Ch2 Wireless Transmission

Wireless & Mobile CommunicationsChapter 2: Wireless Transmission Frequencies Signals Antennas Signal propagation Multiplexing Spread spectrum Modulation Cellular systems

ICS 243E - Ch.2 Wireless Transmission

Spectrum AllocationVLF = Very Low FrequencyUHF = Ultra High FrequencyLF = Low Frequency SHF = Super High FrequencyMF = Medium Frequency EHF = Extra High FrequencyHF = High Frequency UV = Ultraviolet LightVHF = Very High Frequency

Relationship between frequency f and wave length : = c/f where c is the speed of light 3x108m/s1 Mm300 Hz10 km30 kHz100 m3 MHz1 m300 MHz10 mm30 GHz100 m3 THz1 m300 THzvisible lightVLFLFMFHFVHFUHFSHFEHFinfraredUVoptical transmissioncoax cabletwisted pair


Frequencies Allocated for Mobile CommunicationVHF & UHF ranges for mobile radioallows for simple, small antennas for carsdeterministic propagation characteristics less subject to weather conditions > more reliable connectionsSHF and higher for directed radio links, satellite communicationsmall antennas with directed transmissionlarge bandwidths availableWireless LANs use frequencies in UHF to SHF spectrumsome systems planned up to EHFlimitations due to absorption by water and oxygen moleculesweather dependent fading, signal loss caused by heavy rainfall, etc.


Allocated FrequenciesITU-R holds auctions for new frequencies, manages frequency bands worldwide for harmonious usage (WRC - World Radio Conferences)


Europe

USA

Japan

Mobile phones

NMT 453-457MHz,

463-467MHz;

GSM 890-915MHz,

935-960MHz;

1710-1785MHz,

1805-1880MHz

AMPS, TDMA, CDMA 824-849MHz, 869-894MHz;TDMA, CDMA, GSM 1850-1910MHz,1930-1990MHz;

PDC 810-826MHz, 940-956MHz; 1429-1465MHz, 1477-1513MHz

Cordless telephones

CT1+ 885-887MHz,

930-932MHz;

CT2

864-868MHz

DECT

1880-1900MHz

PACS 1850-1910MHz,

1930-1990MHz

PACS-UB 1910-1930MHz

PHS 1895-1918MHz

JCT

254-380MHz

Wireless LANs

IEEE 802.11

2400-2483MHz

HIPERLAN 1

5176-5270MHz

IEEE 802.11

2400-2483MHz

IEEE 802.11 2471-2497MHz

Signals Iphysical representation of datafunction of time and locationsignal parameters: parameters representing the value of data classificationcontinuous time/discrete timecontinuous values/discrete valuesanalog signal = continuous time and continuous valuesdigital signal = discrete time and discrete valuessignal parameters of periodic signals: period T, frequency f=1/T, amplitude A, phase shift sine wave as special periodic signal for a carrier: s(t) = At sin(2 ft t + t)


Fourier Representation of Periodic Signals1010ttideal periodic signalreal composition(based on harmonics)


Signals IIDifferent representations of signals amplitude (amplitude domain)frequency spectrum (frequency domain)phase state diagram (amplitude M and phase in polar coordinates)

Composite signals mapped into frequency domain using Fourier transformationDigital signals needinfinite frequencies for perfect representation modulation with a carrier frequency for transmission (->analog signal!) f [Hz]A [V]I= M cos Q = M sin A [V]t[s]


AntennasAntennas are used to radiate and receive EM waves (energy)Antennas link this energy between the ether and a device such as a transmission line (e.g., coaxial cable)Antennas consist of one or several radiating elements through which an electric current circulatesTypes of antennas:omnidirectionaldirectionalphased arraysadaptiveoptimalPrincipal characteristics used to characterize an antenna are:radiation patterndirectivitygainefficiency


Isotropic AntennasIsotropic radiator: equal radiation in all directions (three dimensional) - only a theoretical reference antennaReal antennas always have directive effects (vertical and/or horizontal) Radiation pattern: measurement of radiation around an antennaidealisotropicradiator


Omnidirectional Antennas: simple dipolesReal antennas are not isotropic radiators but, e.g., dipoles with lengths /4, or Hertzian dipole: /2 (2 dipoles) shape/size of antenna proportional to wavelength

