Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks

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1 I.J. Wireless an Microwave Technologies, 04,, 0-49 Publishe Online January 04 in MECS( OI: 0.585/ijwmt Available online at Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks Ahme M. Alaa a, Hazim Tawfik b a,b esign Laboratory for Electronics an Communication Systems (LECS), Faculty of Engineering, Cairo University, Gizah, Egypt Abstract anom Frequency Hopping (FH) is a key feature of GSM networks that allows for capacity enhancement. The increase co-channel interference experience in networks with tight frequency reuse schemes can be mitigate by aopting frequency hopping. Frequency hopping iversifies the interference signals over sparse transmitte bursts. This effect is calle Interference iversity. Interference iversity allows the Forwar Error Correcting coes (FEC) to easily correct the corrupte bits. Thus, frequency hopping allows the network operator to use a tighter frequency reuse scheme without exhibiting higher levels of co-channel interference. iscontinuous Transmission (TX) is another interference mitigation metho that utilizes the user s silence frames to reuce the transmitte power, while Power Control (PC) links the transmitte hanset power with its relative istance from the Base Station (BTS). In this work, we stuy the impact of ranom FH, TX an PC on the Spectral Capacity of GSM cellular networks by means of combine link level an system level simulation. It is shown that a spectral capacity gain is obtaine in a 3/9 reuse scheme that eploys PC, TX an FH compare to a conventional 4/ reuse scheme. Inex Terms: anom Frequency Hopping (FH), Power Control (PC), iscontinuous Transmission (TX), Interference iversity, Frequency iversity, Spectral Capacity. 04 Publishe by MECS Publisher. Selection an/or peer review uner responsibility of the esearch Association of Moern Eucation an Computer Science. Introuction The increasing number of subscribers imposes capacity constraints on network operators ue to the limite spectrum assigne to each operator. Techniques for capacity enhancement are aopte by operators to meet the increasing capacity eman. Increasing the system capacity can be achieve by aopting a lower reuse scheme. The implication of ecreasing the reuse figure is increasing co-channel interference an thus, the quality egraes. Techniques for increasing the interference immunity will consequently increase the capacity as we can aopt a lower reuse figure without sacrificing the Quality of Service (QoS). Those techniques inclue: * Corresponing author. Tel.: ; fax: aress: zhuzhipan888@63.com

2 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks iscontinuous Transmission (TX), Power Control (PC) an Frequency Hopping (FH). Frequency hopping is a process of changing the F carrier frequency in a prescribe rate. There are two classes of frequency hopping accoring to the hopping rate: Slow FH an Fast FH. Slow frequency hopping refers to changing the F carrier for every new burst, while fast FH refers to changing the F carrier in a rate higher than the moulation rate. Frequency hopping is also classifie base on frequency selection approach into: anom FH an Cyclic FH. The cyclic hopping follows a pre-efine list of frequencies in a regular orer, while ranom hopping transceivers selects a frequency ranomly out of a preefine list. FH transceivers are also classifie base on their implementation: Baseban FH (BH) requires a eicate transceiver for each F carrier within the hopping sequence, while Synthesizer FH (SH) relies on tuning the transceiver on a specific carrier frequency (this requires wieban F equipment). In this work, we consier slow frequency hopping with ranom, baseban hopping frequency generation for GSM transmission. The bursts within a TMA (Time ivision Multiple Access) frame are subjecte to ifferent values of cochannel interference because hopping causes ifferent signals to interfere with carrier signal at ifferent times. This effect is calle interference iversity. On a system level, the effective interference between users is reuce; this effect is calle interference averaging. In aition to the Interference iversity effect, frequency hopping results in a Frequency iversity effect; the frequency selective faing pattern is change ue to the change of the F carrier. Hence, consecutive bursts are less probable to be subjecte to faing ips. The QoS criterion for systems with ranom frequency hopping is base on threshols of Bit Error ate (BE) or Frame Error ate (FE). This means that we nee to map the Carrier-to-Interference ratio (C/I) values on ifferent bursts to corresponing FEs/BEs. To accomplish this, we have to integrate a link level moel with a system moel. The C/I values obtaine from the system moel are fe into the link moel to obtain error rate estimates. The goal of this work is to stuy how the incorporate interference mitigation techniques can allow the network operator to aopt a tighter frequency reuse scheme, increasing the network s overall capacity. The paper is ivie as follows. Section II presents the GSM system level moel, the simulation methoology an the C/I statistical results for the system with Power Control (PC) an iscontinuous Transmission (TX) features enable. Section III iscusses frequency hopping an the concepts behin it, an presents the link level moel use for mapping C/I ratios to FE/BE base on the GSM physical layer. Section IV shows the aopte propagation an channel moels use in the simulation. Finally, simulation results for FE an BE CF are presente an the spectral capacity gain ue to interference iversity is shown for a simulation environment that accounts for all practical consierations.. System Moel The basic system level simulation consiers the first tier of co-channel interferers only. Thus, for all reuse schemes, the number of interferers is limite to 6. Figure shows the home cell an the six reuse cells representing the first tier of interferers. The istance enotes the cell raius, while the istance enotes the reuse istance. The Carrier-to-interference (C/I) ratio is the performance metric that is use to express the level of cochannel interference. The more the C/I ratio is, the less co-channel interference we have an there is a room for applying a tighter reuse figure without loss of quality. The C/I value shoul not be less than a certain threshol for more than 0% of the service area. This percentage is calle the outage probability. The C/I cumulative ensity function is use to calculate the C/I value that is satisfie at 0% of the service area. This value will inicate the interference-wise performance of the network. By aopting ifferent interference mitigation techniques (i.e. PC, FH an TX), we expect the C/I ratio that occurs at 0% of the service area will increase. This work is part of the research activity for ABUPT project (A BTS for ural Unerevelope Population Tier) sponsore by the NTA (National Telecomm egulatory Authority) esign Laboratory for Electronics an Communications Systems (LECS) Cairo University 03

