3.2.1 System Parameters
Figure 2.2 depicts the block diagram of the NC receiver designed for our code acquisition scheme using MIMO. The MAT formulae provided for the single-path scenario of SDSS in Section 2.4.1.1 are also employed for the performance analysis of the NC scheme of this section. The system parameters employed are summarised in Table 3.1. In Table 3.2 we outlined the maximum SINR degradation imposed by both the Doppler shift and the clock-drift-induced frequency mismatch between the transmitter and receiver in conjunction with a coherent integration interval of N chip durations. The length of the PN sequence in our system was assumed to be (215− 1)·Tc = 65534·Tc, where the chip-duration is
Tc = 1/1.2288µs. It may be deemed sufficient at this point to integrate the detector
output seen in Figure 2.2 over N = 256 chips, which is equivalent to two 128-chip modulated symbols used for coherent accumulation. This value was calculated by using Equation. 2.9 provided for determining the performance degradation owing to both the Doppler shift and the frequency mismatch. The spreading factor of the Walsh code to be acquired was selected to be 128. The frequency mismatch was assumed to be 1000 Hz [3], while the carrier frequency was 1.9 GHz. As an example of a high mobile speed, it is reasonable to postulate 160 km/h. We also assumed that the sampling inaccuracy caused by having a finite search step size of ∆ = 1/2Tc was -0.91 dB, which is a typical value for the search
step size [3, 15]. Accordingly, we considered three performance degradation factors, which encompassed the clock-drift-induced frequency mismatch, the Doppler shift and the effects of the finite sampling distance. All these imperfections were taken into account, when calculating the correct detection probability. Finally, two additional parameters have to be stipulated for the analysis of SDSS. Specifically, the total uncertainty region was assumed to entail 65,534 hypotheses, and in the spirit of [15], the false locking penalty factor was assumed to be 1000 chip-durations.
3.2.2 System Performance Results
Figure 3.1 illustrates the correct detection probability versus false alarm probability, pa- rameterised by both the number of transmit antennas for P = 1,2 as well as 4 and the
3.2.2. System Performance Results 90
Table 3.1: System Parameters
Bandwidth 1.25 MHz Carrier frequency 1.9 GHz Spreading factor 128 Diversity: Transmit 1,2,4,6,8,10 Receive 1,2,4 Frequency mismatch 1000 Hz Mobile speed 160km/h
Coherent integration interval 256chips Total uncertainty region 65,534
False locking penalty factor 1000 chip-durations
Table 3.2: Maximum SINR degradation inflicted by both the Doppler shift and a 1000 Hz frequency mismatch in conjunction with the coherent integration interval of N chip durations at a carrier frequency of 1.9 GHz
N (Chips) 64 128 256 384 512
Degradation (dB) 0.061 0.2449 0.9969 2.3144 4.3213
Ec/I0 value. In case of Ec/I0 = -10 dB, the achievable performance enhancement gradually
saturates, as the transmit diversity order is increased from P = 1 to 4. By contrast, PD
decreases as the number of transmit antennas P increases, when the mobile station experi- ences a relatively low Ec/I0 value of -19 dB, as evidenced by the three curves corresponding
to the relatively low PD values in Figure 3.1. Figures 3.2 and 3.3 characterise the correct
detection probability versus false alarm probability, parameterised by both the number of transmit antennas for P = 1,2 as well as 4 in conjunction with both R = 2 (Figure 3.2) and R = 4 (Figure 3.3) receive antennas as a function of the Ec/I0 value.
When having R = 2 receive antennas as portrayed in Figure 3.2, the results show similar trends to those of Figure 3.1. By contrast, in the scenario of R = 4 receive antennas as seen in Figure 3.3, there is a sufficiently high spatial diversity gain, which has beneficial effects on the achievable acquisition performance PD. However, as seen in Figure 3.3, increasing
the transmit diversity order imposes a degradation of the achievable PD performance. The
specific Ec/I0 abscissa values used in Figures 3.1 to 3.3 were chosen to exemplify the
typical achievable values. In all the remaining figures we will assume an operation in the range of ‘finger locking’, which may be considered to be the range between Ec/I0
3.2.2. System Performance Results 91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.4 0.5 0.6 0.7 0.8 0.9 1
False Alarm Probability
Detection Probability P4R1 P2R1 P1R1
0
Ec/Io = − 10 dB Ec/Io = − 19 dB0
Figure 3.1: Correct detection versus false alarm probability for P = 1,2 and 4 transmit antennas in conjunction with R = 1 receive antenna, when using the schematic of Figure 2.2 and Table 3.1. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
False Alarm Probability
Detection Probability P4R2 P2R2 P1R2
0
0
Ec/Io = − 19 dB Ec/Io = − 13 dBFigure 3.2: Correct detection versus false alarm probability for P = 1,2 and 4 transmit antennas in conjunction with R = 2 receive antennas, when using the schematic of Figure 2.2 and Table 3.1.