Example: Radiation pattern of a simple Hertzian dipole

Gain: ratio of the maximum power in the direction of the main lobe to the power of an isotropic radiator (with the same average power)

side view (xy-plane)xyside view (yz-plane)zytop view (xz-plane)xzsimpledipole/4


Directional AntennasOften used for microwave connections (directed point to point transmission) or base stations for mobile phones (e.g., radio coverage of a valley or sectors for frequency reuse)side view (xy-plane)xyside view (yz-plane)zytop view (xz-plane)xztop view, 3 sectorxztop view, 6 sectorxzdirectedantennasectorizedantenna


Array AntennasGrouping of 2 or more antennas to obtain radiating characteristics that cannot be obtained from a single element Antenna diversityswitched diversity, selection diversityreceiver chooses antenna with largest outputdiversity combiningcombine output power to produce gaincophasing needed to avoid cancellation


Signal Propagation RangesTransmission rangecommunication possiblelow error rateDetection rangedetection of the signal possibleno communication possible, high error rateInterference rangesignal may not be detected signal adds to the background noise

distancesendertransmissiondetectioninterference


Signal Propagation IRadio wave propagation is affected by the following mechanisms:reflection at large obstaclesscattering at small obstaclesdiffraction at edges


Signal Propagation IIThe signal is also subject to degradation resulting from propagation in the mobile radio environment. The principal phenomena are:pathloss due to distance covered by radio signal (frequency dependent, less at low frequencies)fading (frequency dependent, related to multipath propagation)shadowing induced by obstacles in the path between the transmitted and the receiver


Signal Propagation IIIInterference from other sources and noise will also impact signal behavior:co-channel (mobile users in adjacent cells using same frequency) and adjacent (mobile users using frequencies adjacent to transmission/reception frequency) channel interferenceambient noise from the radio transmitter components or other electronic devices, Propagation characteristics differ with the environment through and over which radio waves travel. Several types of environments can be identified (dense urban, urban, suburban and rural) and are classified according to the following parameters:terrain morphologyvegetation densitybuildings: density and heightopen areaswater surfaces


Pathloss IFree-space pathloss:To define free-space propagation, consider an isotropic source consisting of a transmitter with a power Pt W. At a distance d from this source, the power transmitted is spread uniformly on the surface of a sphere of radius d. The power density at the distance d is then as follows:

Sr = Pt/4pd2

The power received by an antenna at a distance d from the transmitter is then equal to:

Pr = PtAe/4pd2

where Ae is the effective area of the antenna.


Pathloss IINoting that Ae = Gr/(4p/l2)where Gr is the gain of the receiverAnd if we replace the isotropic source by a transmitting antenna with a gain Gt the power received at a distance d of the transmitter by a receiving antenna of gain Gr becomes:

Pr = PtGrGt/[4p(d/l)]2

In decibels the propagation pathloss (PL) is given by:

PL(db) = -10log10(Pr/Pt) = -10log10(GrGt/[4p(d/l)]2)

This is for the ideal case and can only be applied sensibly to satellite systems and short range LOS propagation.


Multipath Propagation ISignal can take many different paths between sender and receiver due to reflection, scattering, diffraction

Positive effects of multipath:enables communication even when transmitter and receiver are not in LOS conditions - allows radio waves effectively to go through obstacles by getting around them thereby increasing the radio coverage areasignal at sendersignal at receiver


Multipath Propagation IINegative effects of multipath: Time dispersion or delay spread: signal is dispersed over time due signals coming over different paths of different lengths Causes interference with neighboring symbols, this is referred to as Inter Symbol Interference (ISI)

multipath spread (in secs) = (longest1 shortest2)/c

For a 5ms symbol duration a 1ms delay spread means about a 20% intersymbol overlap. The signal reaches a receiver directly and phase shifted (due to reflections) Distorted signal depending on the phases of the different parts, this is referred to as Rayleigh fading, due to the distribution of the fades. It creates fast fluctuations of the received signal (fast fading). Random frequency modulation due to Doppler shifts on the different paths. Doppler shift is caused by the relative velocity of the receiver to the transmitter, leads to a frequency variation of the received signal.