3 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks Fig the home cell an reuse cells of the first interferers tier Base on a Monte Carlo simulation process, we aim at obtaining the probability an cumulative ensity functions (PF an CF) of the Carrier-to-interference ratio. This is achieve by generating ranom locations for the Mobile Station (MS) in the home cell base on a uniform PF, an the same for the six first tier interferers. Assuming a Monte Carlo process with sufficient iterations, the istance between the MS an the Base station (BTS) for the ith iteration is ri, the istance between the kth interferer an the BTS of the home cell ik an the Propagation exponent γ, the C/I ratio in the ith iteration can be calculate as []: C I i r i 6 ik k () In the absence of faing an setting γ = 4, the C/I value satisfie at 0% outage is B. We expect this value to be booste by aing Power control (PC) an iscontinuous Transmission (TX) features. If the gain obtaine from PC, TX an FH excees the loss of C/I ue to ecreasing the reuse figure, then we can aopt a lower reuse figure with no loss of transmission quality while maintaining the QoS requirements. Figure shows the PF of the C/I ratio in a network with a reuse figure N = 7 an path loss exponent γ = 4. Figure 3 shows the CF of C/I showing that a B carrier to interference ratio is encountere at 0% of the service area. Fig the Carrier-to-Interference ratio probability ensity function with N = 7 an γ = 4

4 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 3 Fig 3 the Carrier-to-Interference ratio cumulative ensity function with N = 7 an γ = 4.. Enabling Power Control Feature Transmit power control algorithms are use to alter the transmit power accoring to the istance between the Mobile Station (MS) an the Base Station (BTS). If the MS is quite near to the BTS, it can transmit the signal with a lower power level. This will allow reucing the interfering power, an the C/I value with 0% outage is expecte to increase significantly. The aopte power control algorithm ivies the cell into seven concentric rings. When the MS is locate at the farthest ring to the BTS, the transmit power is maximum (no attenuation is applie to the transmit signal). The transition between every two rings results in a power attenuation of B. When enabling the power control feature in the Monte Carlo simulation process, the cumulative ensity function of the C/I ratio is shifte to the right an a C/I gain is obtaine. The 0% outage probability is satisfie at 5 B C/I ratio instea of B in the case when no power control was applie. This means that power control offers 3 B gain to the C/I quality metric an we have a room for aopting a tighter reuse scheme with the user experiencing no quality loss. This power control algorithm is epicte mathematically by expressing the attenuation of the transmitte power as a function of the istance between the MS an the BTS. Let the istance between the MS an the BTS be, the cell raius an the power attenuation per ring is M B. The attenuation σ is: 7 M 7 roun () Y-loc X-loc Fig 4 the concentric rings within a hexagonal cell, every new ring results in B attenuation in the transmitte power

5 4 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks.. Enabling iscontinuous Transmission (TX) Feature iscontinuous Transmission (TX) is a capacity enhancement technique that exploits the silence speech frames in orer to switch off or reuce the transmitte power with a preefine attenuation factor. This feature results in power saving in the MS battery, an either a reuction in the overall interference or an increase capacity by lowering the reuse factor of the network. The percentage of time where the user is talking is calle the Voice Activity Factor. From Monte Carlo simulations, it was foun that for a 40% activity factor, a gain of 3.4 B is obtaine in the C/I ratio. A 0% outage is satisfie at 5.4 B Carrier-to-Interference ratio instea of B. Figure 5 shows the effect of ifferent percentages of the voice activity on the Carrier-to-Interference ratio statistics. Fig 5 the CF (Cumulative ensity Function) for VAF of 30%, 40% an 50% compare to the case of no TX.3. Analytical Framework for exact outage probability calculation The results of Monte Carlo simulations can be verifie by comparing the theoretical worst case Carrier-to- Interference ratio with the C/I ratio with minimum CF value obtaine from simulations. In this section, we verify the results of the Monte Carlo simulation results an propose an analytical framework for calculating the outage probability of the C/I ratio. Accoring to [], the worst case interferers configuration is the one shown in figure 6. By efining the cochannel reuse ratio Q = /, the worst case C/I ratio can be given as: C I ( ) ( ) (Q ) (Q ) Q (3) For a reuse figure N = 7, the worst case C/I = 7.7 B. The minimum value C/I obtaine from the simulations is 7.04 B.

