On the Site Selection Diversity Transmission

On the Site Selection Diversity Transmission Jyri Hämäläinen, Risto Wichman Helsinki University of Technology, P.O. Box 3, FIN 215 HUT, Finland Abstract We examine site selection diversity transmission (SSDT) for 3GPP WCDMA forward link by means of analytical tools. Hard handover (HHO), soft handover (SHO) and SSDT are compared by using the receiver bit error probability as a performance measure taking into account the effect of feedback bit errors as well as the shadow fading. Results show that without fast transmission power control the performance gain from SSDT can be seriously degraded by feedback bit errors. I. INTRODUCTION A handover in wireless cellular systems is performed when a mobile station moves from one cell to another. In hard handover (HHO), transmission is disconnected and switched to a new base station when mobile station leaves the cell area, whereas in soft handover (SHO), mobile station may be connected simultaneously to several base stations so that addition and removing a base station from the active set is performed softly. Soft handover implements macro diversity, which improves the quality of the received signal and can be further exploited by reducing the transmit power, which reduces interference and increases system capacity. In multipath channels, the performance of soft handover is limited by the number of RAKE fingers that can be implemented in mobile station. This may lead to the situation, where the mobile station is not able to exploit the signals of all base stations transmitting to it. In this case, SHO does not improve signal quality but increases interference to the system. Furthermore,

updating the active set is slow and requires a lot of higher layer signaling. Site selection diversity transmission (SSDT) [1] in WCDMA was designed to alleviate the problems described above. In SSDT, mobile periodically chooses one of the base stations from the active set based on the instantaneous received powers. Subsequently, the mobile station sends the identification (ID) of the selected base station to all base stations in the active set. According to the identification sent by the mobile, other base stations in the active set suspend their transmission to the mobile station. The selected base station is referred to as primary base station while other base stations are called non-primary base stations. Primary base station is selected by using physical layer signaling, which makes it possible to track fast changes in the connection. High speed downlink packet access (HSDPA) extension of WCDMA [2] contains fast cell selection concept, which is very similar to SSDT. In this paper, we compare SSDT, SHO and HHO using bit error probability as a performance measure. For simplicity, we ignore the latency in SSDT processing so that the results apply to slowly moving users. Recently, SSDT has been studied in [3], [4] using link-level simulations, and it was observed that SSDT gives substantial capacity gains in low mobility environments. The paper is structured as follows: The system model is introduced in Section II while the analysis of the macro diversity methods is carried out in Section III. Paper is concluded in Section IV. A. Hard Handover II. SYSTEM MODEL In hard handover, the transmitting base station among K alternatives is selected directly based on the average signal to interference and noise ratio (SNIR) defined for user k by C k SNIR k = I k + I + N, I k = K l=1,l k where C k is the power of the own cell carrier, N is the noise term, I k is the interference power from an other base station in the active set, and I is the interference from base stations, which do not belong to the active set. We assume that the mean received power in decibels follows Gaussian distribution with expectation µ and standard deviation σ [5]. The deviation σ is based on measurements and values 3 9 db have been reported in the literature depending on the environment. Furthermore, we assume that HHO is too slow to mitigate fast fading. This assumption is reasonable since time delay between consecutive handovers in WCDMA is at least tens of milliseconds, more likely some hundreds of milliseconds. The selection of the base station is assumed to be error free since long term signalling with good reliability can be employed. Received signals from different