Effects of MobilityChannel characteristics change over time and location signal paths changedifferent delay variations of different signal partsdifferent phases of signal parts quick changes in the power received (short term fading)

Additional changes indistance to senderobstacles further away slow changes in the average power received (long term fading)short term fadinglong termfadingtpower


Multiplexing TechniquesMultiplexing techniques are used to allow many users to share a common transmission resource. In our case the users are mobile and the transmission resource is the radio spectrum. Sharing a common resource requires an access mechanism that will control the multiplexing mechanism.As in wireline systems, it is desirable to allow the simultaneous transmission of information between two users engaged in a connection. This is called duplexing.Two types of duplexing exist:Frequency division duplexing (FDD), whereby two frequency channels are assigned to a connection, one channel for each direction of transmission.Time division duplexing (TDD), whereby two time slots (closely placed in time for duplex effect) are assigned to a connection, one slot for each direction of transmission.


MultiplexingMultiplexing in 3 dimensionstime (t) (TDM)frequency (f) (FDM)code (c) (CDM)

Goal: multiple use of a shared medium

s2s3s1ftck2k3k4k5k6k1ftcftcchannels ki


Narrowband versus Wideband These multiple access schemes can be grouped into two categories:Narrowband systems - the total spectrum is divided into a large number of narrow radio bands that are shared.Wideband systems - the total spectrum is used by each mobile unit for both directions of transmission. Only applicable for TDM and CDM.


Frequency Division Multiplexing (FDM)Separation of the whole spectrum into smaller frequency bandsA channel gets a certain band of the spectrum for the whole time orthogonal systemAdvantages:no dynamic coordination necessary, i.e., sync. andframingworks also for analog signalslow bit rates cheaper,delay spread Disadvantages:waste of bandwidth if the traffic is distributed unevenlyinflexibleguard bandsnarrow filtersk2k3k4k5k6k1ftc


Time Division Multiplexing (TDM)A channel gets the whole spectrum for a certain amount of time orthogonal systemAdvantages:only one carrier in the medium at any timethroughput high - supports burstsflexible multiple slotsno guard bands ?!Disadvantages:Framing and precise synchronization necessaryhigh bit ratesat eachTx/Rxftck2k3k4k5k6k1


Hybrid TDM/FDMCombination of both methodsA channel gets a certain frequency band for a certain amount of time (slot). Example: GSM, hops from one band to another each time slot Advantages:better protection against tapping (hopping amongfrequencies)protection against frequency selective interferenceDisadvantages: Framing andsync. requiredftck2k3k4k5k6k1


Code Division Multiplexing (CDM) Each channel has a unique code(not necessarily orthogonal)All channels use the same spectrum at the same timeAdvantages:bandwidth efficientno coordination and synchronization necessarygood protection against interference and tappingDisadvantages:lower user data rates due to high gains required to reduce interferencemore complex signal regeneration2.19.1k2k3k4k5k6k1ftc


Issues with CDMCDM has a soft capacity. The more users the more codes that are used. However as more codes are used the signal to interference (S/I) ratio will drop and the bit error rate (BER) will go up for all users.CDM requires tight power control as it suffers from far-near effect. In other words, a user close to the base station transmitting with the same power as a user farther away will drown the latters signal. All signals must have more or less equal power at the receiver.Rake receivers can be used to improve signal reception. Time delayed versions (a chip or more delayed) of the signal (multipath signals) can be collected and used to make bit level decisions. Soft handoffs can be used. Mobiles can switch base stations without switching carriers. Two base stations receive the mobile signal and the mobile is receiving from two base stations (one of the rake receivers is used to listen to other signals).Burst transmission - reduces interference


Types of CDM ITwo types exist:Direct Sequence CDM (DS-CDM)spreads the narrowband user signal (Rbps) over the full spectrum by multiplying it by a very wide bandwidth signal (W). This is done by taking every bit in the user stream and replacing it with a pseudonoise (PN) code (a long bit sequence called the chip rate). The codes are orthogonal (or approx.. orthogonal). This results in a processing gain G = W/R (chips/bit). The higher G the better the system performance as the lower the interference. G2 indicates the number of possible codes. Not all of the codes are orthogonal.