6 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 5 In orer to obtain the probability ensity function of the C/I ratio we start by consiering the istance between the home MS an the BTS as a ranom variable r an the istance between the ith interferer an the home BTS as i. The C/I ratio is also a ranom variable an is given by the ratio istribution of two ranom variables: C r I I (4) Fig 6 the network configuration for worst case interference scenario The interference power is given by: I 6 - i i (5) The ranom variable r is assume to be sample from a uniform istribution. To allow mathematical tractability, the PF of the variable is approximate as a uniform istribution with maximum an minimum istances from the home BTS as + an - respectively. The variable γ is a constant representing the propagation exponent. The PFs of r an are: pr(r) =, 0 r p() =, (-) (+) (6)

7 6 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks Fig 7 The PF of the ranom variables r an The PF of the ranom variable r-γ is obtaine by applying a transformation process. For a ranom variable x, an a one-to-one transformation y = h(x) is applie to x, where each value of x maps to a unique value of y. To obtain the PF of y, we have to get the function x = u(y) an calculate the Jacobean function: J = u (y). The PF of y is: py(y) = px[u(y)] J (7) By applying the transformation, we want to get the PF of the ranom variable r -γ: r r u[r] r r ) ( ' ] [ r r u J r r r p r, ) ( ) ( (8) Applying the same steps on the ranom variable : ) ( ) (, ) ( ) ( p (9) The interference term is given in equation (5), this term is the summation of six inepenent ranom variables. The PF of the summation of two inepenent ranom variables is the convolution of their iniviual PFs. For six interferers represente by six i.i. (inepenent ientical istributions), the PF of the interference is given by: ) ( ) ( ) ( ) ( ) ( ) ( ) ( i p p p p p p p i (0) r

8 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 7 where enotes convolution. To simplify the problem an avoi the complicate convolution process, we apply Fourier transform to iniviual PFs an multiply them then apply inverse Fourier transform. Let the operators Ƒ {.} an Ƒ - {.} enote the Fourier an inverse Fourier transform. 6 - i ) F F p( ) i p( 6 An equivalent solution can be obtaine by manipulating the characteristic functions of the ranom variables. A characteristic function is use to completely escribe the PF. Manipulation of ranom variables through their characteristic functions simplifies the problem. For a ranom variable x, the characteristic function is: () jxt e x ( t) E p( x) e jxt x () While obtaining the PF from a characteristic function resembles an inverse Fourier transform process: p x ( x) x ( t) e jxt x (3) Thus, the probability ensity function an the characteristic function are the Fourier transform pairs of each other. An important property of the characteristic function is that the aition of two inepenent ranom variables will have a characteristic function equal to the multiplication of the iniviual characteristic functions. This can be simply conclue by calculating the mean value of the complex exponential with an exponent x+y: E[e j(x+y)t] = E[ejxt ejyt] = E[ejxt] E[ejyt] (4) Hence, the characteristic function of two ae inepenent ranom variables is: x y ( t) ( t) ( t) x y (5) by extening this relation to a summation of n i.i. ranom variables: Z n x i i ( t) ( t) z n i xi (6) Thus, by calculating the characteristic function of a single interferer s ranom variable

9 8 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks ( ) ( ) e jt (7) Finally, the PF of the overall interference can be calculate as: 6 p( i ) ( t) i 6 e jt (8) After calculating the probability ensity function of both the signal an the six interferers, we have to obtain the probability ensity function of their ratio. The problem becomes extremely teious an one woul encounter integrals that have no close form solution. Hence, approximate formulas for the outage probability an C/I ratio statistics are presente in the next section..4. Approximate Analytical Expressions for Carrier-to-Interference ratio PF in Single an Multiple Interferer Networks In this section, analytical expressions for the C/I ratio probability ensity function is evelope in orer to verify the results obtaine from simulations. By consiering the basic problem of a single co-cell interferer problem: C I r (9) Base on the probability ensity functions of the ranom variables r an, the ratio istribution r / must be evaluate first in orer to get the PF of the C/I ratio. Assume a new ranom variable u that represents the ratio u = r /. The joint PF of the two ranom variables r an assuming that the two variables are inepenent is given by p(r, ) = p(r) p() an is plotte in figure 9. euse Cell Home Cell Fig 8 hexagonal cell configuration with single interferer

10 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 9 p(r, ) 0 r - + Fig 9 the joint PF of the istance between the home user an the home cell, an the istance between the interferer user an the home cell The PF of the ratio u can be obtaine by ifferentiating its CF. For every real number u, the CF of the real value ranom variable r/ is given by P(r/ u). This is equivalent to evaluating P(r u) which means that we nee to multiply the area where r is less than the values boune by the straight line r = u by the uniform PF amplitue of /. In orer to obtain the CF of u, we have to split the solution into two regions on the u axis. The two regions of the u variable are mappe to two separate integrals on the r- plane as shown in figure. The first region is when the slope u of the straight line r = u is so large that the straight line crosses the upper borer of the r- plane (the borer ientifie by the line = + ), let this region be enote as region a. The secon region is boune by the straight line that has a small slope causing the line to cross the vertical borer r =. This region will be enote as region b. Hence, the CF an PF of the ranom variable u will have a piecewise efinition. egion (a) is obtaine when the straight line crosses the horizontal borer of the r- plane. This is satisfie when u(+) is less than. egion (b) is obtaine if u(+) excees an u(-) is less than. For region (a) For 0 u < P(r u) = r = [u(-) + u. ] = [u - u + u] u = (0)

11 30 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks egion (a) egion (b) u + + /u - - p(r, ) u( - ) u( + ) r p(r, ) u( - ) r Fig 0 the regions of solution on the r- plane an its mapping to the u axis For region (b) For u = -. P(r u). [ u ( )] [ u ( )] = - u [ u (-)]. = - u [ u + u + u u + u].

