assumed that SF

ranges from 4 to 32. But, SF can indeed range from 4 to 512. For instance, the SFs of the treelayers may be 4, 8, 32, and 128.

requesting codes with SF = 8, then each layer is assumed to be assigned a code with SF = 8. Ingeneral, any layer of the tree can have X / 8 orthogonal codes with the spreading factor of X , where X is a power of 2 ranging from 8 to 512. This implies that, without considering the standby code H , there may be at most 64 codes in each layer. When H is also considered, one layer can have asmany as 128 codes.

Case 3: NOVSF codes with four initial orthogonal codes with SF from 4 to 512 .In this case, as shown in Figure 8, there are initially four orthogonal codes, namely, A, B, C , and D as in Case 1. It is the same as Case 1 except that the descendants of a code in this case can beassigned more than one layer with the condition that only orthogonal descendants can be assigned.

3.3 Type 3 of NOVSF Codes

This type of NOVSF codes are generated systematically when there is no limit on the upper boundof SF. To describe the systematic generation of all orthogonal codes for SF 4, we rst deneBOVSF codes and then NOVSF codes.

BOVSF codes : 1) Let A = [1] be the root BOVSF code, as A = [1] is also the root OVSF code. 2)Use each BOVSF code X to generate two orthogonal codes: [ X , X , X , X ] and [ X , X ], where X is the inverted sequence of X . Using this procedure recursively, generate all BOVSF codesthat can be represented as nodes of a balanced binary tree. BOVSF codes have the same property as


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8,1C = (A)

16,1C = (B,B)

16,2C = (B,B)

32,3C = (C,C,C,C)

32,4C = (C,C,C,C)

64,2C = (D,D,D,D,D,D,D,D)

128,2C = (E,E,...,E,E)

256,2C = (F,F,...,F,F)

32,2C = (C,C,C,C)

32,1C = (C,C,C,C)

512,2C = (G,G,...,G,G)

SF = 8 SF = 16 SF = 32 SF = 64 SF = 128 SF = 256 SF = 512

layer 3 layer 4 layer 6layer 5layer 1layer 0

2 codes 4 codes 8 codes 16 codes 32 codes 64 codes

H =( 1,1,1, 1,1,1, 1,1)

E =( 1,1, 1,1,1,1,1,1)

D =( 1, 1,1,1,1,1,1,1)

C =( 1, 1,1,1,1,1,1,1)

B =( 1, 1, 1, 1,1,1,1,1)

A =( 1, 1, 1, 1, 1, 1, 1, 1)

Orthogonal Codes: A, B, C, D, E, F, G, H

1 code

F =( 1,1, 1,1,1,1,1,1)

G =( 1,1,1, 1,1,1,1, 1)

layer 2

Figure 7: The binary code tree for NOVSF codes with 8 SF 512. Only one NOVSF code isillustrated in layers 4 to 7 due to space limitations.

8,1C = (B,B)

8,2C = (B,B)

4,1C = (A)

16,2C = (C,C,C,C)

16,1C = (C,C,C,C)

32,8C = (C,C,C,C,C,C,C,C)

32,7C = (C,C,C,C,C,C,C,C)

32,6C = (C,C,C,C,C,C,C,C)

32,5C = (C,C,C,C,C,C,C,C)

64,2C = (D,D, ..., D)

64,1C = (D,D, ..., D)

64,14C = (D,D, ..., D)

128,32C = (D,D, ..., D)

128,29C = (D,D, ..., D)

Orthogonal Codes: A, B, C, D

A =( 1, 1, 1, 1)

B =(1,1,1,1)

C =(1,1,1,1)

D =(1,1,1,1)

SF = 32SF = 8SF = 4 SF = 16 SF = 64 SF = 128

Figure 8: The binary code tree for NOVSF codes with 4 SF 512.