Types of CDM IIFrequency hopping CDM (FH-CDM) FH-CDM is based on a narrowband FDM system in which an individual users transmission is spread out over a number of channels over time (the channel choice is varied in a pseudorandom fashion). If the carrier is changed every symbol then it is referred to as a fast FH system, if it is changed every few symbols it is a slow FH system.


Orthogonality and CodesAn m-bit PN generator generates N=2m - 1 different codes.Out of these codes only m codes are orthogonal -> zero cross correlation.For example a 3 bit shift register circuit shown below generates N=7 codes.


Orthogonal CodesA pair of codes is said to be orthogonal if the cross correlation is zero: Rxy(0) = 0 .For two m-bit codes: x1,x2,x3,...,xm and y1,y2,y3,...,ym:

For example: x = 0011 and y = 0110. Replace 0 with -1, 1 stays as is. Then: x = -1 -1 1 1 y = -1 1 1 -1-----------------Rxy(0) = 1 -1 +1 -1 = 0


Example of an Orthogonal Code: Walsh CodesIn 1923 J.L. Walsh introduced a complete set of orthogonal codes. To generate a Walsh code the following two steps must be followed:Step 1: represent a NxN matrix as four quadrants (start off with 2x2)Step 2: make the first, second and third quadrants indentical and invert the fourth


ModulationDigital modulationdigital data is translated into an analog signal (baseband)ASK, FSK, PSK - main focus in this chapterdifferences in spectral efficiency, power efficiency, robustnessAnalog modulationshifts center frequency of baseband signal up to the radio carrierMotivationsmaller antennas (e.g., /4)Frequency Division Multiplexingmedium characteristicsBasic schemesAmplitude Modulation (AM)Frequency Modulation (FM)Phase Modulation (PM)


Modulation and Demodulationsynchronizationdecisiondigitaldataanalogdemodulationradiocarrieranalogbasebandsignal101101001radio receiverdigitalmodulationdigitaldataanalogmodulationradiocarrieranalogbasebandsignal101101001radio transmitter


Digital ModulationModulation of digital signals known as Shift KeyingAmplitude Shift Keying (ASK):very simplelow bandwidth requirementsvery susceptible to interference Frequency Shift Keying (FSK):needs larger bandwidth

Phase Shift Keying (PSK):more complexrobust against interference101t101t101t


Advanced Frequency Shift Keyingbandwidth needed for FSK depends on the distance between the carrier frequenciesspecial pre-computation avoids sudden phase shifts MSK (Minimum Shift Keying)bit separated into even and odd bits, the duration of each bit is doubled depending on the bit values (even, odd) the higher or lower frequency, original or inverted is chosenthe frequency of one carrier is twice the frequency of the othereven higher bandwidth efficiency using a Gaussian low-pass filter GMSK (Gaussian MSK), used in GSM


Example of MSKdataeven bitsodd bits1111000tlow frequencyhigh frequencyMSKsignalbiteven0 1 0 1odd0 0 1 1signalh n n h value- - + +h: high frequencyn: low frequency+: original signal-: inverted signalNo phase shifts!


Advanced Phase Shift KeyingBPSK (Binary Phase Shift Keying):bit value 0: sine wavebit value 1: inverted sine wavevery simple PSKlow spectral efficiencyrobust, used e.g. in satellite systemsQPSK (Quadrature Phase Shift Keying):2 bits coded as one symbolsymbol determines shift of sine waveneeds less bandwidth compared to BPSKmore complexOften also transmission of relative, not absolute phase shift: DQPSK - Differential QPSK (IS-136, PACS, PHS)

11100001At


Quadrature Amplitude ModulationQuadrature Amplitude Modulation (QAM): combines amplitude and phase modulationit is possible to code n bits using one symbol2n discrete levels, n=2 identical to QPSKbit error rate increases with n, but less errors compared to comparable PSK schemes

Example: 16-QAM (4 bits = 1 symbol)Symbols 0011 and 0001 have the same phase, but different amplitude. 0000 and 1000 have different phase, but same amplitude. used in standard 9600 bit/s modems0000000100111000QI0010


