ECE6604 PERSONAL & MOBILE COMMUNICATIONS. Week 2. Interference and Shadow Margins, Handoff Gain, Coverage Capacity, Flat Fading

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1 ECE6604 PERSONAL & MOBILE COMMUNICATIONS Week 2 Interference and Shadow Margins, Handoff Gain, Coverage Capacity, Flat Fading 1

2 Interference Margin As the subscriber load increases, additional interference is generated from both inside and outside of a cell. With increased interference, the coverage area shrinks and some calls are dropped. As calls are dropped, the interference decreases and the coverage area expands. the expansion/contraction of the coverage area is a phenomenon known as cell breathing. We must introduce an interference degradation margin into the link budget to account for cell breathing. The received carrier-to-interference-plus-noise ratio is Γ IN = Ω p I +N = Ω p/n 1+I/N, where I is the total interference power. The net effect of such interference is to reduce the carrier-tonoise ratio Ω p /N by the factor L I = (1+I/N). To allow for system loading, we must reduce the maximum allowable path loss by an amount equal to L I (db), otherwise known as the interference margin. The appropriate value of (L I ) db depends on the particular cellular system being deployed and the maximum expected traffic loading. 2

3 Shadowing With shadowing the received signal power is Ω p (dbm) (d) = µ Ωp (dbm) (d o ) 10βlog 10 (d/d o )+ǫ (db) = µ Ωp (dbm) (d)+ǫ (db), where the parameter ǫ (db) is the error between the predicted and actual path loss. Very often ǫ (db) is modeled as a zero-mean Gaussian or normal random variable with variance σ 2 Ω, where σ Ω in decibels (db) is called the shadow standard deviation. The probability density function of Ω p (dbm) (d) has the normal distribution { p Ωp (dbm) (d)(x) = 1 ( x µωp (dbm)(d) ) } 2 exp. 2πσΩ Typically, σ Ω ranges from 4 to 12 db depending on the local topography; σ Ω = 8 db is a very commonly used value. 2σ 2 Ω 3

4 km -60 free space -20 db/decade dbm σ Ω db urban macrocell -40 db/decade = 8 db σ Ω Path loss and shadowing in a typical cellular environment. 4

5 Noise Outage The quality of a radio link is acceptable only when the received signal power Ω p (dbm) is greater than the receiver sensitivity Ω th (dbm). An outage occurs whenever Ω p (dbm) < Ω th (dbm). The edge outage probability, P E, is defined as the probability that Ω p (dbm) < Ω th (dbm) at the cell edge. The area outage probability, P O, is defined as the probability that Ω p (dbm) < Ω th (dbm) when averaged over the entire cell area. To maintain an acceptable outage probability in the presence of shadowing, we must introduce a shadow margin. 5

6 Area = 0.1 σ = 8 Ω Ω th M shad received carrier power (dbm) Determining the required shadow margin to give P E =

7 Choose M shad so that the shaded area under the Gaussian density function is equal to 0.1. Hence, we solve ( ) Mshad = Q Q(x) = e y2 /2 dy 2π σ Ω x We have M shad σ Ω = Q 1 (0.1) = 1.28 For σ Ω = 8 db we have M shad = = db The area outage probability (uniform user density, d β path loss, no power control) is where P O = Q(X) exp { XY +Y 2 /2 } Q(X +Y) X = M shad, Y = 2σ Ωln10 σ Ω 10β From this we can solve for the required shadow margin, M shad. Note that P O < P E for the same value of M shad. 7

8 Handoff Gain At the boundary area between two cells, we obtain a macrodiversity effect. Although the link to the serving base station may be shadowed such that Ω p (dbm) is below the receiver threshold, the link to another base station may provide a Ω p (dbm) above the receiver threshold. Handoffs take advantage of macrodiversity to reduce the required shadow margin over the single cell case, by an amount equal to the handoff gain, G HO. There are a variety of handoff algorithms used in cellular systems. CDMA system use soft handoffs, while TDMA systems usually use hard handoffs. The maximum allowable path loss with the inclusion of the margins for shadowing and interference loading, and handoff gain is L max (db) = Ω t (dbm) +G T (db) +G R (db) Ω th (dbm) M shad (db) L I (db) +G HO (db). 8