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OVSF codes, that is, i) all BOVSF codes of the same layer of the BOVSF code-tree are orthogonalto each other, and ii) any two codes of different layers are orthogonal except for the case that oneof the two codes is a parent code of the other.

NOVSF codes : For each BOVSF code Y of length k , generate the following so-called NOVSFcode of length 4 k : [Y , Y , Y , Y ], where Y is the inverted sequence of Y . By repeatingthis procedure for each and every BOVSF code, generate all NOVSF codes that can be representedas nodes of a balanced binary tree. NOVSF and BOVSF codes are represented by C sn , i and B

sn , i,

respectively, where s, n, and i stand for spreading factor, number of codes in a layer of code tree,and index of code, respectively.

The recursive generation of BOVSF and NOVSF codes are shown by code trees in Figures9, 10, and 11. The tree-structured generation of BOVSF codes is very similar to that of OVSF

4

4,4B = (C,C)=(G)

8

4,2B = (B,B)=(E)

16

4,1B = (B,B,B,B)=(D)

8

4,3B = (C,C,C,C)=(F)

4

8,1B = (D,D,D,D)=(H)

32

8,2B = (D,D)=(I)

32

8,3B = (E,E,E,E)=(J)

16

8,4B = (E,E)=(K)

32

8,5B = (F,F,F,F)=(L)

16

8,6B = (F,F)=(M)

42,1B = (A,A,A,A) = (B)

2

2,2B = (A,A) = (C)

16

8,7B = (G,G,G,G)=(N)

8

8,8B = (G,G)=(O)

1

1,1B = (1) = (A)

SF = 16,32,64

Root

SF = 2,4 SF = 4,8,16

Figure 9: BOVSF code tree.

codes. To consolidate their similarity, the following lemma shows that BOVSF codes have thesame orthogonality properties as OVSF codes. Then, the next theorem proves that all NOVSFcodes are orthogonal to each other.

BOVSF codes have the same orthogonality property as OVSF codes, that is, i) all BOVSFcodes of the same level of BOVSF code-tree are orthogonal to each other, and ii) any two codes of different layers are orthogonal except for the case that one of the two codes is a parent code of theother.

Proof . It follows from the denition of BOVSF codes that a BOVSF code Bsn , i generates twocodes B4 s2 n , 2 i 1 and B

2 s2 n , 2 i.

B4 s2 n , 2 i 1 = [ Bsn , i, B

sn , i, B

sn , i, B

sn , i]


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4

1,1C = (A,A,A,A)

16

2,1C = (B,B,B,B)

8

2,2C = (C,C,C,C)

64

4,1C = (D,D,D,D)

32

4,2C = (E,E,E,E)

32

4,3C = (F,F.F,F)

16

4,4C = (G,G,G,G)

256

8,1C = (H,H,H,H)

128

8,2C = (I,I,I,I)

1288,3C = (J,J,J,J )

64

8,4C = (K,K,K,K)

128

8,5C = (L,L,L,L)

64

8,6C = (M,M,M,M)

64

8,7C = (N,N,N,N)

32

8,8C = (O,O,O,O)

SF = 32,64,128,256SF = 8,16 SF = 16,32,64SF = 4

Figure 10: Code tree of NOVSF codes.

4

4,4B = (C,C)=(G)

8

4,2B = (B,B)=(E)11,1B = (1) = (A)

16

4,1B = (B,B,B,B)=(D)

8

4,3B = (C,C,C,C)=(F)

64

8,1B = (D,D,D,D)=(H)

32

8,2B = (D,D)=(I)

32

8,3B = (E,E,E,E)=(J)

16

8,4B = (E,E)=(K)

32

8,5B = (F,F,F,F)=(L)

16

8,6B = (F,F)=(M)

4

2,1B = (A,A,A,A) = (B)

2

2,2B = (A,A) = (C)

16

8,7B = (G,G,G,G)=(N)

8

8,8B = (G,G)=(O)

128

8,5C = (L,L,L,L)