12 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 3 = - 4 u [ u + u + u u + u] = + - u 4 + u [ ] () Thus, the piecewise efinition of the cumulative ensity function is: P(u) = u u u u u,0, () The probability ensity function is the erivative of the cumulative function p(u) = P(u), thus, the ratio istribution is given by: p(u) = u u u 0,, (3) ecall that the quality reuse ratio Q is given by Q =, thus, the probability ensity function can be reformulate as: p(u) = 0,, 4 Q u Q Q u Q Q u (4) Note that the expression presente in (4) satisfies all the properties of a PF: the PF integrates to unity over the u omain = an continuity of the function is maintaine at, note that the PF vanishes at.

13 3 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks P (u) Q 0 u Fig the ratio istribution as a function of the quality reuse ratio By evaluating the mean an the variance of this PF, we obtain: μ = ln 4 Q Q (5) σ = /3 Q ln Q 6 Q (6) By applying a non-linear transformation for the ranom variable raise to the path loss exponent; Z = ( )-γ an thus, = Z /γ. The Jacobean J =, the PF of the transforme variable Z is given by p(z) = p[ u(z) ] J, thus, the PF of Z is: Z 4 p(z) = Q Q Z Z,, ( Q ) ( Q ) Z Z ( Q ) (7) The result obtaine in equation (7) represents the probability ensity function of the Carrier-to-Interference ratio for a single interferer network. The lower boun on the ratio Z is equal to (Q - )γ represents the worst case interference when the home user is at the home cell borer (at a istance from the home base station) an the interferer is at the nearest point to the home BTS (at a istance from the BTS). In this case the ratio C/I = (-γ / ( - )-γ) = (( - ) γ / ) γ = (/ - )γ = (Q - )γ. On the other han, the maximum possible ratio is attaine when the home cell is coinciing with the home base station leaing to an infinite C/I ratio. Let the variable Z = CI enote the Carrier-to-Interference ratio, the outage probability is efine as: P(CI ɛ) = CI (8)

14 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 33 For ɛ (Q + ) γ, the outage probability is: Pout = CI = [ + - (Q-)] (9) Notice that the outage probability for a certain threshol ɛ increases as the quality reuse ratio Q increases. The outage probability for ɛ > (Q + ) γ Pout = CI + CI = + (Q+) + (Q-) (Q+)- = Q [ - ] + [(Q+) + - (Q-)] (30) Thus, the piecewise efinition of the outage probability is given by: Pout = The expression obtaine in (3) is vali only for the single interferer scenario. For the case of six inepenent interferers, we can apply the Union Boun principle (Boole s Inequality), which states that for a set of events Ai: (3) P ( ) (3) Thus, for six inepenent an ientical interferers, the outage probability is approximate as: Pout (33)

15 34 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks. Approximation of the TX an PC C/I gain As iscusse before, the TX an PC features in GSM help to reuce the interference power, allowing the network operator to reuce the reuse factor without losing quality an thus increasing the network s capacity. In this section, we aim at verifying the values of the C/I gains obtaine from TX an PC from the Monte Carlo simulation by eriving approximate formulas for them. TX is use to lower the transmitte power uring the user s silence frames. The percentage of non-silent speech frames (with uration T) is known as the VAF (Voice Activity Factor) η. Assume a iscrete binary anom Process σ (t=nt) that escribes whether the current TMA frame carries speech or not. This process will follow the Probability Mass Function (PMF): F (σ) = (34) where M is the TX attenuation factor (M < ) an σ is a ranom variable escribing the attenuation in a certain speech/silence frame. The home MS an the six interferers form the ensemble of this ranom process. The ranom process is a function of time an emits either or M for every frame transmitte by user equipment. The temporal mean of this ranom process is intuitively given by: < σ (t) > = + (- )M (35) Equation (35) escribes the time mean of the ranom process shown in figure. The attenuation is in a fraction η of the frames an the attenuation is M in (-η) of the frames. Thus, the average attenuation value is (-η) M + η. Because we calculate the C/I ratio per frame, an assuming that the ranom process is ergoic, the ensemble mean at time t is equal to the temporal mean. In every time instant, η interferers transmit with full power an (- η) others have an attenuation of M. Thus, the interference power is average to be (-η) M + η per frame, the TX gain is then equal to the time an ensemble averages: TX gain = < σ (t) >B = B = - 0 log0 ( + (- )M) (36) For an attenuation of M = 0 B an a voice activity factor of 40 %, the TX gain is 3.37 B which matches the results obtaine from the Monte Carlo simulation. By enabling the Power Control (PC) feature, the transmitte signal from a MS epens on the location of the user relative to its associate BTS. The hexagonal cell is ivie into seven concentric rings with the farthest ring transmitting with full power, an each transition between two rings cause a B attenuation of the transmitte power. The PMF of the PC attenuation is shown in figure 3. The C/I ratio can be given as: = (37)

16 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 35 σ(t, ζ ) T T 3T 4T 5T 6T 7T 8T 9T 0T σ(t, ζ ) t T T 3T 4T 5T 6T 7T 8T 9T 0T t σ(t, ζ 6 ) T T 3T 4T 5T 6T 7T 8T 9T 0T t Fig the TX attenuation ensemble for the six interferers /7 F(P i ) P P P 3 P 4 P 5 P 6 P 7 P i Fig 3 the PMF of the Power Control attenuation The analytical expression for the outage probability with PC is very ifficult to obtain as we have a new ranom variable p plugge into the equation, an extra variable transformations must be applie. However, an approximate boun for the PC gain can be obtaine. The PC results in interference averaging; the average PC attenuation is: Pavg = (38) The best scenario for the C/I is when no attenuation ue to PC (the MS is at farthest point to the BTS): PC gain 0 log0 ( ) (39)