9 Hard vs. Soft Handoff Consider a cluster of 7 cells; the target cell is in the center and surrounded by 6 adjacent cells. Although the MS is located in the center cell, it is possible that the MS could be connected to any one of the 7 BSs. We wish to the calculate the area averaged noise outage probability for the target cell, assuming that the MS location is uniform distributed over the target cell area. Assume that the links to the serving BS and the six neighboring BSs experience correlated log-normal shadowing. To generate the required shadow gains, we express the shadow gain at BS i as where ǫ i = aζ +bζ i, a 2 +b 2 = 1, and ζ and ζ i are independent Gaussian random variables with zero mean and variance σ 2 Ω. It follows that the shadow gains (in decibel units) have the correlation E[ǫ i ǫ j ] = a 2 σ 2 Ω = ρσ 2 Ω where ρ = a 2 is the correlation coefficient. Here we assume that ρ =

10 Hard vs. Soft Handoff Soft handoff algorithm: the BS that provides the largest instantaneous received signal strength is selected as the serving BS. If any BS has an associated received signal power that is above the receiver sensitivity, Ω th (dbm), then the link quality is acceptable; otherwise an outage will occur. Hard handoff algorithm: The received signal power from the serving BS is equal to Ω p,0 (dbm). If this value exceeds the receiver sensitivity, Ω th (dbm), then the link quality is acceptable. Otherwise, the six surrounding BSs are evaluated for handoff candidacy by using a mobile assisted handoff algorithm. A BS that qualifies as a handoff candidate must have Ω p,k (dbm) Ω p,0 (dbm) H (db), where H (db)) is the handoff hysteresis. We then check those BSs passing the hysteresis test. If the received signal power for any of these BSs is above the receiver sensitivity, Ω th (dbm), then link quality is acceptable; otherwise an outage occurs. 10

11 Coverage (%) Soft Handoff Hard handoff Single Cell Shadow Margin (db) Typical handoff gain for hard and soft handoffs. In this plot shadow margin is defined as M shad G HO, where M shad is the shadow margin required for a single cell. We also plot the area averaged outage rather than the edge outage. 11

12 Cellular Radio Coverage Radio coverage refers to the number of base stations or cell sites that are required to cover or provide service to a given area with an acceptable grade of service. The number of cell sites required to cover a given area is determined by the maximum allowable path loss and the path loss exponent. To compare the coverage of different cellular systems, we first determine the maximum allowable path loss, L max (db), for the different systems by using a common quality criterion. Then L max (db) = C +10βlog 10 d max where d max is the radio path length that corresponds to the maximum allowable path loss and C is a constant. The quantity d max is equal to the radius of the cell. To provide good coverage it is desirable that d max be as large as possible. 12

13 Comparing Coverage Suppose that System 1 has L max (db) = L 1 and System 2 has L max (db) = L 2, with corresponding radio path lengths of d 1 and d 2, respectively. The difference in the maximum allowable path loss is related to the cell radii by or looking at things another way L 1 L 2 = 10β(log 10 d 1 log 10 d 2 ) ( ) d 1 = 10β log 10 d 2 d 1 d 2 = 10 (L 1 L 2 )/(10β) Since the area of a cell is equal to A = πd 2 (assuming a circular cell) the ratio of the cell areas is and, hence, A 1 A 2 = d2 1 d 2 2 = ( ) 2 d1 d 2 A 1 A 2 = 10 2(L 1 L 2 )/(10β). 13

14 Suppose that A tot is the total geographical area to be covered. Then the ratio of the required number of cell sites for Systems 1 and 2 is N 1 N 2 = A tot/a 1 A tot /A 2 = A 2 A 1 = 10 2(L 1 L 2 )/(10β) Example: Suppose that β = 3.5 and L 1 L 2 = 2 db. N 2 /N 1 = Conclusion: System 2 requires 30% more base stations to cover the same geographical area for only a 2 db difference in link budget. Note that the required interference margin and realized handoff gain have a large impact. Coverage comparisons should be done under conditions of equal traffic loading. 14

