NAVAL POSTGRADUATE SCHOOL
`Monterey, California
`
`THESIS
`
`EVALUATION AND METHODS TO REDUCE CO-
`CHANNEL INTERFERENCE ON THE REVERSE
`CHANNEL OF A CDMA CELLULAR SYSTEM
`
`by
`
`Adem Durak
`
`March 1999
`
`Thesis Advisor: Tri T. Ha
`Co-Advisor: Ralph D. Hippenstiel
`
`Approved for public release; distribution is unlimited.
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`xmc QUAuarcr EXPECTED I
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`REPORT DOCUMENTATION PAGE
`
`Form Approved OMB No. 0704-0188
`
`Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources,
`gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this
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`20503.
`
`AGENCY USE ONLY (Leave blank)
`
`REPORT DATE
`March 1999
`
`REPORT TYPE AND DATES COVERED
`Master's Thesis
`
`4. TITLE AND SUBTITLE
`Evaluation and Methods to Reduce Co-Channel Interference on the Reverse
`Channel of a CDMA Cellular System.
`6. AUTHOR(S) Durak, Adem
`
`7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
`Naval Postgraduate School
`Monterey, CA 93943-5000
`
`9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
`
`5. FUNDING NUMBERS
`
`8. PERFORMING
`ORGANIZATION
`REPORT NUMBER
`
`10. SPONSORING/MONITORING
`AGENCY REPORT NUMBER
`
`11. SUPPLEMENTARY NOTES The views expressed in this thesis are those of the author and do not reflect the
`official policy or position of the Department of Defense or the U.S. Government.
`
`12a. DISTRIBUTION/AVAILABDLITY STATEMENT
`Approved for public release; distribution is unlimited.
`
`12b. DISTRIBUTION CODE
`
`13. ABSTRACT (maximum 200 words)
`With increasing exploitation of information, the demand for mobile access to high data rate multimedia services
`including high speed internet connection, high quality video/images, teleconferencing, and file transfer continues to grow
`rapidly for a wide variety of military as well as commercial applications.
`The current mobile communication systems are narrowband and optimized for voice. They can not support high
`data rate applications. Simply increasing the bandwidth of existing systems will result in severe degradation due to
`frequency selective fading, resulting in loss of quality and reliability. It appears that CDMA is the strongest candidate for
`the third generation mobile communication systems to support these demands. CDMA minimizes the effects of frequency
`selective fading while reducing the probability of detection and interception by non-authorized users.
`The primary restriction of the performance of CDMA is the co-channel interference. Since CDMA capacity is only
`interference limited, the interference reduction equates to better quality of service and greater user capacity. This thesis
`focuses on analyzing the co-channel interference on the reverse channel of the proposed CDMA cellular systems operating
`with perfect power control and investigating methods such as sectoring and microzoning in an effort to reduce the
`interference.
`
`14. SUBJECT TERMS Cellular Communications, Spread Spectrum, CDMA, Co-Channel
`Interference, Reverse Channel, Interference Reduction.
`
`17. SECURITY CLASSIFI-
`CATION OF REPORT
`Unclassified
`
`18. SECURITY CLASSD7I-
`CATION OF THIS PAGE
`Unclassified
`
`19. SECURITY CLASSD7I-
`CATION OF
`ABSTRACT
`Unclassified
`
`15. NUMBER OF
`PAGES
`102
`16. PRICE CODE
`20. LIMITATION OF
`ABSTRACT
`UL
`
`NSN 7540-01-280-5500
`
`Standard Form 298 (Rev. 2-89)
`Prescribed by ANSI Std. 239-18 298-102
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`Approved for public release; distribution is unlimited.
`
`EVALUATION AND METHODS TO REDUCE CO-CHANNEL INTERFERENCE
`ON THE REVERSE CHANNEL OF A CDMA CELLULAR SYSTEM
`
`AdemDurak
`Lieutenant Junior Grade, Turkish Navy
`B.S., Turkish Naval Academy, 1993
`
`Submitted in partial fulfillment of the
`requirements for the degree of
`
`MASTER OF SCD2NCE IN ELECTRICAL ENGINEERING
`
`from the
`
`NAVAL POSTGRADUATE SCHOOL
`March 1999
`
`Author:
`
`Approved by:
`
`Nx,' T H^.