17 36 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks For the case of B attenuation step between each two concentric rings, the approximate gain boun is 4.4 B, while the gain attaine is 3 B. 3. Frequency Hopping Increasing the capacity of the cellular system is achieve by reucing the reuse figure. However, a lower reuse figure will cause a high level of cochannel interference. The reuction of reuse factor must be associate with interference mitigation techniques to compensate the expecte loss of quality ue to the increase cochannel interference. In section II, we presente PC an TX techniques to improve the outage C/I ratio. Another technique for interference mitigation in GSM is Frequency Hopping. Frequency Hopping (FH) is a process of changing the F carrier frequency in a prescribe rate. GSM aopts slow FH transmission, where the F carrier is change for every new burst. Besies, the F carrier selection is one on a ranom basis rather than cyclic one. In contrast to Cyclic FH, ranom FH offers worse frequency utilization an better interference iversity. Assume that we have a hopping sequence with 8 F carriers, in a set of 8 frames, ranom hopping woul result in the selection of 5 frequencies only, unlike cyclic hopping where all the 8 frequencies woul be use []. Thus, frequency iversity in cyclic FH is better than ranom hopping. However, in cyclic FH, the user an the cochannel interferers may keep transmitting at the same F carrier for several consecutive bursts. This is not possible in ranom FH, where interference averaging results from interference iversity. While cyclic FH network has to be esigne base on the worst case interference, ranom FH is esigne base on the average interference. 3.. Generation of the Frequency Hopping Sequence In this section, the FH sequence generation algorithm is presente. The algorithm complies with the GSM specifications [3]. The following parameters are use to etermine the hopping sequence: MAI (Mobile Allocation Inex): The MAI is obtaine through a sequence generation algorithm. It is use to inex an MA table that maps it to an F channel. MA (Mobile Allocation): The MA is the look up table giving the relation between ifferent MAI (inex) numbers an the corresponing F channel numbers (AFCN). MAIO (MAI offset): An offset in the MAI use to generate a shifte hopping sequence; this is specific for each transceiver an offers uncorrelate hopping sequence for each MS within the same site to avoi intra-cell interference. HSN (Hopping Sequence Number): A number that specifies the hopping sequence use. This number varies from cell to cell but is constant for each cell. Cyclic hopping occurs when HSN = 0. T, T an T3: are internal timers to create the hopping sequence perioicity. The hopping sequence has a perio of Frame Number (FN): A number that is incremente per TMA frame an triggers the T, T an T3 timers, where: T = FN mo 64 T = FN mo 6 T3 = FN mo 5 The flow chart in figure 4 epicts the sequence generation algorithm. The frequency utilization in cyclic hopping an ranom hopping are compare in figure 5. In cyclic hopping, a sequence of N possible F carriers are utilize every N bursts. While in ranom FH, utilization ecreases an thus, frequency iversity is better in cyclic hopping (HSN = 0).

18 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 37 MA MAIO T T T3 Yes HSN = 0? No MAI = (T+MAIO) mo N MAI = T + N Table [(HSN XO T) + T3] M = M mo NB T = T3 mo NB No M < N? Yes S = (M + T ) mo N S = M MAI = (MAIO+S) mo N Fig 4 the flow chart for hopping sequence generation. Courtesy of [3] 3.. Effect of ranom FH on the Carrier-to-Interference ratio As iscusse before, ranom FH introuces the interference iversity effect, which results in interference averaging. The C/I ratio is booste ue to the averaging of the interferer power over time. The C/I ratio statistics (PF an CF) are obtaine via Monte Carlo simulation for ranom FH. Because the multipath effects an frequency selective faing were not inclue yet, the frequency iversity has no impact on the results obtaine from this simulation.

19 38 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks Fig 5 comparison of the frequency utilization in cyclic an ranom frequency hopping schemes The Monte Carlo simulations are carrie out with the following settings: every co-cell has a ifferent HSN number to generate a ifferent hopping sequence, the N users within each co-cell are active with probability of LSB users, where N is the number of hopping frequencies an LSB is the system loa (the percentage of utilize channels). Within each cell, all users have the same hopping sequence but with a frequency offset, realize by varying their MAIO number. The MS instances generate for Monte Carlo simulation are kept alive for a specific perio of time (statistically sufficient to emonstrate the interference averaging effect) to measure the average C/I ratio. Note that the collision between the home MS an the interferers is function of the number of hopping frequencies an the system loa. As the number of available hopping frequencies increase, the probability of collision ecreases. The effect of system loa is ecreasing the probability of collision as the loa ecreases. Hence, the maximum interference iversity gain is expecte in networks with fractional loa an tight frequency reuse [4][5]. Simulations for 8 hopping frequencies an various system loas are plotte in figure 6. As shown in the figure, ecreasing the system loa shifts the mean C/I curve to the right, which means that we obtain C/I performance gain for systems with low loa. A 00% loa means that there will be no interference iversity an we retain the C/I CF of the case when no hopping occurs Impact of FH on the Quality of Service (QoS) In systems with fixe or cyclic hopping, the Bit Error ate an Frame Erasure ate (BE, FE) can be mappe uniquely to the mean Carrier-to-Interference ratio observe on the raio link [][4].This one-to-one mapping is also inepenent of the system loa. For these reasons, we approve the C/I value satisfying a 0% outage probability as a irect measure of the perceive QoS. On the other han, in ranom FH systems, the C/I ratio is a stochastic process where interference iversity oesn t only reuce the mean C/I ratio, but also changes the istribution of the interference; ifferent bursts perceive ifferent C/I ratios. This istribution woul efinitely have an impact on the FEC (Forwar Error Correction) performance an other Physical layer functions of GSM transceivers. Base on this, the mapping between mean C/I an the BE/FE is not unique an the same mean C/I may result in ifferent Error rates ue to the varying interference istribution. Thus, QoS can t be irectly relate to the mean C/I, but we have to estimate the FE resulting from mean C/I an interference istribution, an then the QoS can be relate to the obtaine FE statistics.