15 Spectral Efficiency Spectral efficiency can be expressed in terms of the following parameters: G c = offered traffic per channel (Erlangs/channel) N slot = number of channels per RF carrier N c = number of RF carriers per cell area (carriers/m 2 ) W sys = total system bandwidth (Hz) A = area per cell (m 2 ). One Erlang is the traffic intensity in a channel that is continuously occupied, so that a channel occupied for x% of the time carriers x/100 Erlangs. Adjustment of this parameter controls the system loading and it is important to compare systems at the same traffic load level. For an N-cell reuse cluster, we can define the spectral efficiency as follows: η S = N cnn slot G c W sys A Erlangs/m 2 /Hz. 1

16 Spectral Efficiency (con td) Recognizing that the bandwidth per channel, W c, is equal to W sys /(NN c N slot ), the spectral efficiency can be written as the product of three efficiencies, viz., where η S = 1 W c 1 A G c = η B η C η T, η B = bandwidth efficiency η C = spatial efficiency η T = trunking efficiency Unfortunately, these efficiencies are not at all independent so the optimization 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 N c N slot = W sys W c N where, again, W c is the bandwidth per channel and N slot is the number of traffic channels multiplexed on each RF carrier. 2

17 Trunking Efficiency The cell Erlang capacity equal to the traffic carrying capacity of a cell (in Erlangs) for a specified call blocking probability. The Erlang capacity can be calculated using the famous Erlang-B formula B(ρ,m) = ρ m m! m k=0 where B(ρ, m) is the call blocking probability, m is the total number of channels in the trunk and ρ = λµ is the total offered traffic in Erlangs (λ is the call arrival rate and µ is the mean call duration). The cell Erlang capacity accounts for the trunking efficiency, a phenomenon where larger groups of channels are able to carry more traffic per channel for a given blocking probability than smaller groups of channels. ρ k k! 3

18 B(ρ,m) 10-2 m = 1 m = 2 m = 5 m = G c (Erlangs) Blocking probability B(ρ,m) against offered traffic per channel G c = ρ/m. 4

19 F F 3 F 1 F 2 omni 3-sector F = F 1 + F 2 + F 3 Trunkpool schemes. 5

20 10 0 Blocking Probability c-sec 7c-omni 4c-sec 4c-omni Channel Usage Efficiency Channel usage efficiency η C = ρ(1 B(ρ,m)/m for different trunkpool schemes; 416 channels. 6

21 GSM Cell Capacity A 3/9 (3-cell/9-sector) reuse pattern is achievable for most GSM systems 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 onto a single radio frequency carrier, and the carriers are spaced 200 khz apart. Therefore, the bandwidth per channel is roughly 25 khz, which was common in first generation European analog mobile phone systems. In a nominal bandwidth of 1.25 MHz (uplink or downlink) there are 1250/25 = 6.25 carriers spaced 200 khz apart. Hence, there are 6.25/ carriers per sector or 6.25/3 = carriers/cell. Each carrier commonly carries half-rate traffic, such that there are 16 channels/carrier. Hence, the 3/9 reuse system has a sector capacity of channels/sector or a cell capacity of channels/cell in 1.25 MHz. 7

22 IS-95 Cell Capacity Suppose there are N users in a cell; one desired user and N 1 interfering users. For the time being, ignore the interference from surrounding cells. Consider the reverse link, and assume perfectly power controlled MS transmissions that arrive chip and phase asynchronous at the BS receiver. Treating the co-channel signals as a Gaussian impairment, the effective carrier-to-noise ratio is (the factor of 3 accounts for chip and phase asynchronous signals) Γ = 3 N 1, and the effective received bit energy-to-noise ratio is where G = B w /R b. E b N o = Γ B w R b = 3G N 1 3G N, For a required E b /N o, (E b /N o ) req, the cell capacity is N 3G (E b /N o ) req. 8

23 IS-95 Cell Capacity (cont d) Suppose that 1.25MHz of spectrum is available and the source coder operates at R b = 4kbps. Then G = 1250/4 = If (E b /N o ) req = 6dB (a typical IS-95 value), then the cell capacity is roughly N = /4 234 channels per cell. This is roughly 7 times the cell capacity of GSM. This rudimentary analysis did not include out-of-cell interference which is typically 50 to 60% of the in-cell interference. This will result 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 improving receiver sensitivity. For example, if (E b /N o ) req can be reduced by 1dB, then the cell capacity N increases by a factor of CDMA systems are known to be sensitive to power control errors. An rms power control error of 2 db will reduce the capacity by roughly a factor of 2. 9

