ECE6604

PERSONAL & MOBILE COMMUNICATIONS

Week 2

Interference and Shadow Margins, Handoff Gain, Coverage

Capacity, Flat Fading

1

Interference Margin

As the subscriber load increases, additional interference is generatedfrom both inside and outside of a cell. With increased interference,the coverage area shrinks and some calls are dropped. As calls aredropped, the interference decreases and the coverage area expands.

the expansion/contraction of the coverage area is a phenomenonknown as cell breathing.

We must introduce an interference degradation margin into the linkbudget to account for cell breathing.

The received carrier-to-interference-plus-noise ratio is

IN =p

I +N=

p/N

1+ I/N,

where I is the total interference power.

The net effect of such interference is to reduce the carrier-to-noise ratio p/N by the factor LI = (1+I/N). To allow for systemloading, we must reduce the maximum allowable path loss by anamount equal to LI (dB), otherwise known as the interferencemargin.

The appropriate value of (LI)dB depends on the particular cel-lular system being deployed and the maximum expected trafficloading.

2

Shadowing

With shadowing the received signal power isp (dBm)(d) = p (dBm)(do) 10 log10(d/do) + (dB)

= p (dBm)(d) + (dB) ,

where the parameter (dB) is the error between the predicted andactual path loss.

Very often (dB) is modeled as a zero-mean Gaussian or normal ran-dom variable with variance 2, where in decibels (dB) is calledthe shadow standard deviation.

The probability density function of p (dBm)(d) has the normal distri-bution

pp (dBm)(d)(x) =12

exp

{(x p (dBm)(d)

)222

}.

Typically, ranges from 4 to 12 dB depending on the local topog-raphy; = 8 dB is a very commonly used value.

3

-50

-80

dBm

1.0 10.0 100.0 km

free space-20 dB/decade

urban macrocell-40 dB/decade

= 8 dB

dB

-60

-70

Path loss and shadowing in a typical cellular environment.

4

Noise Outage

The quality of a radio link is acceptable only when the received signalpower p (dBm) is greater than the receiver sensitivity th (dBm).

An outage occurs whenever p (dBm) < th (dBm).

The edge outage probability, PE, is defined as the probability thatp (dBm) < th (dBm) at the cell edge.

The area outage probability, PO, is defined as the probability thatp (dBm) < th (dBm) when averaged over the entire cell area.

To maintain an acceptable outage probability in the presence ofshadowing, we must introduce a shadow margin.

5

thpower (dBm)

Mshad

Area = 0.1

received carrier

= 8

Determining the required shadow margin to give PE = 0.1.

6

Choose Mshad so that the shaded area under the Gaussian densityfunction is equal to 0.1. Hence, we solve

0.1 = Q

(Mshad

)Q(x) =

x

12

ey2/2dy

We haveMshad

= Q1(0.1) = 1.28

For = 8 dB we haveMshad = 1.28 8 = 10.24 dB

The area outage probability (uniform user density, d path loss, nopower control) is

PO = Q(X) exp{XY + Y 2/2

}Q(X + Y )

where

X =Mshad

, Y =

2 ln 10

10

From this we can solve for the required shadow margin, Mshad.

Note that PO < PE for the same value of Mshad.

7

Handoff Gain

At the boundary area between two cells, we obtain a macrodiversityeffect.

Although the link to the serving base station may be shadowed suchthat p (dBm) is below the receiver threshold, the link to another basestation may provide a p (dBm) above the receiver threshold.

Handoffs take advantage of macrodiversity to reduce the requiredshadow margin over the single cell case, by an amount equal to thehandoff gain, GHO.

There are a variety of handoff algorithms used in cellular systems.CDMA system use soft handoffs, while TDMA systems usually usehard handoffs.

The maximum allowable path loss with the inclusion of the marginsfor shadowing and interference loading, and handoff gain is

Lmax (dB) = t (dBm)+GT (dB)+GR (dB)th (dBm)Mshad (dB)LI (dB)+GHO (dB) .

8

Hard vs. Soft Handoff

Consider a cluster of 7 cells; the target cell is in the center andsurrounded by 6 adjacent cells. Although the MS is located in thecenter cell, it is possible that the MS could be connected to any oneof the 7 BSs.

We wish to the calculate the area averaged noise outage probabil-ity for the target cell, assuming that the MS location is uniformdistributed over the target cell area.