`
`Tri T. Ha, Thesis Advisor
`
`RalpH D. HippenstieL Co-Advisor
`
`Jeffrey Kn^rr, Chairman
`Department of Electrical and Computer Engineering
`
`in
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`ABSTRACT
`
`With increasing exploitation of information, the demand for mobile access to high
`
`data rate multimedia services including high speed internet connection, high quality
`
`video/images, teleconferencing, and file transfer continues to grow rapidly for a wide
`
`variety of military as well as commercial applications.
`
`The current mobile communication systems are narrowband and optimized for
`
`voice. They can not support high data rate applications. Simply increasing the bandwidth
`
`of existing systems will result in severe degradation due to frequency selective fading,
`
`resulting in loss of quality and reliability. It appears that CDMA is the strongest candidate
`
`for the third generation mobile communication systems to support these demands. CDMA
`
`minimizes the effects of frequency selective fading while reducing the probability of
`
`detection and interception by non-authorized users.
`
`The primary . restriction of the performance of CDMA is the co-channel
`
`interference. Since CDMA capacity is only interference limited, the interference
`
`reduction equates to better quality of service and greater user capacity. This thesis focuses
`
`on analyzing the co-channel interference on the reverse channel of the proposed CDMA
`
`cellular systems operating with perfect power control and investigating methods such as
`
`sectoring and microzoning in an effort to reduce the interference.
`
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`TABLE OF CONTENTS
`
`I. INTRODUCTION 1
`
`A. THESIS OUTLINE 1
`
`B. THESIS CONTRIBUTION 2
`
`C. EVOLUTION OF CODE DIVISION MULTIPLE ACCESS 2
`
`D. CDMA CONCEPT 3
`
`E. DEMAND FOR HIGH DATA RATE CELLULAR SYSTEMS .4
`
`F. SPREAD SPECTRUM SIGNAL PROPERTIES 5
`
`G. CAPACITY AND ADVANTAGES OF CDMA SYSTEM 7
`
`H. CO-CHANNEL INTERFERENCE AND INTERFERENCE REDUCTION
`METHODS TO INCREASE THE CDMA CAPACITY : 9
`
`H. REVERSE CHANNEL ANALYSIS IN CDMA CELLULAR SYSTEMS
`EMPLOYING OMNI-DIRECTIONAL ANTENNAS 11
`
`A. THE GENERALIZED SIGNAL TO INTERFERENCE RATIO 12
`
`B. THE CELL STRUCTURE AND LOCATION OF THE MOBILE
`STATIONS 15
`
`C. THE DISTANCE CALCULATIONS OF THE MOBILE STATIONS
`OF OTHER CELLS TO THE REFERENCE BASE STATION 16
`
`D. PROPAGATION MODEL 18
`
`E. SIGNAL TO INTERFERENCE RATIO EXPRESSION IN TERMS
`OF DISTANCES 20
`
`HI. REVERSE CHANNEL ANALYSIS IN CDMA CELLULAR
`SYSTEMS USING SECTORING 25
`
`A. PERFECT AND IMPERFECT SECTORING 26
`
`B. SIGNAL TO INTERFERENCE RATIO 29
`
`C. SOFT AND SOFTER HANDOFF 31
`
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`D. OTHER EFFECTS OF SECTORING 33
`
`IV. THE MICROZONE CONCEPT 35
`
`A. DEFINITION OF THE MICROZONE CONCEPT 35
`
`B. REVERSE LINK PROCESS 37
`
`C. MICROZONE STRUCTURE AND ANTENNA PATTERN 37
`
`D. SIGNAL TO INTERFERENCE RATIO 40
`
`E. REDUCTION OF THE HANDOFFS 43
`
`F. SYSTEM CAPACITY AND ADVANTAGES OF
`MICROZONING SYSTEM 44
`
`V. NUMERICAL ANALYSIS 47
`
`A. SPECIFIC PARAMETERS FOR SIGNAL TO INTERFERENCE
`RATIO ANALYSIS 47
`
`B. INTERPRETATION OF RESULTS 48
`
`VI. CONCLUSION 85
`
`APPENDIX 87
`
`LIST OF REFERENCES 91
`
`INITIAL DISTRIBUTION LIST 93
`
`Vlll
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`I. INTRODUCTION
`
`The demand for mobile access to high data rate multimedia services including
`
`high speed internet connection, high quality video/images, teleconferencing, and file
`
`transfer is increasing. The current mobile communication systems are narrowband and
`
`optimized for voice. They can not support high data rate applications. Increasing the
`
`bandwidth of existing systems will result in degradation due to frequency selective
`
`fading, resulting in loss of quality and reliability. Code Division Multiple Access
`
`(CDMA) is a strong candidate for the third generation mobile communication systems to
`
`support these demands. CDMA minimizes the effects of frequency selective fading while
`
`reducing the probability of detection and interception by non-authorized users.