3.2.2. System Performance Results 92 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
False Alarm Probability
Detection Probability P4R4 P2R4 P1R4
0
0
Ec/Io = − 19 dB Ec/Io = − 16 dBFigure 3.3: Correct detection versus false alarm probability for P = 1,2 and 4 transmit antennas in conjunction with R= 4 receive antennas, when using the schematic of Figure 2.2 and Table 3.1.
we will investigate in more detail the somewhat unexpected phenomenon of experiencing a degraded acquisition performance in the presence of multiple transmit antennas. The correct detection probabilities seen in Figure 3.4 and Figure 3.5 were obtained assuming a false locking probability of PF = 0.1 for all scenarios considered, where ′S′ denotes
the simulation results, whilst ′A′ presents the numerical analysis results calculated from both Equations. 2.28 and 2.29. The simulations always represent a slightly better correct detection probability than the analysis at the same false alarm probability. This is because in the analysis a constant Doppler shift value was added to the total frequency mismatch in Equation. 2.9, which was calculated for the high mobile speed scenario. However, in a practical scenario, the Doppler shift may have either a positive or a negative impact on the PD performance, depending upon the specific conditions encountered.
In Figures 3.4 and 3.5, the relationship between PD and the number of transmit antennas
is portrayed both with and without multiple receive antennas for different values of Ec/I0,
respectively. More explicitly, Figure 3.4 portrays the correct detection probability versus the number of transmit antennas, parameterised by the pilot channel’s Ec/I0 value. At
Ec/I0 = -10 dB a slight PD improvement is observed upon increasing the number of trans-
3.2.2. System Performance Results 93
characterises the correct detection probability versus both the number of MIMO, parame- terised by the pilot channel’s Ec/I0 value. The left illustration of Figure 3.5 characterises
the scenario of R = 2 receive antennas, while the one at the right was valid for R = 4 receive antennas. The curve recorded for Ec/I0 = -10 dB at the right of Figure 3.5 overlapped with
that plotted for Ec/I0 = -13 dB, because all the achievable detection probabilities were
PD ≈ 1. Both Figures 3.4 and 3.5 illustrate that PD tends to decrease, as the number of
transmit antennas increases, especially when the MS experiences a low Ec/I0 value. We can
observe in both Figure 3.4 and Figure 3.5 that the highest detection probabilities marked by circles were achieved, when the per-branch Ec/I0 value was -19 dB for a given total Ec/I0
value in the range of ‘finger locking’. Owing to the above-mentioned facts, the range of the minimum Ec/I0 values required for reaching ‘finger locking’ may vary, depending upon the
number of transmit antennas.
1 2 3 4 5 6 7 8 9 10 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Number of Transmit Antennas (P)
Detection Probability −10dB(S) −10dB(A) −13dB(S) −13dB(A) −16dB(S) −16dB(A) −19dB(S) −19dB(A)
0
0
0
Figure 3.4: Correct detection probability versus the number of transmit antennas for P = 1,2,4,6,8 and 10, parameterised by the pilot channel’s Ec/I0 value, when using the schematic
of Figure 2.2 and Table 3.1.