Assume that the links to the serving BS and the six neighboringBSs experience correlated log-normal shadowing. To generatethe required shadow gains, we express the shadow gain at BSi as

i = a + bi ,

where

a2+ b2 = 1 ,

and and i are independent Gaussian random variables with zeromean and variance 2.

It follows that the shadow gains (in decibel units) have the correla-tion

E[ij] = a22 =

2

where = a2 is the correlation coefficient. Here we assume that = 0.5.

9

Hard vs. Soft Handoff

Soft handoff algorithm: the BS that provides the largest instan-taneous received signal strength is selected as the serving BS.

If any BS has an associated received signal power that is abovethe receiver sensitivity, th (dBm), then the link quality is accept-able; otherwise an outage will occur.

Hard handoff algorithm: The received signal power from the serving BS is equal to p,0 (dBm).If this value exceeds the receiver sensitivity, th (dBm), then thelink quality is acceptable.

Otherwise, the six surrounding BSs are evaluated for handoff can-didacy by using a mobile assisted handoff algorithm. A BS thatqualifies as a handoff candidate must have p,k (dBm)p,0 (dBm) H(dB), where H(dB)) is the handoff hysteresis.

We then check those BSs passing the hysteresis test. If thereceived signal power for any of these BSs is above the receiversensitivity, th (dBm), then link quality is acceptable; otherwise anoutage occurs.

10

0 2 4 6 8 10 1290

91

92

93

94

95

96

97

98

99

100

Shadow Margin (dB)

Cove

rage

(%) Soft Handoff Hard handoff Single Cell

Typical handoff gain for hard and soft handoffs. In this plot shadow margin isdefined as MshadGHO, where Mshad is the shadow margin required for a singlecell. We also plot the area averaged outage rather than the edge outage.

11

Cellular Radio Coverage

Radio coverage refers to the number of base stations or cell sitesthat are required to cover or provide service to a given area withan acceptable grade of service.

The number of cell sites required to cover a given area is determinedby the maximum allowable path loss and the path loss exponent.

To compare the coverage of different cellular systems, we first de-termine the maximum allowable path loss, Lmax (dB), for the differentsystems by using a common quality criterion.

ThenLmax (dB) = C + 10log10dmax

where dmax is the radio path length that corresponds to the maximumallowable path loss and C is a constant.

The quantity dmax is equal to the radius of the cell.

To provide good coverage it is desirable that dmax be as large aspossible.

12

Comparing Coverage

Suppose that System 1 has Lmax (dB) = L1 and System 2 has Lmax (dB) =L2, with corresponding radio path lengths of d1 and d2, respectively.The difference in the maximum allowable path loss is related to thecell radii by

L1 L2 = 10 (log10d1 log10d2)= 10

(log10

d1

d2

)or looking at things another way

d1

d2= 10(L1L2)/(10)

Since the area of a cell is equal to A = d2 (assuming a circular cell)the ratio of the cell areas is

A1

A2=

d21d22

=

(d1

d2

)2and, hence,

A1

A2= 102(L1L2)/(10) .

13

Suppose that Atot is the total geographical area to be covered. Thenthe ratio of the required number of cell sites for Systems 1 and 2 is

N1

N2=

Atot/A1

Atot/A2=

A2

A1= 102(L1L2)/(10)

Example: Suppose that = 3.5 and L1 L2 = 2 dB. N2/N1 = 1.30.

Conclusion: System 2 requires 30% more base stations to coverthe same geographical area for only a 2 dB difference in linkbudget.

Note that the required interference margin and realized handoff gainhave a large impact. Coverage comparisons should be done underconditions of equal traffic loading.

14

Spectral Efficiency

Spectral efficiency can be expressed in terms of the following pa-rameters:

Gc = offered traffic per channel (Erlangs/channel)

Nslot = number of channels per RF carrier

Nc = number of RF carriers per cell area (carriers/m2)

Wsys = total system bandwidth (Hz)

A = area per cell (m2) .

One Erlang is the traffic intensity in a channel that is continuouslyoccupied, so that a channel occupied for x% of the time carriersx/100Erlangs. Adjustment of this parameter controls the systemloading and it is important to compare systems at the same trafficload level.