`
`The primary restriction of the performance of CDMA is the co-channel
`
`interference. Interference reduction equates to better quality of service and greater user
`
`capacity. This thesis focuses on analyzing the co-channel interference on the reverse
`
`channel of the proposed CDMA cellular systems operating with perfect power control. It
`
`also investigates sectoring and microzoning methods in an effort to reduce the
`
`interference.
`
`A. THESIS OUTLINE
`
`Chapter I presents the evolution, concept, capacity, and advantages of the CDMA
`
`technology, and explains the reason why to go to high data rate cellular systems. Chapter
`
`II presents the generalized signal to interference ratio, cell structure, and propagation
`
`model which will be used. It also derives the Signal to interference ratio (SIR) for the
`
`CDMA systems employing omni-directional antennas. Chapter IE presents the reverse
`
`channel analysis and SIR for the sectoring, perfect and imperfect sectoring cases, and the
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`soft/softer handoff technique, which is one of the most important advantages of CDMA
`
`cellular systems. Chapter IV applies the microzoning concept, originally devised for
`
`narrowband systems, to the CDMA system and presents the analysis and SIR of the
`
`CDMA system using the microzoning concept. Chapter V presents simulations which
`
`compare three different CDMA configurations employing omni-directional antenna,
`
`sectoring, and microzoning.
`
`B. THESIS CONTRIBUTION
`
`The primary restriction of the performance of CDMA is the co-channel
`
`interference. Since the CDMA capacity is only interference limited, the interference
`
`reduction equates to better quality of service and greater user capacity in CDMA. This
`
`thesis focuses on analyzing the co-channel interference on the reverse channel of the
`
`proposed CDMA cellular systems operating with perfect power control and investigates
`
`methods such as sectoring and microzoning in an effort to reduce the interference. The
`
`analysis and simulations show that microzoning coupled with 60° sectoring provide the
`
`necessary interference reduction to enable the operation of the third generation high data
`
`rate cellular systems.
`
`C. EVOLUTION OF CODE DIVISION MULTIPLE ACCESS
`
`Spread spectrum (SS) communication technology is the basis of CDMA system
`
`and has been used in military communications (specially by the US Military) for many
`
`years. In this area, spread spectrum techniques were generally used to overcome the
`
`effects of strong intentional interference by hostile jamming, and to hide the desired
`
`signal from the eavesdropper. Both goals can be achieved by spreading the signal's
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`spectrum by reducing the spectral density of the signal. This tends to make the signal
`
`virtually indistinguishable from the channel noise.
`
`The application of the CDMA system to the commercial mobile communication
`
`area was proposed in the 1950's, but its practical application did not take place until
`
`1980's due to the many technical obstacles and the sufficiency of the mobile systems in
`
`use at that time.
`
`Increases in demand and the poor quality of the existing service led mobile
`
`service providers to research different ways to improve the quality of service and to
`
`support more users in their systems. Because the amount of frequency spectrum available
`
`for mobile cellular communication use was limited, efficient use of the required
`
`frequencies was needed for mobile cellular coverage.
`
`During 1980's Qualcomm investigated Direct Sequence CDMA (DS-CDMA)
`
`techniques, and demonstrated that CDMA would work as well in practice as it did in
`
`theory. This led to the standardization of CDMA known as IS-95.
`
`D. CDMA CONCEPT
`
`CDMA technology makes use of the "direct sequence" method of spread
`
`spectrum. Direct sequence is a spread spectrum technique in which the bandwidth of a
`
`signal is increased by artificially increasing the transmission rate. This is done by
`
`breaking each bit into a number of sub-bits called "chips".
`
`Each user is assigned a unique sequence that it uses to encode its information-
`
`bearing signal. The receiver, knowing the code sequences of the user, decodes a received
`
`signal after reception and recovers the original data. This is possible since the
`
`crosscorrelations between the code of the intended user and the codes of the other users
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`are small. Since the bandwidth of the code signal is chosen to be much larger than the
`
`bandwidth of the information-bearing signal, the encoding process enlarges or spreads the
`
`spectrum of the signal and is known as spread spectrum modulation [Ref. 1].