64

4,1C = (D,D,D,D)

32

4,2C = (E,E,E,E)

32

4,3C = (F,F.F,F)

16

4,4C = (G,G,G,G)

128

8,2C = (I,I,I,I)

128

8,3C = (J,J,J,J)

64

8,4C = (K,K,K,K)

64

8,6C = (M,M,M,M

64

8,7C = (N,N,N,N)

328,8C = (O,O,O,O)

16

2,1C = (B,B,B, B)

8

2,2C = (C,C,C,C)

4

1,1C = (A,A,A,A)

256

8,1C = (H,H,H,H)

SF = 32,64,128,256SF = 8,16 SF = 16,32,64SF = 4

Figure 11: Code tree of both NOVSF and BOVSF codes.


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and B2 s2 n , 2 i = [ B

sn , i, B

sn , i].

Note that each half of B4 s2 n , 2 i 1 is orthogonal to B2 s2 n , 2 i because their inner product is is equal to

| Bsn , i | | Bsn , i | = 0.

Therefore, B4 s2 n , 2 i 1 and B2 s2 n , 2 i are orthogonal to each other, but BOVSF code B

sn , i is not orthogonal

to them. Furthermore, all BOVSF codes are generated recursively in a complete binary tree struc-ture, starting with the root code A = [1] in the same way OVSF codes are generated. Therefore,BOVSF codes have the same orthogonality property as as OVSF codes.

Theorem 3.1 Any NOVSF code is orthogonal to all other NOVSF codes.

Proof . We now show that any NOVSF code, say C 4 sn , i, is orthogonal to its all descendant NOVSFcodes. Note that the two children of C 4 sn , i are

C 16 s2 n , 2 i 1 = [ B4 s2 n , 2 i 1 , B

4 s2 n , 2 i 1 , B

4 s2 n , 2 i 1 , B

4 s2 n , 2 i 1 ]

andC 8 s2 n , 2 i = [ B

2 s2 n , 2 i, B

2 s2 n , 2 i, B

2 s2 n , 2 i, B

2 s2 n , 2 i].

To show that C 4 sn , i is orthogonal to both C 16 s2 n , 2 i 1 and C

8 s2 n , 2 i, it sufces to show that

C 4 sn , i = [ Bsn , i, B

sn , i, B

sn , i, B

sn , i]

is orthogonal to both

B4 s2 n , 2 i 1 = [ Bsn , i, Bsn , i, Bsn , i, Bsn , i]and

B2 s2 n , 2 i = [ Bsn , i, B

sn , i].

Note that the inner product of any pair of these three codes is equal to zero and, therefore, they areorthogonal to each other. In addition, all NOVSF codes are generated recursively in a completebinary tree structure, starting with the root code C 41

,1 . Therefore, all NOVSF codes are orthogonal

to each other.

4 Encoding Binary Numbers on NOVSF Time SlotsWhen OVSF codes are used in CDMA based systems, a chip sequence represents either 0 or 1.Therefore, the only way to increase the throughput of WCDMA is to use adaptive modulation sothat the number of bits in a symbol can be increased depending on the channel conditions. How-ever, to increase network capacity or total aggregate data rate, NOVSF codes can take advantageof time slots assigned to a channel in the rst type of NOVSF codes. The incoming data stream is


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rst examined whether it has certain data patterns or not. Depending on the type and frequency of patterns in input data, each time slot or chip sequence may represent more than one bit. Assumingthat a communication channel is assigned S time slots for S 1, the incoming data stream is splitinto k -bit blocks (or numbers), for k 1 and 2 k (2 S ). Each k -bit block is represented by thetransmission of a chip sequence or its complement in a time slot. A data block may be represented

by more than one slot if it has more repetitions in the incoming data.