For an N-cell reuse cluster, we can define the spectral efficiency asfollows:

S =NcNNslotGc

WsysAErlangs/m2/Hz .

1

Spectral Efficiency (contd)

Recognizing that the bandwidth per channel, Wc, is equal to Wsys/(NNcNslot),the spectral efficiency can be written as the product of three effi-ciencies, viz.,

S =1

Wc 1AGc

= B C T ,where

B = bandwidth efficiency

C = spatial efficiency

T = trunking efficiency

Unfortunately, these efficiencies are not at all independent so theoptimization of spectral efficiency can be quite complicated.

For cellular systems, the number of channels per cell (or cell sector)is sometimes used instead of the Erlang capacity. We have

NcNslot =Wsys

Wc Nwhere, again, Wc is the bandwidth per channel and Nslot is the numberof traffic channels multiplexed on each RF carrier.

2

Trunking Efficiency

The cell Erlang capacity equal to the traffic carrying capacity of acell (in Erlangs) for a specified call blocking probability.

The Erlang capacity can be calculated using the famous Erlang-Bformula

B(,m) =m

m!m

k=0k

k!

where B(,m) is the call blocking probability, m is the total numberof channels in the trunk and = is the total offered traffic inErlangs ( is the call arrival rate and is the mean call duration).

The cell Erlang capacity accounts for the trunking efficiency, a phe-nomenon where larger groups of channels are able to carry more traf-fic per channel for a given blocking probability than smaller groupsof channels.

3

0.0 0.2 0.4 0.6 0.8 1.0G

c (Erlangs)

10-3

10-2

10-1

100

B(,

m)

m = 1m = 2m = 5m = 10

Blocking probability B(,m) against offered traffic per channel Gc = /m.

4

F2

F1F3

3-sectoromni

F

F1 F2 F3F = + +

Trunkpool schemes.

5

0.2 0.4 0.6 0.8 1.0Channel Usage Efficiency

10-4

10-3

10-2

10-1

100

Bl

ocki

ng P

roba

bilit

y

7c-sec 7c-omni 4c-sec 4c-omni

Channel usage efficiency C = (1 B(,m)/m for different trunkpoolschemes; 416 channels.

6

GSM Cell Capacity

A 3/9 (3-cell/9-sector) reuse pattern is achievable for most GSMsystems that employ frequency hopping; without frequency hopping,a 4/12 reuse pattern may be possible.

GSM has 8 logical channels that are time division multiplexed ontoa single radio frequency carrier, and the carriers are spaced 200 kHzapart. Therefore, the bandwidth per channel is roughly 25 kHz,which was common in first generation European analog mobile phonesystems.

In a nominal bandwidth of 1.25MHz (uplink or downlink) there are1250/25 = 6.25 carriers spaced 200 kHz apart. Hence, there are6.25/9 0.694 carriers per sector or 6.25/3 = 2.083 carriers/cell.

Each carrier commonly carries half-rate traffic, such that there are16 channels/carrier. Hence, the 3/9 reuse system has a sectorcapacity of 11.11 channels/sector or a cell capacity of 33.33 chan-nels/cell in 1.25MHz.

7

IS-95 Cell Capacity

Suppose there are N users in a cell; one desired user and N 1interfering users. For the time being, ignore the interference fromsurrounding cells. Consider the reverse link, and assume perfectlypower controlled MS transmissions that arrive chip and phase asyn-chronous at the BS receiver.

Treating the co-channel signals as a Gaussian impairment, the ef-fective carrier-to-noise ratio is (the factor of 3 accounts for chip andphase asynchronous signals)

=3

N 1 ,and the effective received bit energy-to-noise ratio is

Eb

No= Bw

Rb

=3G

N 1 3G

N,

where G = Bw/Rb.

For a required Eb/No, (Eb/No)req, the cell capacity is

N 3G(Eb/No)req

.

8

IS-95 Cell Capacity (contd)

Suppose that 1.25MHz of spectrum is available and the source coderoperates at Rb = 4 kbps. Then G = 1250/4 = 312.5. If (Eb/No)req =6 dB (a typical IS-95 value), then the cell capacity is roughly N =3 312.5/4 234 channels per cell. This is roughly 7 times the cellcapacity of GSM.

This rudimentary analysis did not include out-of-cell interferencewhich is typically 50 to 60% of the in-cell interference. This willresult in a reduction of cell capacity by a factor of 1.5 and 1.6,respectively.