Let us now proceed by defining the MAT gain as the quotient of the MAT achieved by a particular MIMO configuration and that attained by the conventional [P = 1, R = 1] = P 1R1 scheme. However, the transmit power reduction imposed by using multiple transmit antennas can be partially compensated for with the aid of multiple receive antennas. In this case it is more appropriate to use the MAT of the P 1R2 or P 1R4 schemes. Figure 3.6 characterises the MAT gain/degradation as a function of the Ec/I0 values considered. Here
3.2.2. System Performance Results 94 P1 P2 P4 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Number of Receive Antennas = 2
Detection Probability P1 P2 P4 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Number of Receive Antennas = 4
Detection Probability −10dB(S) −10dB(A) −13dB(S) −13dB(A) −16dB(S) −16dB(A) −19dB(S) −19dB(A) −10dB(S) −10dB(A) −13dB(S) −13dB(A) −16dB(S) −16dB(A) −19dB(S) −19dB(A)
0
0
0
0.20
0
0
Figure 3.5: Correct detection probability versus the number of transmit antennas for P = 1,2 as well as 4 and the number of receive antennas for both R = 2 (Left figure) and R = 4 (Right figure), parameterised by the pilot channel’s Ec/I0 value, when using the schematic
of Figure 2.2 and Table 3.1.
the MAT gain/degradation recorded for the different scenarios was presented by defining the MAT ratios of the scenarios (P 1R1/P xR1), (P 1R2/P xR2) and (P 1R4/P xR4), where we have x = 2 or 4. To elaborate a little further, there would have been some benefit in using the same normalisation factor such as the MAT of the single receiver system R1 for all the different scenarios, but we found that the above-mentioned definitions were more suitable for explicitly demonstrating the impact of the number of transmit antennas. As shown in Figure 3.6, for example the P 2R1 and P 2R2 scenarios exhibit a modest MAT gain for Ec/I0
values between -11 and -8 dB and between -12 and -9 dB, respectively, but in the rest of the SINR region a MAT degradation is experienced. Here all the performance curves have been generated at the threshold value of Ec/I0 = -13 dB, which was considered as the minimum
value required for reliable finger locking. More quantatively, observe in Figure 3.6 that in order to achieve the MAT ratio of unity, corresponding to no transmit-antenna-induced MAT loss, we need about 2 dB more power for the P 2R1 scenario. Alternatively, the cell radius would have to be reduced by an appropriate path-loss-dependent factor, if no transmit-antenna-induced MAT degradation can be tolerated. Therefore the employment of MIMO may lead to the reduction of the attainable cell size, since no communications are possible until code acquisition has been completed.
3.2.3. Conclusion 95 −13 −12 −11 −10 −9 −8 −7 −6 −5 −4 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05
SINR per chip (Ec/Io)
MAT Ratio P2R1 P4R1 P2R2 P4R2 P2R4 P4R4
Figure 3.6: MAT ratio versus Ec/I0 value, when using the schematic of Figure 2.2 and
Table 3.1.
In summary, multiple transmit antennas constitute an efficient means of improving the attainable diversity gain, and/or system throughput, when communicating over mobile channels. However, for the sake of fair comparisons, the total signal power transmitted from the multiple transmit antennas must be fixed, regardless of their number. In other words, the total transmit power must be equally shared by all the transmit antennas. This implies that an excessively low level of per-branch received signal strength would lead to a low acquisition performance, even if the transmit multiplexing/diversity gain is high. In other words, a high diversity order effectively results in an acquisition performance loss, as a consequence of the insufficiently high transmit signal strength per branch. In case of employing both multiple transmit and receive antennas, this trend is still observable, although using two or four receive antennas has the potential of mitigating the associated acquisition performance degradation imposed by the low per-branch Ec/I0 values encountered.
3.2.3 Conclusion
In this section, we analysed the MIMO aided initial acquisition performance of the inter- cell synchronous CDMA DL. Ironically, our findings suggest that increasing the number of transmit antennas results in combining the low-energy, noise-contaminated signals of the
3.3. Initial and Post-Initial Acquisition in Co-located Scenario 96
transmit antennas, which ultimately reduces the correct detection probability, as evidenced by Figures 3.1 to 3.5. However, it is extremely undesirable to degrade the achievable ac- quisition performance, when the system is capable of attaining its target bit error rate performance at reduced SINR values, as a benefit of employing multiple transmit antennas. It may be concluded that the achievable cell coverage determined by the received pilot chan- nel power may be reduced, as observed in Figure 3.6, as the number of transmit antennas is increased, which is a highly undesirable phenomenon, since it has grave repercussions in terms of having to tolerate a high number of handovers per cell.