`
`It is the spectral spreading of the transmitted signal that gives CDMA its multiple
`
`access capability. It is therefore important to know the techniques to generate spread
`
`spectrum signals and the properties of these signals. Spread spectrum modulation
`
`technique uses two concepts: (1) the transmission bandwidth is much larger than the
`
`information bandwidth, and (2) the resulting radio-frequency bandwidth is determined by
`
`a code other than the information being sent (so the bandwidth is independent of the
`
`information signal). Therefore, spread spectrum modulation transforms an information-
`
`bearing signal into a transmission signal with a much larger bandwidth. This spreads the
`
`original signal power over a much broader bandwidth, resulting in a lower power spectral
`
`density. The receiver correlates the received signal with a synchronously generated
`
`replica of the code signal to recover the original information-bearing signal. This requires
`
`that the receiver must know the code signal used to modulate the data [Ref. 1].
`
`E. DEMAND FOR HIGH DATA RATE CELLULAR SYSTEMS
`
`The main purpose of the mobile communication systems is to provide mobile
`
`users sufficient communication opportunity anytime and anywhere. With the increasing
`
`demand of the information age, we need to add one more important objective to the
`
`current mobile communication systems. That is to provide multimedia services including
`
`high speed internet connection, high quality video/images, and teleconferencing
`
`capabilities to mobile users.
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`However, the current mobile communication systems, that is second generation
`
`systems, are narrowband and optimized for voice. They can not support high data rate
`
`applications. Simply increasing the bandwidths of the existing systems will result in
`
`severe degradation due to the frequency-selective fading, resulting in loss of quality and
`
`reduced reliability [Ref. 2]. Therefore, to support these demands toward the goal of
`
`wideband mobile multimedia services, a third generation high data rate mobile
`
`communication system which is called IMT-2000 (International Mobile
`
`Telecommunications System-2000) is being developed. It appears that CDMA is the
`
`strongest candidate for the third generation mobile communication systems. CDMA
`
`utilizes site diversity and exploits multipath fading through Rake combining [Ref. 2],
`
`while reducing the probability of detection and interception.
`
`F. SPREAD SPECTRUM SIGNAL PROPERTIES
`
`Because of the coding and the resulting enlarged bandwidth, spread spectrum
`
`signals have a number of properties that differ from the properties of narrowband signals.
`
`The most important properties of spread spectrum signals are discussed below [Ref. 1].
`
`1. Multiple access capability. If multiple users transmit spread spectrum signals
`
`at the same time, the receiver will still be able to distinguish between the
`
`users, provided each user has a unique code that has a sufficiently low cross-
`
`correlation with the other codes. Correlating the received signal with a code
`
`signal from a certain user will then only despread the signal of this user, while
`
`the other spread spectrum signals will remain spread over a large bandwidth.
`
`Thus, within the information bandwidth the power of the desired user will be
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`much larger than the interfering power provided there are not too many
`
`interferes, and the desired signal can be extracted.
`
`2. Protection against multipath interference. In a radio channel there is not just
`
`one path between a transmitter and receiver. Due to reflections (and
`
`refractions) a signal will be received over a number of different paths. The
`
`signals of the different paths are all copies of the transmitted signal but with
`
`different amplitudes and phases. Adding these signals at the receiver will be
`
`constructive at some of the frequencies and destructive at others. In the time
`
`domain, this results in a dispersed signal. Spread spectrum modulation can
`
`combat this multipath interference. Although multipath is usually detrimental
`
`to an analog or Time Division Multiple Access (TDMA) signal, it is actually
`
`an advantage to CDMA, since the CDMA "Rake receiver" can use multipath
`
`to improve a signal. The CDMA receiver has a number of receive "fingers"
`
`which are capable of receiving the various multipath signals. The receiver
`
`locks onto the dominant received multipath signals, time shifts them, and then
`
`sums them together to produce a signal that is better than any of the individual
`
`signal components. Adding the multipath signals together enhances the signal
`
`rather than degrading it.
`
`3. Privacy. The transmitted signal can only be despread and the data recovered if
`
`the code is known to the receiver.
`
`4. Interference rejection. Cross-correlating the code signal with a narrowband
`
`signal will spread the power of the narrowband signal thereby reducing the
`
`interfering power in the information bandwidth.