Fig. 12 illustrates a possible encoding of 2-bit blocks to the chip sequences of each timeslot, along with an example for a data sequence of 010101000001010111 whose bits are assumedto be transmitted from left to right. The physical bits 1 and 0 in the gure correspond to thetransmission of the chip sequence and its complement, respectively. Since the rst 2-bit block is01 and it is represented by the transmission of the chip sequence complement in the second timeslot, the physical bit 0 (i.e., the complement of chip sequence) is transmitted in the second slot,and the rst time slot does not transmit anything because the rst 2-bit block is neither 00 or 11.Since those time slots that do not send anything are wasted, it is crucial to determine the data

patterns accurately in the data stream and then to represent them by the time slots in the best wayto maximize the network capacity. We aim to investigate cost-efcient algorithms to search datapatterns and efciently map them to time slots.

channel 1 A AA A

channel 1 A AA A

A =(1,1,1,1,1,1,1,1)Code:

320Physical slot label

data block for physical bit 0

data block for physical bit 1

00 01 01

1011

01

1

11 00

Example:

Let data sequence be 010101000001010111.

Transmitted physical bits in 1st cycle

Transmitted physical bits in 2nd cycle

Transmitted physical bits in 3rd cycle

0 0 0

0 0

0

1

1

0

Figure 12: To increase network capacity, 2-bit blocks are represented by the transmission of a chipsequence or its complement in time slots of a channel. Bits 1 and 0 in each time slot correspondsto the transmission of chip sequence and its complement, respectively.

We propose to employ a binary tree network to determine the frequency of binary patterns inthe input data. Input data is rst partitioned into binary numbers of k bits, x1 x2 . . . xk , and is thenrouted through a k -stage tree-type network labeled from left to right starting with 1 as shown inFig. 13, for k = 3. Each switching box of the network is a 1 by 2 demultiplexer, that is, it has 1input and 2 outputs. Each binary number is routed from the root node toward the leaf nodes usingthe destination tag routing algorithm in which the binary number is both the destination address


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and routing tag where the k th bit of the number is the control bit for the k th stage (or layer) of thetree-type network. If the control bit is 0, then the number is routed to the upper output; otherwise,the number is routed to the lower output.

X X X1 2 3

0 X X 2 3

1 X X 2 3

0 0 X 3

0 1 X 3

1 0 X 3

1 1 X 3

counter for 000

counter

counter

counter

counter

counter

counter

counter

for 100

for 101

for 110

for 111

for 001

for 010

for 011

input data

stage 2stage 1 stage 3

Figure 13: A tree-type network with one input and eight outputs is used to determine how manytimes the binary numbers of 3 bits are repeated in input data. Each switching box of the network is a 1 by 2 demultiplexer that routes the input to the upper or lower output depending on whetherthe control bit is 0 or 1, respectively. Control bits at each stage are denoted by the arrows. Eachoutput has a counter that is incremented by 1 whenever a binary number of three bits arrives in it.

Each leaf has a counter that counts the number of binary numbers arriving at the counter. Ob-viously, the binary number whose counter has the maximum value is repeated the most frequentlyin the input data. Based on the values of the counters, mapping from the binary numbers to timeslots of a channel is performed, which is called pattern encoding on time slots. The binary numbersof those counters having much higher values are represented by more time slots than those binarynumbers repeated less frequently. Hence, a chip sequence transmitted by each time slot may rep-resent a binary number of more than one bit. The information about the pattern encoding on timeslots is sent to the receiver along with data. While data is transmitted, some time slots may nottransmit any chip sequences at some time instances. Therefore, an important goal of the proposedpattern encoding technique is to minimize the number of those time instances at which no chip

sequence is transmitted in one or more time slots.