3.3
Initial and Post-Initial Acquisition in Co-located Sce-
nario
3.3.1 Concept of Initial and Post-Initial Acquisition
The classic serial search techniques designed for initial acquisition [3] have been traditionally employed in specific scenarios, where the uncertainty region (or search window width) is quite wide (i.e. 215 − 1) and hence in the context of serial search it is the MAT, which constitutes the most pertinent performance criterion, as seen for example in the DL of the inter-cell synchronous CDMA-2000 system [3]. In the case of initial acquisition contrived for DS-CDMA, the main design goal is to acquire accurate timing of the first received signal path impinging at the receiver, since this timing information is used as that of the reference finger of the Rake receiver. By contrast, the post-initial acquisition procedure that extracts the accurate timing positions of the remaining delayed paths and identifies the appropriate paths earmarked for processing by the Maximum Ratio Combining (MRC) scheme of the Rake receiver, has a major impact on the performance of the Rake receiver [8]. There are two main differences between the initial and post-initial acquisition procedures. First of all, once the first Rake finger is synchronised, the uncertainty region that has to be explored will be shrunk to ± ξ hypotheses surrounding the time-instant, where the first received path was found. This reduced interval will be referred to as the ’reduced uncertainty region’ to be explored after the initial acquisition [7]. This search window width is defined by both the dispersion of the multipath propagation environment encountered as well as by the appearance and disappearance of propagation paths [111]. Secondly, the post-initial acquisition procedure commences after the Automatic Frequency Control (AFC) operation was activated for the sake of fine tracking, following the successful initial acquisition. Hence,
3.3.2. System Parameters 97
the performance degradation imposed by the associated frequency mismatch is considerably reduced compared to that immediately after the initial acquisition. Accordingly, these two factors are taken into account in our forthcoming analysis.
3.3.2 System Parameters
Figure 2.5 depicts the block diagram of the NC receiver designed for our code acquisi- tion scheme using MIMO. The MAT formulae of both the SDSS and DDSS provided in Sections 2.4.1 and 2.4.2 are also employed for the performance analysis of this section. The associated system parameters are summarised in Table 3.3. In Tables 3.4 and 3.5 we outlined the maximum SINR degradation imposed by both the Doppler shift and the clock- drift-induced frequency mismatch between the transmitter and receiver in conjunction with the coherent integration interval of N chip durations seen in Figure 2.5 for both initial and post-initial acquisition. The length of the PN sequence in our system was assumed to be (215− 1) · Tc, where the chip-duration was Tc = 1/1.2288µs. In the case of the initial
Table 3.3: System Parameters
Bandwidth 1.25 MHz Carrier frequency 1.9 GHz Spreading factor 128 Diversity: Transmit 1,2,4 Receive 1,2,4 Frequency mismatch (Initial) 1000 Hz Frequency mismatch (Post-Initial) 200 Hz Mobile speed 160km/h
Num. of chip SDSSDDSS 128 chips32 and 256 (or 128) chips Total uncertainty region
(Initial)
65,534 hypotheses
Total uncertainty region (Post-Initial)
124 hypotheses
False locking penalty factor 1000 chip-durations Number of paths single and three path(s)
acquisition scheme of Figure 2.5, it was found to be sufficient to integrate the detector output seen in Figure 2.5 over N =128 chips for the sake of analysing SDSS, while the num- ber of chips over which the accumulator Σ of Figure 2.5 sums the (·)2 envelope detector’s
3.3.2. System Parameters 98
Table 3.4: Maximum SINR degradation inflicted by both the Doppler shift and a 1000 Hz frequency mismatch in conjunction with the coherent integration interval of N chip durations at a carrier frequency of 1.9 GHz
N(Chips) 64 128 256 384 512
Degradation(dB) 0.061 0.2449 0.9969 2.3144 4.3213
Table 3.5: Maximum SINR degradation inflicted by both the Doppler shift and a 200 Hz frequency mismatch in conjunction with the coherent integration interval of N chip durations at a carrier frequency of 1.9 GHz
N(Chips) 128 256 384 512 640 768
Degradation(dB) 0.032 0.128 0.289 0.5159 0.812 1.179