base stations in flat fading environment are modeled as follows: Let s k be the transmitted symbol from kth base station, 1 k K. Then the received signals are of the form r k = h k s k +n k, where h k and n k refer to channel impulse response and noise, respectively. We assume that h k and n k are complex zero-mean Gaussian variables and denote by γ k = h k 2 the instantaneous SNR corresponding to the kth base station. The selection between base stations in HHO is based on the mean signal levels, denoted by γ k = E{γ k }. B. Soft Handover In soft handover, two or more base stations transmit the same data to the mobile station and the received signals are combined at the mobile station by maximal ratio combining (MRC), and the instantaneous SNR is given by γ = K γ k. I l,

C. Site Selection Diversity Transmission In SSDT, mobile selects the base station with the largest received instantaneous SNR using fast physical layer signaling. Hence, γ = max{γ k : 1 k K}. We assume that the feedback bit error probability is constant and bit errors are uniformly distributed in time. The model can be considered to be approximately valid in FDD WCDMA since the fast uplink power control is applied to the dedicated control channel carrying the feedback information. Naturally, the assumption does not hold any more with high mobile speeds when the delay of the feedback loop exceeds the coherence time of the channel. However, the assumption is well justified within low mobility environments. III. ANALYSIS Here we will study the performance of HHO, SHO and SSDT in terms of bit error probabilities (BEP) assuming BPSK modulation and flat Rayleigh fading environment. Under the assumptions, BEP of single antenna transmission (SA) as well as the BEP corresponding to MRC and selection combining (SC) are well known. The mathematical formulas are the same for both uplink and downlink direction provided that powers are properly scaled. When base station antennas are not placed within the shadow fading coherence distance, mean received powers γ k (µ k ) of fast fading process are different, and BEP can be written in the form P( γ) := P( γ 1 (µ 1 ), γ 2 (µ 2 ),..., γ K (µ K )), where µ k refers to average power level of shadow fading from kth base station. After finding the suitable BEP formulas, the remaining problem concerns with the selection of µ k. We assume that µ k are identically distributed, because the assumption favours SHO and SSDT. Although being identically distributed, the values of µ k are not equal but follow Gaussian distribution. It is well known that bit-error probabilities of composite fading channels cannot be solved in closed form. Instead, we approximate the BEP by replacing {µ k } K statistics by mean values of the corresponding order µ (k) = E{µ (k) }, µ (1) µ (2) µ (K), where the subscript in the brackets refers to the ranking of the variables. The final BEP results are then given in the form P( γ) := P( γ 1 ( µ (1) ), γ 2 ( µ (2) ),, γ K ( µ (K) )), where γ is the total system power and the scaling of the powers is defined as γ k = γν k /ν, ν k = 1 µ (k)/1, ν = K ν k. (1) Hence, γ 1 + γ 2 + + γ K = γ. We note that first moments of order statistics for Gaussian distribution are needed to make comparisons between the three methods. It will be seen that approximative analytical results align well with simulation results of composite log-normal and Rayleigh fading channels. A. Hard Handover Hard handover is based on long term channel measurements, and the average received power corresponding to the dedicated base station is given by µ (1) = max{µ 1, µ 2,..., µ K }, (2) where µ k is the mean SNR (in decibels) corresponding to the base station k. We assume that HHO is too slow to mitigate the fast fading and therefore the BEP corresponding to HHO depends only on µ (1). This results in the problem of finding the maximum among Gaussian variables. In general, the distribution of the maximum of K n.i.i.d random variables is given by K K f(µ) = f k (µ) F l (µ), (3) l=1,l k where f k ( ) is the pdf and F k ( ) is the cdf of the average SNR related to kth base station. In the proposed