20 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 39 Fig 6 C/I performance gains are obtaine for system loas of 5%, 50% an 00%. C/I CF C/I CF.0 C/I mean.0 C/I mean (a) FE Fig 7 (a) the mapping of mean C/I to FE is unique in non-hopping or cyclic hopping system (b) mapping of C/I an FE epens on the interference istribution In orer to evaluate the FE an BE, a link level moel has to be evelope. This link level moel inclues the bit interleavers, Viterbi equalizer, channel coing an moulation. The usage of an actual physical layer moel, will introuce extreme complexity to the Monte Carlo simulation. Instea of an actual link level moel, a statistical interface between system an link level moels is use. A simple approach is presente in [6], [7] an [8], the output of the system level part of the simulator, expresse in signal to interference values, is use as input for look up tables, which lea to a BE an a Frame Erasure ate (FE) for each raio link. The link moel is simply a Statistical Link Level Mapper (SLLM) that maps C/I mean values an istributions to corresponing FE. The two-step mapping proceure is applie by first mapping the C/Iburst (Signal to Interference ratio over a burst) obtaine from the system level moel to a corresponing number of erroneous bits in the burst. Then, the Bit Errors are groupe to compose a frame an we ecie whether the frame is erase or not base on common link level statistics. Figure 8 is a block iagram that epicts the integrate System an Link level moels. The link level moel s results incorporate with the system moel are epenent on the channel an simulation conitions. Hence, a isavantage of this moel is that we can never (b) FE

21 40 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks obtain link level FE an BE performance curves for all possible channel conitions, an the obtaine results will normally be limite to a certain egree of accuracy. As iscusse before, the link level BE an FE curves are epenent on the channel moel. The next section presents the aopte simulation settings; channel moel, shaowing moel an path loss moel. The interference iversity gain will be calculate base on the statistical moel presente in this section together with the simulation environment iscusse in the next section. 4. Simulation Environment Practical consierations for simulating the system an link level GSM moels inclue: Antenna aiation Patterns, the Path loss moel, the Shaowing (large scale faing) moel, an the Multipath propagation profile. The selection of these moels an parameters woul affect the reference statistical link level curves that are use for interfacing with the system moel. In our simulations, we consier a reuse factor of N = 7, a path loss exponent γ = 4, a cell raius of km an a completely interference limite system. Ajacent Channel Interference (ACI) is neglecte. We assume 3-sector base sites. Fig 8 a block iagram for the integrate system an link level moels 4.. Antenna aiation Pattern A practical antenna raiation pattern is incorporate in the system level moel. The antenna has 0 B beamwith of 0o. The antenna is suitable for 3-sector sites. Employing 3-sector sites into the network woul ecrease the number of interferers from 6 to. Thus we expect a boost in the C/I outage ratio by 0 log0(4) = 6 B. This gain is not exactly achieve as the rejecte interferers are not completely suppresse at the BTS ue to the non-zero gain of the sector antenna. After re-plotting the C/I F curve, a 0% outage is satisfie at 9.6 B (correspons to a gain of 5.6 B compare to the Omni-irectional cells case).

22 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 4 (a) (b) Fig 9 (a) a polar plot of the sector antenna horizontal plane raiation pattern (b) linear plot of the antenna gain versus the spatial angle. Courtesy of Voafone Egypt 4.. Pathloss Moel The pathloss moel escribes attenuation observe in the mean receive power as function of istance an path loss exponent. As efine in the GSM aio transmission an reception specifications [9] the path loss is efine as: L[B] = γ log ([m]) (40) 4.3. Large Scale Faing (Lognormal Shaowing) The large scale faing (shaowing) ue to obstacles intercepting the signal in its way to the receiver is usually moele as a log-normal ranom variable. The log-normal probability ensity function characterizes a ranom variable x if log(x) follows a normal istribution. The overall attenuation has a mean value equivalent to the path loss an fluctuations ecie by the stanar eviation of the log-normal shaowing. Accoring to GSM [9] the stanar eviation σf is set to Multipath Propagation Profile The multipath propagation results in fast faing (also known as small scale faing). The spatial interference between ifferent reflecte versions of the signal may be constructive or estructive. This leas to spatial variations in the receive power, an with a moving receiver, the power fluctuations become also time variant. The Power elay Channel Profiles (PP) aopte in simulations are typical TU3 an TU50 [0] (Typical Urban Moels with spee of 3 km/hr an 50 km/hr) in aition to rural environments moel (A moel). A ayleigh istribution is assume for the temporal channel gain. It is assume that the hop size is greater than the channel coherence banwith an the burst uration is greater than the coherence time of the channel. Base on this, we consier a new channel gain for each burst (hop) sample from a -imensional timefrequency channel response an a constant lognormal shaow faing gain for every frame. Note that the frequency hopping alters the observe frequency selective faing pattern. This frequency iversity effect is useful for the FEC (Forwar Error Correction) as it iversifies the corrupte bursts. The TU channel moel is applicable for ense urban areas, where numerous multipath components cause frequency selective channel