Spread spectrum technology: CDMProblem of radio transmission: frequency dependent fading can wipe out narrow band signals for duration of the interferenceSolution: spread the narrow band signal into a broad band signal using a special codeprotection against narrow band interference

protection against narrowband interferenceSide effects:coexistence of several signals without dynamic coordinationtap-proofAlternatives: Direct Sequence, Frequency Hopping

detection atreceiverinterferencespread signalsignalspreadinterferenceffpowerpower


Effects of spreading and interferencePfi)Pfii)senderPfiii)Pfiv)receiverfv)user signalbroadband interferencenarrowband interference2.28.1P


Spreading and frequency selective fadingfrequencychannel quality123456narrow band signalguard space2.29.1narrowband channelsspread spectrum channels


DSSS (Direct Sequence Spread Spectrum) IXOR of the signal with pseudo-random number (chipping sequence)many chips per bit (e.g., 128) result in higher bandwidth of the signalAdvantagesreduces frequency selective fadingin cellular networks base stations can use the same frequency rangeseveral base stations can detect and recover the signalsoft handoverDisadvantagesprecise power control necessary2.30.1user datachipping sequenceresultingsignal0101101010100111XOR01100101101001=tbtctb: bit periodtc: chip period


DSSS (Direct Sequence Spread Spectrum) IIXuser datachippingsequencemodulatorradiocarrierspreadspectrumsignaltransmitsignaltransmitterdemodulatorreceivedsignalradiocarrierXchippingsequencelowpassfilteredsignalreceiverintegratorproductsdecisiondatasampledsumscorrelator2.31.1


FHSS (Frequency Hopping Spread Spectrum) IDiscrete changes of carrier frequencysequence of frequency changes determined via pseudo random number sequenceTwo versionsFast Hopping: several frequencies per user bitSlow Hopping: several user bits per frequencyAdvantagesfrequency selective fading and interference limited to short periodsimple implementationuses only small portion of spectrum at any timeDisadvantagesnot as robust as DSSSsimpler to detect

2.32.1


FHSS (Frequency Hopping Spread Spectrum) IIuser dataslowhopping(3 bits/hop)fasthopping(3 hops/bit)01tb011tff1f2f3ttdff1f2f3ttdtb: bit periodtd: dwell time2.33.1


FHSS (Frequency Hopping Spread Spectrum) IIImodulatoruser datahoppingsequencemodulatornarrowbandsignalspreadtransmitsignaltransmitterreceivedsignalreceiverdemodulatordatafrequencysynthesizerhoppingsequencedemodulatorfrequencysynthesizernarrowbandsignal2.34.1


Concept of Cellular CommunicationsIn the late 60s it was proposed to alleviate the problem of spectrum congestion by restructuring the coverage area of mobile radio systems.The cellular concept does not use broadcasting over large areas. Instead smaller areas called cells are handled by less powerful base stations that use less power for transmission. Now the available spectrum can be re-used from one cell to another thereby increasing the capacity of the system. However this did give rise to a new problem, as a mobile unit moved it could potentially leave the coverage area (cell) of a base station in which it established the call. This required complex controls that enabled the handing over of a connection (called handoff) to the new cell that the mobile unit moved into.In summary, the essential elements of a cellular system are:Low power transmitter and small coverage areas called cellsSpectrum (frequency) re-useHandoff


Cell structureImplements space division multiplex: base station covers a certain transmission area (cell)Mobile stations communicate only via the base station

Advantages of cell structures:higher capacity, higher number of usersless transmission power neededmore robust, decentralizedbase station deals with interference, transmission area etc. locallyProblems:fixed network needed for the base stationshandover (changing from one cell to another) necessaryinterference with other cellsCell sizes from some 100 m in cities to, e.g., 35 km on the country side (GSM) - even less for higher frequencies2.35.1


Cellular Network


Some DefinitionsForward path or down link - from base station down to the mobileReverse path or up link - from the mobile up to the base stationThe mobile unit - a portable voice and/or data comm. transceiver. It has a 10 digit telephone number that is represented by a 34 bit mobile identification number -> (215) 684-3201 is divided into two parts: MIN1: 215 translated into 10bits and MIN2: 684-3201 translated into 24bits. In addition each mobile unit is also permanently programmed at the factory with a 32 bit electronic serial number (ESN) which guards against tampering.The cell - a geographical area covered by Radio Frequency (RF) signals. It is essentially a radio communication center comprising radios, antennas and supporting equipment to enable mobile to land and land to mobile communication. Its shape and size depend on the location, height , gain and directivity of the antenna, the power of the transmitter, the terrain, obstacles such as foliage, buildings, propagation paths, etc. It is a highly irregular shape, its boundaries defined by received signal strength! But for traffic engineering purposes and system planning and design a hexagonal shape is used.