model we have 1 f k (µ) = e (µ µ k) 2 /2σk 2, 2πσk F k (µ) = 1 ( ( µ µk 1 + erf )). 2 2σk (4) In the following analysis we consider the case where path loss and shadow fading characteristics of all base stations are the same µ := µ 1 = µ 2 = = µ K, σ := σ 1 = σ 2 = = σ K, and the distribution of the maximum is now given by f (1) (µ) = K f (µ)f (µ) K 1. The performance of HHO is evaluated as follows: First we compute the expectation for the average received power, µ (1) = E{µ (1) } = Kµf (µ)f (µ) K 1 dµ. (5) Then the result is substituted into the BEP formula of single antenna transmission, which in case of flat Rayleigh fading is given by P HHO ( γ) = 1 ( γ ) 1, (6) 2 1 + γ where γ = 1 µ (1)/1 refers to the mean SNR. Let us consider the special case of two base stations, which allows a closed-form solution for µ (1) given by µ (1) = µ + σ. (7) π A detailed computation of the result can be found in the Appendix. More closed-form and numerical results for the moments of order statistics of Gaussian random variables up to K = 7 can be found in [6], [7]. B. Soft Handover The distribution of the instantaneous SNR, received from kth base station is given by f k (γ) = 1 γ k e γ/ γ k, γ > (8) and in the following we have γ k γ l if k l. This is due to the assumption that base stations are not placed within the shadow fading coherence distance, see [8]. With MRC the distribution of the received SNR from K base stations is known to be K f(γ) = a k f k (γ), a k = K l=1,l k γ k. γ k γ l and after proper integration the bit error probability becomes P SHO ( γ) = 1 2 K γk ) a k (1. (9) 1 + γ k C. Site Selection Diversity Transmission Now the distribution f( ) of SNR is obtained by combining (3), (8), and the cumulative distribution corresponding to (8). Bit error rate of BPSK modulation for a fixed mean SNR is given in terms of complementary error function, and the bit error probability as a function of SNR is given by P SSDT ( γ) = f(γ)g(γ)dγ, g(γ) = 1 2 erfc( γ). Let us briefly recall the computation of BEP for SSDT when mean received powers are not equal. Assume that F( ) is the cumulative distribution function corresponding to f( ). Using integration by parts we find that P SSDT ( γ) = F(γ)g (γ)dγ. Here the expression for g ( ) is obtained from 7.1.19 of [9] and we find that the bit error probability attains the form P SSDT ( γ) = 1 e γ K (1 e γ/ γ k )dγ. 4π γ The product term can be expressed as a sum K (1 e γ/ γ k ) = L a l e blγ, l=1 where L = 2 K and coefficients a l and b l are easily found when K is small. By employing the sum expression and analytical integration we find that P SSDT ( γ) = 1 L a l 4π l=1 e γ(1+b l) γ dγ = 1 2 L l=1 a l 1 + bl. (1)

The same power normalization is applied as explained before. In the special case of two base stations the BEP attains the form joint feedback word w λ. P SSDT ( γ) = 1 ( γ1 γ2 γ 1 γ 2 Since ) received feedback words in different base 1 +, 2 1 + γ 1 1 + γ 2 γ 1 + γ 2 + γ 1 γ stations 2 are independent we find that where γ 1 and γ 2 are defined according to (1). K p(w λ w ) = p(w k,λ w ). (12) Feedback Errors: In FDD WCDMA, the number of base stations in SSDT is limited to eight due to the length of the temporary ID field. Based on the received ID, base stations independently decide whether to transmit or not, and in case of feedback errors it is possible that none of the base stations, or more than one base station are transmitting. In the latter case we assume that the receiver is able to combine all the transmitted signals using MRC, and transmit power is evenly divided among the transmitting base stations. For simplicity, we assume that feedback error probability p is the same in all base stations, although in practice, error probabilities vary due to different shadow fading and path loss characteristics. Consider first a general model concerning a system of K base stations and feedback word length of κ bits, and assume that a feedback word w is transmitted from mobile station. Then, after being corrupted by the physical channel, feedback words w k, k = 1, 2,..., K are received in the K base stations. There are K L, L = 2 κ different combinations of received feedback words in total, and we introduce an additional subscript λ and denote by w λ = (w k,λ ) K the joint received feedback word, where λ refers to the set Λ of indices corresponding to all possible combinations. The BEP of SSDT in the presence of feedback errors can now be expressed in the form P p SSDT ( γ) = λ Λp(w λ w )P( γ w λ ), (11) where p(w λ w ) is the probability that base stations receive the feedback words w k,λ on the condition