With CDMA receivers, great gains can be obtained by improvingreceiver sensitivity. For example, if (Eb/No)req can be reduced by1 dB, then the cell capacity N increases by a factor of 1.26.

CDMA systems are known to be sensitive to power control errors.An rms power control error of 2 dB will reduce the capacity byroughly a factor of 2.

9

Some Elements for High Capacity

Our emphasis is on physical wireless communications

At the physical layer, some of the key elements to high capacityfrequency reuse systems are

adaptive power and bandwidth efficient modulation

multipath-fading mitigation/exploitation (transmit and receiverdiversity, error control coding, multiuser diversity)

techniques to mitigation time delay spread (OFDM, equalizers,RAKE receivers)

co-channel interference cancellation (single and multi-antennainterference cancellation)

coding modulation (Turbo trellis coding, bit interleaved codedmodulation)

co-channel interference control (handoffs, power control, space-division multiple access)

10

Multipath-Fading Mechanism

base station

mobile subscriber

local scatterers

A typical macrocellular mobile radio environment.

11

Multipath-Fading Mechanism

mobile station

local scatterers

mobile station

local scatterers

Typical mobile-to-mobile radio propagation environment.

12

area mean (dB)local mean (dB)

envelope fading

Path loss, shadowing, envelope fading.

13

Doppler Shift

y

x

n

n th incoming wave

vmobile station

A typical wave component incident on a mobile station (MS).

The Doppler shift is fD,n = fm cos n, where fm = v/c (c is the carrierwavelength, v is the mobile station velocity).

14

Multipath Propagation

Consider the transmission of the band-pass signals(t) = Re

{s(t)ej2fct

} At the receiver antenna, the nth plane wave arrives at angle n andexperiences Doppler shift fD,n = fm cos n and propagation delay n.

If there are N propagation paths, the received bandpass signal is

r(t) = Re

[N

n=1

Cnejnj2cn/c+j2(fc+fD,n)ts(t n)

],

where Cn, n, fD,n and n are the amplitude, phase, Doppler shift andtime delay, respectively, associated with the nth propagation path,and c is the speed of light.

The delay n = dn/c is the propagation delay associated with the nthpropagation path, where dn is the length of the path. The pathlengths, dn, will depend on the physical scattering geometry whichwe have not specified at this point.

15

Multipath Propagation

The received bandpass signal r(t) has the formr(t) = Re

[r(t)ej2fct

]where the received complex envelope is

r(t) =

Nn=1

Cnejn(t)s(t n)

and

n(t) = n 2cn/c+2fD,ntis the time-variant phase associated with the nth path.

The phase n is randomly introduced by the nth scatterer and canbe assumed to be uniformly distributed on [, ).

16

Flat Fading -time domain

The channel can be modeled by a linear time-variant filter havingthe complex low-pass impulse response

g(t, ) =

Nn=1

Cnejn(t)( n)

If the differential path delays ij are small compared to the durationof a modulated symbol, T , then the n are all approximately equalto their average value .

The channel impulse response has the form

g(t, ) = g(t)( ) , g(t) =N

n=1

Cnejn(t) .

The received complex envelope isr(t) = g(t)s(t )

which experiences fading due to the time-varying complex channelgain g(t).

17

Flat Fading - frequency domain

In the frequency domain, the received complex envelope isR(f) = G(f) S(f)ej2f

Since the channel changes with time, G(f) has a finite non-zerowidth in the frequency domain.

Due to the convolution operation, the output spectrum R(f) willbe larger than the input spectrum S(f). This broadening of thetransmitted signal spectrum is caused by the channel time variationsand is called frequency spreading.

18

Channel Transfer Function - Flat Fading

The corresponding time-variant channel transfer function is obtainedby taking the Fourier transform of the time-variant channel impulseresponse g(t, ) with respect to the delay variable , i.e.,

T(t, f) = g(t)ej2f .

Since the magnitude response is |T(t, f)| = |g(t)|, all frequency com-ponents in the received signal are subject to the same time-variantamplitude gain |g(t)|, while the phase response is a linear function offrequency with slope 2 .

The received signal is said to exhibit flat fading, because themagnitude of the time-variant channel transfer function is constant(or flat) with respect to frequency variable f.

19