More definitionsThe base station (BS) - a transmitter and receiver that relays signals (control and information (voice or data)) from the mobile unit to the MSC and vice versa.The mobile switching center (MSC) - a switching center that controls a cluster of cells. Base stations are connected to the MSC via wireline links. The MSC is directly connected to the PSTN and is responsible for all calls related to mobiles located within its domain. MSCs intercommunicate using a link protocol specified by IS (International Standard) 41. This enables roaming of mobile units (i.e. obtaining service outside of the home base). The MSC is also responsible for billing, it keeps track of air time, errors, delays, blocking, call dropping (due to handoff failure), etc. It is also responsible for the handoff process, it keeps track of signal strengths and will initiate a handoff when deemed necessary (note to handoff or not to handoff is not a trivial issue!)


The Basic Cellular Communication Protocol IEvery mobile unit whether at home or roaming, has to register with the MSC controlling the area it is in. If it does not register then the MSC does not know of its existence and will not be able to process any of its calls.The home location register (HLR) is used to keep information regarding a mobile unit/user, it is a database for storing and managing subscriber information. When roaming, a mobile unit registers with a foreign MSC and data from its HRL is relayed to the visitor location register (VLR). The VLR is a dynamic database used to store roaming mobile subscriber information. The HLR and VLR communicate via the MSCs using IS 41.The cellular system uses out of band signalling. Most of the control information is sent over different channels from the user information (voice or data) channels. Inband signalling is used for control during the connection (disconnect, handoff, etc.)


The Basic Cellular Communication Protocol IIA mobile unit when enabled (power on) scans the control channels and tunes to the one with the strongest signal. The control channels are known and carry signals pertaining to the cell sites, e.g. transmission power to be used by the mobile unit in a particular cell. This process is called initialization.If the mobile wants to initiate a call, it sends in a service request on the reverse path control link. The service request contains the destination phone number and identification information (MIN1, MIN2, and ESN) of the source mobile unit to verify the originator. When the base station receives the request, it relays it to the MSC. The MSC then checks to see it is it a number of another mobile or of a fixed user. If the latter the call is forwarded to the PSTN. If the former, it checks to see if the destination mobile unit is a subscriber (local or visitor/roamer). If not it relays the call to the PSTN to forward to the appropriate MSC.


The Basic Cellular Communication Protocol IIIIf the destination is within its cluster it sends out a paging message to all the base stations. Every base station then relays this message by broadcasting it on its control channel. If the destination mobile unit is enabled (power on) it will detect this message and respond to the base station. The base station relays this response to the MSC. The MSC then allocates channels to both the source mobile unit and the destination mobile unit. The corresponding base stations pass this information on to the respective mobile units. The mobile units then tune to the correct channels and the communication link is established.


Spectrum and Capacity IssuesSpectrum is limited


Frequency Re-use ITo be able to increase the capacity of the system, frequencies must be re-used in the cellular layout (unless we are using spread spectrum techniques).Frequencies cannot be re-used in adjacent cells because of co-channel interference. The cells using the same frequencies must be dispersed across the cellular layout. The closer the spacing the more efficient the scheme!


Frequency Re-use IIFor an omni-directional antenna, with constant signal power, each cell site coverage area would be circular (barring any terrain irregularities or obstacles). To achieve full coverage without dead spots, a series of regular polygons for cell sites are required. The hexagonal was chosen as it comes the closest to the shape of a circle, and a hexagonal layout requires fewer cells (when compared to triangles or rectangles, it has the largest surface area given the same radius R) -> less cells.Goal is to find the minimum distance between cells using same frequencies.


Frequency re-use distance I


Frequency re-use distance IIFor two adjacent cells: D=31/2R The closest we can place the same frequencies is called the first tier around the center cell (minimal re-use distance -> lower -> more capacity!).For simplicity we only take the first tier of cells into account for co-channel interference (i.e., we ignore 2nd, 3rd, etc. tiers, cause much less interference, negligible!).