that word w is transmitted from mobile station and P( γ w λ ) is the receiver BEP in the mobile station on the condition that downlink transmission obeys the Let us denote by p = 1 (1 p) κ the probability of a feedback word error in the presence of feedback bit error probability p. Without losing the generality we can assume that the first base station (k = 1) is selected according to uncorrupted feedback word w. Then we have {p, 1 p }, k = 1, p(w k,λ w ) { p L 1, 1 p L 1 }, k > 1, where p /(L 1) is the probability that a base station which is not selected according to w will receive an erroneous feedback word asking for the transmission. Consider next a lower bound for BEP of SSDT. If all base stations suspend their transmission, then the BEP in the receiver is 1/2 and there holds P p SSDT ( γ) 1 ( 2 p 1 p ) K 1 1 = L 1 2 p out, (13) where the last term in the right indicates the probability of no transmission denoted by p out. It is found that the receiver BEP strongly depends on p out which further depends on the feedback bit error probability p. If channel coding is not applied, then estimate (13) shows that SSDT will work properly only if p is very small. For example, WCDMA simulations typically assume a nominal 4 % feedback bit error probability. Then, according to the bound (13) the receiver BEP is 5 6 % depending on the number of base stations when κ = 3. Furthermore, it is straightforward to calculate the corresponding feedback word error probabilities for different ID codes given in [1]. The situation is not that bad when channel coding is employed, because the decoder in the mobile

station may take into account the reliability of the received soft bits and the lack of the received signal is practically seen as a code puncturing. If the SSDT selection is done several times during the interleaving period, the rate of the code puncturing remains small. In WCDMA, the maximum number of updates is five per 1 ms radio frame [1]. In this case we may ignore the probability of no transmission, and the probabilities of different joint feedback words need to be scaled by p out in (11). Furthermore, WCDMA specification [1] states that base station is selected as a non-primary one if the received ID does not match the base station s ID and the received signal quality is less than a predefined threshold. The additional threshold condition has the effect of decreasing the value of p out when compared to that in (13). Let us study in more detail the case K = 2. Assume that w refers to the first base station and further, assume that w 1 refers to the joint event Only the first base station is transmitting, w 2 refers to the event Only the second base station is transmitting and w 3 refers to the event Both base stations are transmitting. Then we obtain ( p(w 1 ) = (1 p ) 1 p ), p(w 2 ) = p2 L 1 L 1, p ( p(w 3 ) = (1 p ) L 1, p out = p 1 p ). L 1 The corresponding receiver bit error probabilities for w 1, w 2 and w 3 are given by P( γ w 1 ) = P SSDT ( γ), P( γ w 2 ) = P Min ( γ), P( γ w 3 ) = P SHO ( γ), where P Min ( ) refers to the BEP corresponding to the transmission from the second base station for which γ = min{γ 1, γ 2 }. By employing the derivations presented in this section it is not difficult to see that P Min ( γ) = 1 γ 1 γ 2. 2 γ 1 + γ 2 + γ 1 γ 2 Now we have means to compute P p SSDT ( ) from (11). Bit Error Probability 1 1 1 2 1 3 1 5 5 1 15 2 SNR [db] Fig. 1. Bit error probabilities for SSDT with p = (solid line), p =.1 ( ), p =.4 ( ) and p =.1 ( ) when K = 2 and σ = 6. D. Performance Comparisons In the following we assume that κ = 3 corresponding to the WCDMA specification. Let us begin by studying the effect of feedback errors to the performance of SSDT. Figure 1 depicts BEP curves when K = 2 and σ = 6 db for different feedback bit error rates. First set of curves corresponds to the case where BEP of event No transmission is 1/2, and the presence of error floor is clearly seen. The BEP curves in the second set are computed by neglecting the effect of suspended transmission. The curves in the second set do not seriously suffer from erroneous feedback. It is found that the BEP of SSDT is heavily corrupted by feedback bit errors if event No transmission is not taken into account in the channel decoding scheme. Figures 2 and 3 depict performance results for HHO, SHO and SSDT in terms of BEP for K = 4 and σ = 6 db and σ = 12 db, respectively, assuming error-free feedback in SSDT. Solid lines refer to analytical approximations and dashed lines denote BEP obtained by simulating composite fading channels. It is found that SSDT provides the best performance when feedback is error free. Moreover, for high BEP