23 4 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks behavior. This moel is not applicable for all practical environments. In ural, low population areas, the A (ural Areas) Moel better escribes the channel response. Only six channel taps are inclue with quite less elay sprea an a frequency flat response. Fig 0 the path loss attenuation in B plotte versus istance for various value of the path loss exponent Fig the overall path loss an lognormal shaowing with a stanar eviation of 7 B. The time-frequency channel gri is obtaine as follows: a train of impulses with a perio of N samples is applie to the channel. The resultant signal observe at the channel output is a train of impulse responses. Because the channel is time variant, this train oesn t have an ientical output every N samples. The number of samples N is chosen to be the same as the number of hopping frequencies an the perio of the impulse train must be smaller than the coherence time. The output train of impulse responses is segmente into frames of N samples an every frame is applie to an N-point FFT (Fast Fourier Transform) operation to obtain the channel transfer function. The obtaine FFT frames are arrange sequentially in a matrix giving a two imensional channel representation. Each row represents a temporal inex ientifying a specific burst, while each column is a frequency bin. The values composing a row show how the gain associate with this frequency component varies with time. Because the MS is kept alive for a specific perio of time for each Monte Carlo simulation instance, the fast faing gain observe by a certain MS at a certain time instant is ecie by the burst inex an the current hopping frequency. Those two inexes extract a channel gain from the channel matrix.

24 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 43 Impulse esponse Train NT Impulse Train h(t) t t NT t h(τ, t) Segmentatio n H(f, t) N-point FFT f t /NT NT Fig 3 the channel matrix generation block iagram Various time-frequency faing channel gris are presente in figures 4, 5 an 6. Figure 4 shows a timeinvariant TU channel. When the receiver is stationary, the channel impulse response is kept constant an no variations in the channel gain are encountere for ifferent bursts. Because the elay sprea of the TU moel is relatively large, the channel is frequency selective. When the receiver is moving with a consierable spee, the transfer function becomes time variant (TU3 an TU50 moels). Figure 5 shows a frequency selective channel encountere by a moving receiver. Every burst encounters a new channel response. Frequency hopping woul have a esirable effect in frequency selective channels. ue to the presence of frequencies with eep faes, consecutive bursts are corrupte in a fixe hopping scheme. However, in frequency hopping networks, ifferent bursts are transmitte at ifferent frequencies an thus, if a burst is subjecte to a faing ip, the next burst is unlikely to be fae. This effect is calle frequency iversity an is far more significant for slow moving receivers. For fast moving receivers, the channel gain varies rastically for every burst, an frequency iversity becomes inherite from the channels extremely short coherence time. The ural channel moels (A moels) have less elay sprea values an thus a flat frequency response is offere by A channels. Figure 6 shows a typical A flat channel where the gain for all frequency components is the same an varies with time for moving receivers. In A channels, frequency iversity has no impact on the system performance as all frequencies have the same channel gain.

25 44 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks Fig 4 a time-invariant frequency selective channel (stationary receiver) Fig 5 a frequency selective time variant TU channel moel Fig 6 a frequency-flat time-variant A channel moel

26 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks Impact On Frequency Planning an Spectral Capacity Calculation The implications for frequency planning are obvious; to make the best usage of frequency hopping, the system shoul be planne with as tight frequency reuse as possible. The system can be esigne with a low system loa without loss of capacity. Furthermore, it allows hopping over many frequencies. In this section the Har an Soft blocking limits are efine, the effect of the system loa an number of hopping frequencies on the system s FE is shown, the improvements in the C/I statistics ue to interference iversity is iscusse an finally we introuce the Spectral Capacity as a qualitative assessment parameter for the operator s revenue compare to investment cost. The objective of this section is to verify that interference mitigation techniques (PC, TX an FH) can allow reucing the reuse figure of the network preserving the call quality expresse in terms of the FE. 5.. Har an Soft Blocking Limits The capacity of a network with a specific reuse figure is limite by a certain QoS criterion. There are two basic QoS criteria []: Har blocking limit: This is also known as blocking ue to no resources available (in the call setup phase). The capacity is limite by the amount of traffic that causes % blocking probability experience by users. This is calculate by the Erlang-B Formula. Soft blocking limit: epresents the call failure ue to low link quality (or equivalently high interference power in the connecte moe). It is characterize by performance parameters threshols such as C/I, BE an FE. Usually the C/I is require to be greater than 9 B or the FE is less than % in 90% in the service area. Hence, for each reuse scheme, we have to check whether it is interference limite or limite by blocking probability. Base on this, we calculate the maximum afforable system loa (either from Erlang-B formula or from FE curves). 5.. Impact of System loa an Number of Hopping Frequencies on FE performance The impact of the system loa on the CF of the FE in a Frequency Hopping scenario was stuie. It was foun that interference iversity is improve when the system loa ecreases []. For a constant number of hopping frequencies, the less loa on the system, the less likelihoo that the interferers are using the same frequency of the home cell for transmission. As shown in figure 7, a FH system with 8 hopping frequencies with 3/9 reuse pattern is stuie. The CF of the FE is plotte for system loa of 5%, 50% an 00%. It is obvious that the FE < % criterion is satisfie for a larger service area when the system loa is low. The impact of the number of hopping frequencies is also stuie for the same reuse pattern with, 4 an 8 hopping frequencies. As shown in figure 8, increasing the number of hopping frequencies results in an improvement of the FE CF. A larger portion of the service area experiences a FE less than % when the number of hopping frequencies is increase. Thus, it is esirable that FH networks have low system loas with large number of hopping frequencies. This correspons to aopt fractional loaing an a tight reuse pattern.