5 Conclusion

Current OVSF codes have a code blocking property that causes spectral efciency loss up to 25%.To minimize the adverse effects of code blocking, several heuristic scheduling schemes were pro-


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posed in the literature. This paper has introduced NOVSF codes that are orthogonal to each other.No NOVSF code blocks the assignment of any other NOVSF code and, therefore, no code reas-signment is needed. Hence, NOVSF codes increase substantially the utilization of NOVSF codes.In addition to NOVSF codes, this paper has also introduced how to encode data patterns of inputdata on the time slots of the rst type of NOVSF codes in order to enhance network capacity. This

technique, along with adaptive modulation and coding, can be used to support higher user datarates in 3G and beyond wireless systems.

AcknowledgmentThe author thanks Kiran Vadde for obtaining simulation results illustrated by Figures 4 and 5 inSection 3.

References

[1] A.J. Viterbi, CDMA: Principles of Spread Spectrum Communication, Addison-Wesley, 1995.

[2] 3GPP TS 25.213, v3.3.0, Spreading and Modulation (FDD), Oct. 1999.

[3] F. Adachi, M. Sawahashi, and K. Okawa, Tree-structured generation of orthogonal spreadingcodes with different length for forward link of DS-CDMA mobile radio, Electronic Letters,vol. 33, no. 1, pp. 27-28, Jan. 1997.

[4] T. Minn and K.Y. Siu, Dynamic assignment of orthogonal variable spreading factor codesin W-CDMA, IEEE J. on Selected Areas in Communications , vol. 18, no. 8, pp. 1429-1440,

Aug. 2000.

[5] R.G. Cheng and P. Lin, OVSF code channel assignment for IMT-2000, Proc. of VTC2000,vol. 3, pp. 2188-2192, May 2000.

[6] A.C. Kam, T. Minn, and K.Y. Siu, Reconstruction methods of tree structure of orthogonalspreading codes for DS-CDMA, IEICE Trans. Fundamentals , vol. E83-A, no. 11, pp. 2078-2084, Nov. 2000.

[7] F. Shueh, H.C. Lai, and W.E. Chen, On-line preemption of code assignment for IMT-2000,Proc. of 3Gwireless01, pp. 814-819, May 2001.

[8] A.C. Kam, T. Minn, and K.Y. Siu, Supporting rate guarantee and fair access for bursty datatrafc in WCDMA, IEEE J. on Selected Areas in Communications , vol. 19, no. 11, pp.2121-2130, Nov. 2001.

[9] H. Cam, Nonblocking OVSF Codes for 3G Wireless and Beyond Systems, in Proc. of 3Gwireless2002 & WAS2002, 2002 International Conference on Third Generation Wirelessand Beyond , pp. 148-153, May 28-31, 2002, San Francisco, CA, USA.


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[10] R.G. Cheng and P. Lin, OVSF code channel assignment for IMT-2000, Proc. of IEEE Ve-hicular Tech. Conf, vol. 3, pp. 2188-2192, 2000.

[11] R. Fantacci and S. Nannicini, Multiple access protocol for integration of variable bit ratemultimedia trafc in UMTS/IMT-2000 based on wideband CDMA, IEEE J. on Selected

Areas in Communications , vol. 18, no. 8, pp. 1441-1454, Aug. 2000.[12] C.E. Fossa, Dynamic code sharing algorithms for IP quality of service in wideband CDMA

3G wireless networks, PhD thesis, Virginia Polytechnic Institute and State University, April2002.

[13] P. Goria, C. Guerrini, and A. Vaillant, Signalling delay of code allocation strategies, Proc.of IST Mobile & Wireless Telecommunications Summit, Thessaloniki, Greece, June 16-19,2002.

[14] TS 3GPP RAN 25.331 v3.7.0., RRC Protocol Specication, June 2001.

[15] K. Vadde and H. Cam, A Code Assignment Algorithm for Nonblocking OVSF Codes inWCDMA, Submitted to a Special Issue of Telecommunication Systems .

[16] H. Cam and K. Vadde, Performance analysis of nonblocking OVSF codes in WCDMA,Proc. of The 2002 International Conference on Wireless Networks , June 24-27, 2002, LasVegas, USA.

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