Frequency re-use distance III


Frequency re-use distance IIIRadius = dist. between two co-channel cells = (3R2[i2+j2+ij])1/2 = DSince the area of a hexagon is proportional to the square of the distance between its center and a vertex (i.e., its radius), the area of the large hexagon is:Alarge = k[Radius]2 = k[3R2[i2+j2+ij]]where k is a constant.Similarly the area of each cell (i.e., small hexagon) is:Asmall = k[R2]Comparing these expressions we find that:Alarge/Asmall = 3[i2+j2+ij] = D2/R2


Frequency re-use distance IVFrom symmetry we can see that the large hexagon encloses the center cluster of N cells plus 1/3 the number of the cells associated with 6 other peripheral hexagons. Thus the total number of cells enclosed by the first tier is:N+6(1/3N) = 3NSince the area of a hexagon is proportional to the number of cells contained within it:Alarge/Asmall = 3N/1 = 3N Substituting we get:3N = 3[i2+j2+ij] = D2/R2Or:D/R = q =(3N)1/2q is referred to as the reuse ratio!


Co-channel Interference IThe co-channel interference ratio S/I is given as:

S = desired signal power in a cell (note that many texts use C instead of S), Ik = interference signal power from the kth cell, Ni = number of interfering cells.If we only assume the first tier of interfering cells, then Ni=6,and all cells interfere equally (they are all equidistant!). The signal power at any point is inversely proportional to the inverse of the distance from the source raised to the g power. (2

Co-channel Interference IIIk is proportional to Dg , and S is proportional to Rg , where g is the propagation path loss and is dependent upon terrain environment. For cellular systems it is often taken as = 4. Therefore:

The relationship between SNR (signal to noise ratio - Eb/No) and S/I for cellular systems with Rayleigh fading channels: SNR = S/I(db) 9db.


For a given S/I how to get NRecall that: D/R = q =(3N)1/2An S/I = 18db (decibels=10logS/I) = 63.1, gives an acceptable voice quality.Therefore q = [6x63.1]1/4 = 4.41 when g = 4Substituting for N we get N = (4.41)2/3 equals approx. 7This means that if we have 49 frequency channels available, each cell gets 49/7 = 7 frequency channels. If we have 82 available then 82/7 = 11.714 -> which means that 5 cells will have 12 and 2 cells will have 11!How does that translate to i and j for a cell layout? N = [i2+j2+ij], find i,j that satisfy the equation!


Calculating i, j, and D from N


Frequency planningFrequency reuse only with a certain distance between the base stationsStandard model using 7 frequencies:

Fixed frequency assignment:certain frequencies are assigned to a certain cellproblem: different traffic load in different cellsDynamic frequency assignment:base station chooses frequencies depending on the frequencies already used in neighbor cellsmore capacity in cells with more trafficassignment can also be based on interference measurements2.36.1


Increasing CapacityWe can see that by reducing the area of a cell we can increase capacity as we will have more cells each with its own set of frequencies.What is drawback of shrinking the size of the cells (cell splitting)? Increase in the number of handoffs -> increased load on the system! Also need more infrastrucutre -> base stations (each cell needs a BS).An easier solution exists, sectorization. It does not reduce handoffs, its advantage: it does not require more infrastructure.


Sectorization IWe can also increase the capacity by using sectors in cells. Directional antennas instead of being omnidirectional, will only beam over a certain angle.

3 cell cluster3 cell cluster with 3 sectors


Sectorization IIWhat does that mean?We can now assign frequency sets to sectors and decrease the re-use distance or improve S/I ratio (i.e. signal quality).Question: By how much? Depends on number of sectors (i.e., 60% or 120%).


Other Capacity or Signal Improvement Tech.Dynamic channel allocation (DCA): allows cells to borrow frequencies from other cells within the cluster if not used by them. Can be used to alleviate hotspots. Another implementation basically has all channels available to all cells, they get allocated based upon demand.Power control: by reducing the transmitted power, the battery life of a mobile can be extended. It also helps in reducing -channel and adjacent channel interference.


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Ch2 Wireless Transmission