27 46 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks Fig 7 impact of the system loa on the FE performance in a TU3 channel Fig 8 impact of the number of hopping frequencies on the FE performance in TU3 channel 5.3. Carrier-to-Interference ratio aggregate gain ue to TX, PC an FH As state before, interference mitigation techniques improve the C/I statistics an relax the soft blocking limit. By applying slow faing, fast faing an path loss for a 3/9 reuse pattern scheme with 3 sector sites, the C/I gain at 0% outage was evaluate ue to TX, PC an FH. Without any features, the C/I ratio satisfie at 0% outage is B. By enabling iscontinuous transmission, Power control an Frequency Hopping with 8 hopping frequencies an 5% system loa, the C/I ratio at 0 % outage is booste to 0 B. This correspons to 9 B aggregate gain ue to the three interference mitigation techniques Spectral Capacity Calculation The Spectral Capacity η of a cellular network is obtaine by relating the capacity (revenue) to the network investment costs spent for the license spectrum an builing up of the network structure. The spectral capacity is calculate as []:

28 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks 47 η =. λcell. Nsec (40) B : system banwith allocate to the operator (Hz) λ cell : Traffic in Erlang N sec : Number of sectors per site Our goal is to compare the spectral capacity of the conventional 4/ reuse GSM network with a 3/9 reuse pattern network that aopts TX, PC an FH. The spectral capacity is calculate base on the maximum offere traffic impose by either har or soft blocking limits. It is expecte that, without loss of signal quality, a capacity gain is achieve ue to the reuce reuse factor. The capacity gain is quantifie in terms of spectral capacity as it relates network operator s revenues to the investment costs. Assume that the GSM Network operator has an allocate banwith of 4.4 MHz. As the banwith of the single GSM channel is 00 khz, we have a total of 7 F channels per cluster. In a 4/ reuse pattern, this correspons to 6 F channels per sector. The TMA frame can hol 8 users resulting in a total number of 48 channels. Because a fully loae 4/ reuse scheme can pass the FE criterion, the system is thus subjecte to the har blocking limit. By substituting the Erlang-B formula with 48 channels per sector an % blocking, the offere traffic is foun to be Erlang/sector (5 Erlang/site). By substituting in equation (40), the spectral capacity is foun to be 8 Erl/(site- MHz). By aopting a 3/9 reuse scheme, then we have a total of 8 F channels per sector, an thus, 8 hopping frequencies are employe. The maximum system loa that keeps the FE < % for 90 % of the service area is 75%. This correspons to 0.75 x 8 x 8 = 48 Erlang/sector (44 Erlang/site). The spectral capacity becomes 0 Erl/(site-MHz). Thus, a capacity boost with a factor of.5 is achieve without loss of quality when PC, TX an FH are applie to the 3/9 reuse scheme. Table 3 spectral capacity calculation for 4/ an 3/9 reuse schemes Blocking Scenario 4/ reuse with har blocking limit 3/9 reuse with soft blocking limit Number of F channels per sector 6 8 Actual number of channels per sector Traffic per sector Erlang 0.75*64 = 48 Erlang Traffic per site 5 Erlang 44 Erlang Spectral Capacity 8 Erl/(site-MHz) 0 Erl/(site-MHz)

29 48 Interference Mitigation Techniques for Spectral Capacity Enhancement in GSM Networks Fig 9 at a maximum system loa of 75% the FE QoS criterion is satisfie at 90% of the service area 6. Conclusions Various interference mitigation techniques can be eploye by the GSM network operator in orer to improve its Carrier-to-Interference ratio statistics. These techniques inclue: iscontinuous transmission (TX), Power Control (PC) an Frequency Hopping (FH). In TX, the silence frames of a MS are exploite as perios of power reuction, an thus the overall interference encountere by the BTS is reuce in proportion with the Voice Activity Factor (VAF). Using Power Control (PC), the relative istance between the MS an BTS controls the amount of transmitte power. A MS that is quite close to the home BTS can transmit far less power an thus, overall network interference is reuce. Another feature of GSM is Frequency Hopping; transmission at a ifferent F carrier every burst reuces the probability that reuse cells interferers collie with the home cell user by a factor that epens on the system loa an number of hopping frequencies. The effect of these techniques was stuie an improvements in C/I statistics were presente for a practical simulation environment that inclues the antenna s raiation pattern, path loss, slow an fast faing. It was shown that capacity of a GSM network can be improve by aopting a tight reuse scheme in conjunction with TX, PC an FH features maintaining QoS perceive by the user. This QoS is quantifie in terms of FE. Spectral Capacity is a network assessment metric that relates the operator s revenues (traffic) with the investment costs (allocate spectrum an base station ensity). The spectral capacity of a conventional reuse scheme of 4/ was compare to a tighter 3/9 scheme that eploys TX, PC an FH. A boost of 5 % in spectral capacity was etecte for the 3/9 scheme maintaining the soft blocking QoS criterion. eferences [] Theoore S. appaport, Wireless Communications: Principles an Practice, Pearson, n eition, 009, p 4. [] Thomas Toftegaar Nielsen, Jeroen Wigar, Performance Enhancements in Frequency Hopping GSM Network, Springer, 000, pp [3] GSM 05.0, Wireless Multiplexing an multiple access on the raio path, ETSI, 996.