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`5. Anti-jamming capability, especially narrowband jamming. This is more or
`
`less the same as interference rejection except the interference is now willfully
`
`inflicted on the system. It is the property together with the next one that makes
`
`spread spectrum modulation attractive for military applications.
`
`6. Low probability of interception. Because of its lower power density, the
`
`spread spectrum signal is difficult to detect.
`
`G. CAPACITY AND ADVANTAGES OF CDMA SYSTEMS
`
`CDMA has a real capacity advantage over other multiple-access techniques in a
`
`high-density multicell network. This is a direct consequence of spatial isolation due to
`
`high propagation losses in the UHF band, spread spectrum immunity to interference, and
`
`monitoring of voice activity. As a result, in a CDMA multiple-cell network it is possible
`
`to use the same frequency band in all cells as opposed to narrowband multiple access
`
`techniques in which the bandwidth used in a given cell can be reused only in a
`
`sufficiently far away cells so that the interference is not significant. In order to compare
`
`CDMA with other multiple access schemes, capacity is measured as the total number of
`
`users in a multiple-cell network rather than the number of users per bandwidth or per
`
`isolated cell. Based on this criterion, capacity of a CDMA high-density multiple-cell
`
`network is much higher than with narrowband multiple access techniques. The key
`
`difference is that CDMA allows 100% frequency of reuse among all cells in a network
`
`[Ref. 3]. In other words, all users in a CDMA system share the same RF spectrum. This is
`
`one of the advantages which gives CDMA its greater capacity over the other multiple
`
`access techniques, but it also makes certain aspects of system planning more
`
`straightforward. It provides simplified system planning through the use of the same
`
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`frequency in every sector of every cell. Thus, engineers will no longer have to perform
`
`the detailed frequency planning which is necessary in other systems.
`
`Another important point is that the capacity of CDMA systems is interference
`
`limited. Thus, the key issue in CDMA network design is minimization of multiple access
`
`interference. Power control is critical to multiple access interference. Each base station
`
`controls the transmit power of its own users.
`
`Another important consideration in increasing the system capacity is voice
`
`activity monitoring. In a two-person conversation, each speaker is active only 35% to
`
`40% of the time and listens to the rest of the time. In CDMA, all the users share one radio
`
`channel. When users assigned to the channel do not talk, all other active users experience
`
`lower interference. Thus, the voice activity monitoring reduces multiple access
`
`interference by 65%. This translates into an increase of the system capacity by a factor of
`
`2.5 [Ref. 3]. CDMA system also uses variable rate vocoders. The variable rate vocoder
`
`will increase its rate, providing the best speech quality, only when voice activity is
`
`detected. Otherwise, when no voice activity is detected, the vocoder will drop its
`
`encoding rate, because there is no reason to have high speed encoding of silence.
`
`Therefore, the variable rate vocoder uses up channel capacity only as needed.
`
`In narrowband systems, additional capacity is needed to maintain low co-channel
`
`interference. In Time Division Multiple Access (TDMA) and Frequency Division
`
`Multiple Access (FDMA) guard times and guard bands take up to 20% of the overall
`
`capacity. CDMA networks are designed to tolerate a certain level of interference and thus
`
`have a capacity advantage in this respect compared to narrowband techniques [Ref. 3].
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`Another important point is reduction of Et/No and Interference Threshold. In the
`
`other systems the desired signal must be at least 17dB (9 dB in Global System for
`
`Mobile-GSM) above any noise or interference [Ref. 4]. The effect of this is that adjacent
`
`cells can not share the same portion of the spectrum. The problem with this is that not all
`
`of the channels in adjacent cells can be used. In CDMA, signals can be received in very
`
`high levels of interference. Under worst case conditions, a signal can be received in the
`
`presence of interference that is 18dB higher than the signal [Ref. 4]. Because of this,
`
`channels can be reused in adjacent cells. Typically half of the interference in a cell is due
`
`to adjacent cells. The ability of a CDMA system to receive a signal under such high noise
`
`interference conditions is a result of the digital coding process used in spreading the
`
`signal. The coding gain of the signal is the ratio of the transmitted bits to the data bits.