levels (BEP>.1) HHO outperforms SHO. Analytical and simulation results agree well except with small BEP, which is partly due to limited number of trials (1) to simulate different shadow fading powers µ k. Comparing the two figures shows that the performance of SSDT and SHO is deteriorated when deviation of the shadow fading increases. Finally, we note that the ranking of the studied three methods from performance point of view may be different when an additional fast transmission power control is applied in the forward link as can be the case in real systems designed for voice transmission. However, then the transmit powers with different handover methods become different, fair comparison between the methods is difficult, and the additional performance gain might be obtained with the cost of additional interference in the network. IV. CONCLUSIONS We compared site selection diversity transmission (SSDT) with hard handover and soft handover using the receiver bit error probability as a performance measure. Results show that feedback bit errors reduce the link level performance of SSDT caused by the error event when all base stations suspend their transmissions. Analytical results approximating the effect of composite fading by first moments of order statistics of log-normal distribution align well with the simulations of composite fading channels. V. APPENDIX Here we consider the computation of the expectation of the maximum of K equally distributed Gaussian variables. By combining (4) and (5) we obtain µ (1) = (µ µ 2 ) 2σ Kµe 2 ( µ 2πσ e (ξ µ 2 ) 2σ 2 2πσ dξ) K 1dµ. Bit Error Probability 1 1 1 2 1 3 Fig. 2. 1 5 5 1 15 2 SNR (db) Bit error probabilities for HHO (x), SHO (*) and SSDT with p = (o) when K = 4 and σ = 6 db. Solid and dashed curves refer to analytical and simulation results, respectively. Bit Error Probability 1 1 1 2 1 3 Fig. 3. 1 5 5 1 15 2 SNR (db) Bit error probabilities for HHO (x), SHO (*) SSDT with p = (o) when K = 4 and σ = 12 db. Solid and dashed curves refer to analytical and simulation results, respectively. Let us substitute t = (ξ µ )/ 2σ and s = (µ µ )/ 2σ. Then the expectation µ (1) attains the from µ (1) = K 2σ π + K µ π se s2( 1 π e s2( 1 π s s e t2 dt) K 1ds e t2 dt) K 1ds. (14) Here the integral in brackets can be written in terms

of error function, s 1 1 e t2 2 (1 + erf(s)), s, dt = π 1(1 erf(s)), s <. 2 After dividing the integration in (14) with respect to point s = we find that µ (1) = K 2σ ( I + π 1 I1 ) K µ ( + I + π 2 + I2 ) (15) where each of I ± k refer to an integral, defined by I 1 ± = se s2( 1 2 (1 ± erf(s))) K 1 ds, I 2 ± = e s2( 1 2 (1 ± erf(s))) K 1 ds. If K = 2 then we have I 1 + I 1 = se s2 erf(s)ds, I 2 + +I 2 = e s2 ds. (16) The latter integral is equal to π/2 and a closed-form expression for the former integral can be obtained by 7.4.19 of [9] after substituting s = u. The result is then given by (7). REFERENCES [1] 3GPP, Physical layer procedures (FDD), 3GPP technical specification, TS 25.214, Ver. 4... [2], Physical layer aspects of UTRA high speed downlink packet access, 3GPP TSG-RAN technical report, TR 25.848, Ver. 4.., 21. [3] H. Furukawa, K. Hamabe, and A. Ushirokawa, SSDT site selection diversity transmission power control for CDMA forward link. [4] N. Takano and K. Hamabe, Enhancement of site selection diversity transmit power control in CDMA cellular systems, vol. 3, 21. [5] M. Hata, Empirical formula for propagation loss in land mobile radio services, IEEE Trans. Veh. Technol., vol. VT-29, no. 3, Aug. 198. [6] H. Jones, Exact lower moments of order statistics in small samples from a normal distribution, Annals of Mathematical Statistics, vol. 19, no. 2, pp. 27 273, June 1948. [7] H. Godwin, Some low moments of order statistics, Annals of Mathematical Statistics, vol. 2, no. 2, pp. 279 285, June 1949. [8] M. Gudmundson, Correlation model for shadow fading in mobile radio systems, vol. 27, no. 23, pp. 2145 2146, Nov. 1991. [9] M. Abramowitz and I. Stegun, Eds., Handbook of Mathematical Functions. 1972. Washington DC: National Bureau of Standards,