output in both the search and the verification modes of DDSS are assumed to be 32 and 256 in the R = 1 receive antenna scenarios or 128 in the R = 4 receive antenna scenario, respectively. By contrast, in the case of the post-initial acquisition scheme of Figure 2.5, the optimised length of coherent summation of the detector output values invoked for the sake of analysing SDSS is given in Table 3.6, whilst 64 is selected as the length of coherent summation in the search mode of DDSS. Finally, the optimised intervals of the coherent summation used in the verification mode of DDSS are portrayed in Table 3.7. The numbers seen in (·) in both Tables 3.6 and 3.7 can be used as an alternative. Its basic operation is identical for both the initial and post-initial acquisition schemes, except for using different coherent summation intervals necessitated by the different frequency mismatch of the two schemes. These optimised parameter values were calculated by using the formulae of the probability of the correct detection and false alarm in Section 2.3.2.3, the MAT expression of Section 2.4 as well as Equation. 2.9 of Section 2.3.2.1 provided for determining the per- formance degradation owing to both the Doppler shift and the frequency mismatch. The spreading factor of the Walsh code to be acquired was selected to be 128. The frequency mismatch was assumed to be 1000 Hz for the initial acquisition [3] and 200 Hz for the post-initial acquisition phases [8], while the carrier frequency was 1.9 GHz. As an example of a high mobile speed, it is reasonable to postulate 160 km/h. We also assumed that the sampling inaccuracy caused by having a finite, rather than infinitesimally low search step size of ∆ = Tc/2 was -0.91 dB, which is a typical value for the search step size [3]. The
total uncertainty region of initial and post-initial acquisition were assumed to entail 65,534 and 124 hypotheses, respectively. Finally, in the spirit of [15], the false locking penalty
3.3.3. System Performance Results 99
factor was assumed to be 1000 chip-durations. Finally, both single-path and multi-path scenarios were considered. In this scenario both a single-path and a group of three paths arriving with a relative time delay of one chip were considered. Both CIRs had the same magnitude for the first received path as well as 3 dB lower for the second and 6 dB lower for the third received paths, respectively, compared to the LOS path of a single-path scenario. All the performance curves, except for Figures 3.12 and 3.13, have been obtained at the optimum decision threshold of Ec/I0 = −13 dB designed for the initial acquisition scheme
and at Ec/I0 = −19 dB invoked for the post-initial acquisition scheme, respectively. The
operational range of the post-initial acquisition scheme was assumed to be 6 dB lower than that of the initial acquisition arrangement, because the signal power of the delayed paths is typically lower than that of the first received path.
Table 3.6: Optimised length of coherent summation of the detector outputs invoked for the sake of analysing SDSS in post-initial acquisition
Transmit/Receive P1R1 P2R1 P4R1 Transmit/Receive P1R4 P2R4 P4R4 Length (Chips) 512 512 640 Length (Chips) 256
(128) 256 (384)
384
Table 3.7: Optimised length of coherent summation of the detector outputs invoked in the verification mode for the sake of analysing DDSS in post-initial acquisition
Transmit/Receive P1R1 P2R1 P4R1 Transmit/Receive P1R4 P2R4 P4R4 Length (Chips) 384 640 768 Length (Chips) 256
(384)
384 512
3.3.3 System Performance Results
Figure 3.7 illustrates the achievable MAT versus SINR per chip performance for our SDSS aided initial acquisition scheme as a function of the number of transmit antennas for P = 1, 2 as well as 4 and that of the number of receive antennas for R = 1 and 4. In the results of Figures 3.7 to 3.11, except for Figure 3.9, the bold lines indicate the scenario of receiving three paths (denoted as M 3 in Figures 3.7 to 3.11, except for Figure 3.9), whereas the thinner lines represent a single-path scenario (denoted as M 1 in Figures 3.7
3.3.3. System Performance Results 100 −11 −10 −9 −8 −7 −6 −5 −4 4 6 8 10 12 14
SINR per chip (Ec/Io)
P4R1M1 P2R1M1 P1R1M1 P4R1M3 P2R1M3 P1R1M3 P4R4M1 P2R4M1 P1R4M1 MAT(sec)
0
R=10
R=4Figure 3.7: MAT versus SINR per chip performance of the initial acquisition scheme for SDSS parameterised with both the number of transmit and receive antennas, when employ-