`
`The North American standard coding gain is 128 or 21dB. Since only 3dB of signal
`
`power is required for signal reception, this means that 18dB of noise can be tolerated
`
`[Ref. 4]. The signal can be resolved because there is minimal cross-correlation between
`
`all of the signals on the channel. This is a characteristic of the orthogonality and
`
`uniqueness of the spreading codes.
`
`H. CO-CHANNEL INTERFERENCE AND INTERFERENCE
`REDUCTION METHODS TO INCREASE THE CDMA CAPACITY
`
`The signal to interference ratio (SIR) determines the quality of service
`
`experienced by the base station in reverse channel (mobile to base station) and by the
`
`mobile user in the forward channel (base station to mobile) in a CDMA system. Co-
`
`channel interference is a limiting factor in a cellular mobile radio system. Therefore,
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`computing the signal to interference ratio is important for determining coverage,
`
`capacity, and quality of service in a CDMA system.
`
`This thesis will examine the signal to noise ratio (S/N) due to the additive white
`
`Gaussian noise (AWGN), intracell interference, and co-channel interference in the
`
`reverse channel of CDMA for several different types of cellular architectures. Several
`
`methods will be introduced and examined in an effort to reduce co-channel interference
`
`in the reverse channel.
`
`The reverse channel presents the most difficulty in CDMA cellular systems for
`
`several reasons. First of all, the base station has complete control over the relative power
`
`of all of the transmitted signals on the forward link; however, because of different radio
`
`propagation paths between each user and the base station, the transmitted power from
`
`each portable unit must be dynamically controlled to prevent any single user from driving
`
`the interference level too high for all other users [Ref. 5]. Second, transmit power is
`
`limited by battery consumption at the portable unit, therefore there are limits on the
`
`degree to which power may be controlled. Finally, to maximize performance, all users on
`
`the forward link may be synchronized much more easily than users on the reverse link
`
`[Ref. 6,7].
`
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`II. REVERSE CHANNEL ANALYSIS OF CDMA CELLULAR SYSTEMS
`EMPLOYING OMNI-DIRECTIONAL ANTENNAS
`
`Consistent with current CDMA designs, we assume that there are separate
`
`frequency bands for the reverse link (mobile to base) and the forward link (base to
`
`mobile). In this chapter, we also assume that all transmitters, whether in bases or in
`
`mobiles, employ omni-directional antennas.
`
`These two assumptions imply that any mobile in the system experiences
`
`interference from all base stations, but does not experience interference from other
`
`mobiles (forward link). Similarly, a given base station experiences interference from all
`
`mobiles in the system, but not from other base stations (reverse link). In this thesis, we
`
`deal with the reverse link only. The forward link analysis was addressed in [Ref. 8].
`
`Although all co-channel cells interfere with each other, we will analyze only the
`
`first and second tiers since the interference from subsequent tiers is negligible when
`
`compared to the first and second tiers.
`
`Using a hexagonal cell layout, the reference cell 0 and the adjacent first (labeled
`
`by a single letter) and second tier (labeled by double letters) cells are shown in Figure 2.1.
`
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`Figure 2.1: Reference cell with the first (gray shaded) and second tier co-channel cells.
`
`To derive an expression for the signal to interference ratio due to co-channel
`
`interference, we have to consider several factors: additive white Gaussian noise (AWGN),
`
`the spreading factor, the number of users in the reference cell 0, the number of users in
`
`each of the co-channel cells, the path loss exponents for each of the cells, and the ratio of
`
`the power of the interfering co-channel users to the desired user's power as received by
`
`the reference base station.
`
`A. THE GENERALIZED SIGNAL TO INTERFERENCE RATIO
`
`Using the approximations in [Ref. 9], we can obtain the generalized expression for the
`
`signal to interference ratio (SIR) of the reverse link of the CDMA system as follows:
`
`-l
`
`s_
`I
`
`+ (s V1 (s V1 ( S V1 + +
`
`in-cell vh
`v'y
`
`
`\ l Jtier-2
`
`tier-\
`
`-1-1
`
`(2.1)
`
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`where Et/No is the signal energy per bit-to-noise ratio, N0 is the one-sided noise power
`
`spectral density, Eb = P0Tb is the average bit energy, Tb is the bit duration, and P0 is the
`
`signal power of the desired user.