24 Some Elements for High Capacity Our emphasis is on physical wireless communications At the physical layer, some of the key elements to high capacity frequency reuse systems are adaptive power and bandwidth efficient modulation multipath-fading mitigation/exploitation (transmit and receiver diversity, error control coding, multiuser diversity) techniques to mitigation time delay spread (OFDM, equalizers, RAKE receivers) co-channel interference cancellation (single and multi-antenna interference cancellation) coding modulation (Turbo trellis coding, bit interleaved coded modulation) co-channel interference control (handoffs, power control, spacedivision multiple access) 10

25 Multipath-Fading Mechanism local scatterers mobile subscriber base station A typical macrocellular mobile radio environment. 11

26 Multipath-Fading Mechanism local scatterers local scatterers mobile station mobile station Typical mobile-to-mobile radio propagation environment. 12

27 local mean Ω (db) area mean µ (db) envelope fading Path loss, shadowing, envelope fading. 13

28 Doppler Shift y n th incoming wave mobile station v θ n x A typical wave component incident on a mobile station (MS). The Doppler shift is f D,n = f m cosθ n, where f m = v/λ c (λ c is the carrier wavelength, v is the mobile station velocity). 14

29 Multipath Propagation Consider the transmission of the band-pass signal s(t) = Re { s(t)e j2πf ct } At the receiver antenna, the nth plane wave arrives at angle θ n and experiences Doppler shift f D,n = f m cosθ n and propagation delay τ n. If there are N propagation paths, the received bandpass signal is [ N ] r(t) = Re C n e jφ n j2πcτ n /λ c +j2π(f c +f D,n )t s(t τ n ), n=1 where C n, φ n, f D,n and τ n are the amplitude, phase, Doppler shift and time delay, respectively, associated with the nth propagation path, and c is the speed of light. The delay τ n = d n /c is the propagation delay associated with the nth propagation path, where d n is the length of the path. The path lengths, d n, will depend on the physical scattering geometry which we have not specified at this point. 15

30 Multipath Propagation The received bandpass signal r(t) has the form r(t) = Re [ r(t)e j2πf ct ] where the received complex envelope is and r(t) = N C n e jφ n(t) s(t τ n ) n=1 φ n (t) = φ n 2πcτ n /λ c +2πf D,n t is the time-variant phase associated with the nth path. The phase φ n is randomly introduced by the nth scatterer and can be assumed to be uniformly distributed on [ π, π). 16

31 Flat Fading -time domain The channel can be modeled by a linear time-variant filter having the complex low-pass impulse response g(t,τ) = N C n e jφn(t) δ(τ τ n ) n=1 If the differential path delays τ i τ j are small compared to the duration of a modulated symbol, T, then the τ n are all approximately equal to their average value ˆτ. The channel impulse response has the form g(t,τ) = g(t)δ(τ ˆτ), g(t) = The received complex envelope is N C n e jφ n(t) n=1. r(t) = g(t) s(t ˆτ) which experiences fading due to the time-varying complex channel gain g(t). 17

32 Flat Fading - frequency domain In the frequency domain, the received complex envelope is R(f) = G(f) S(f)e j2πfˆτ Since the channel changes with time, G(f) has a finite non-zero width in the frequency domain. Due to the convolution operation, the output spectrum R(f) will be larger than the input spectrum S(f). This broadening of the transmitted signal spectrum is caused by the channel time variations and is called frequency spreading. 18

33 Channel Transfer Function - Flat Fading The corresponding time-variant channel transfer function is obtained by taking the Fourier transform of the time-variant channel impulse response g(t,τ) with respect to the delay variable τ, i.e., T(t,f) = g(t)e j2πfˆτ. Since the magnitude response is T(t,f) = g(t), all frequency components in the received signal are subject to the same time-variant amplitude gain g(t), while the phase response is a linear function of frequency with slope 2πˆτ. The received signal is said to exhibit flat fading, because the magnitude of the time-variant channel transfer function is constant (or flat) with respect to frequency variable f. 19