`
`The second term in (2.1) is the intracell interference caused by the other users in
`
`the reference cell given as
`
`Kh
`
`in-cell
`
`, and is given by [Ref. 10];
`
`( s }
`
`V l J in - cell
`
`rf Et
`
`i* k
`
`(2.2)
`
`where y is the normalized variance of the multiuser interference (MUI) within the
`
`reference cell, Ek is the bit energy of the desired mobile, E; is the bit energy of the
`
`undesired mobiles within the reference cell, and K is the number of users in the cell.
`
`For the pseudo-random spreading codes with the rectangular chip pulse shape,
`
`y is given by [Ref. 10] as
`
`r 2 2
`r =
`1-A +-Ai
`
`m
`
`^
`IN
`J
`
`(2.3)
`
`where the normalized offset, A;- = Ti I Tc for the i user is uniformly distributed within
`
`[-Am, Am ] and 0 < Am <1, T i is the delay of the i* user's signal, Tc is the chip period,
`
`and N is the spreading factor.
`
`Assuming an asynchronous reception, that is Am= 1, in the reverse link, we can
`
`rewrite (2.3) as
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`r = 3N
`
`(2.4)
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`We also assume that power control (each mobile transmitter power level is controlled by
`
`its base station) is employed within the each cell, and all mobiles have equal signal power
`
`at the base station within the cell, i.e., Ej = Ek= Eb .
`
`Assuming a channel activity factor a (such as voice activity) and substituting
`
`(2.4) into (2.2), we obtain
`
`I1 )
`
`in - cell
`
`3N
`2a_y E 2(K -l)a
`3iV i = \
`
`and the second term of (2.1) as
`
`-1
`
`f S_ *\
`I
`V^ x J in - cell
`
`2 (K - 1 )oc
`3 TV
`
`where K is the number of users in the reference cell.
`
`(2.5)
`
`(2.6)
`
`The third term in (2.1) is the first tier co-channel interference at the base station of
`
`interest and is given as
`
`-l
`
`(-)
`
`tier -1 = s a, 2a f K,
`
`*
`i* P.
`
`k=\
`
`-i 3N
`
`V
`
`^
`
`(2.7)
`
`where Po is the average received signal power at the reference base station, io is the
`
`th
`number of the first tier co-channel cells, K; is the number of users within the i
`
`co-channel cell, P;k is the average received power at the reference base station due to the
`
`kft user in the i* co-channel cell, and a is the channel activity factor.
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`The last term in (2.1) is the second-tier co-channel interference at the base station
`
`of interest and is given as
`
`tier -2 =± 2a (^ Ps
`
`-l
`
`I1
`
`% 3N
`
`ß
`i po
`
`^
`
`J
`
`(2.8)
`
`where Po is the average received signal power at the reference base station, j0 is the
`
`number of second tier co-channel cells, Kj is the number of users within the jth
`
`co-channel cell, Pjk is the average received signal power at the reference base station due
`
`to the kth user in the j* co-channel cell, and a is the channel activity factor.
`
`B. THE CELL STRUCTURE AND LOCATION OF THE MOBILE STATIONS
`
`In this thesis, we consider a standard, two-dimensional hexagonal cell layout with
`
`base stations in the center of every cell. A mobile station (MS) connects to the closest
`
`base station (BS) and is power controlled by that base station. We also assume that each
`
`cell consists of 7 "small hexagons" and each active user is at the center of one of these
`
`small hexagons, as shown in Figure 2.2.
`
`Figure 2.2: 7 active users in a cell with each mobile at the center of a "small hexagon".
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`C. THE DISTANCE CALCULATIONS OF THE MOBILE STATIONS OF
`OTHER CELLS TO THE REFERENCE BASE STATION
`
`To simplify the calculation of the distances between the reference base station and
`
`the interfering mobile stations in the co-channel cells, we locate the reference base station
`
`at the center of a x-y coordinate system, that is the coordinates of the reference base
`
`station is (0,0). We can then easily obtain the coordinates of the interfering mobile
`
`stations as shown in Figure 2.3.
`
`Figure 2.3: The coordinates of the reference base station and an interfering mobile station.
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`The distance between an interfering mobile station and the reference base station is
`
`d0,ik = 44 + yl (2-9)
`
`where (xjk,yik) is the coordinate of the k01 mobile station in the i* co-channel cell,
`
`relative to the reference base station.
`
`The location of each mobile station in the first and second tier co-channel cells is
`
`determined and its distance to the reference base station calculated (see Appendix).
`
`We also have to know the distance between the interfering mobile station and its
`
`base station to derive transmitted signal power of the interfering m