Unknown Interference Modulation
4.1.2 The Second Stage of the Modified RTS
In the second stage of modified RTS, we will again generate the soft-output LLR values via the help of the counter hypothesis paths.
Since the receiver has no interest to recover the information contained within the interference, only the soft-output LLRs of the desired signals will be generated. For this reason, we modify the sorting and QR-decomposition (SQRD) algorithm [13] such that the symbols corresponding to the desired signals are placed in the first Ns levels of the search tree. Again, in these Ns levels, Q counter hypothesis paths are extended
ŒġŤŰŶůŵŦųġ
Figure 4.4: Illustration of the 2nd stage of the modified RTS for unknown interference modulation
in order to generate the soft-output LLR values. During this process, only the paths corresponding to the best candidate symbol are retained. The process will be repeated until the bottom level of the search tree is reached. An example of the second stage is illustrated in Fig. 4.4.
4.2 Simulation Results
In this section, simulation results for Ns = Ni = 2 and NR = 4 will be presented, which corresponds to the system model
y = HsPsxs+ HiPixi + n
where n denotes the additive white Gaussian noise. In the simulation, the modulations of the desired signals x1 and x2 are 16QAM, whereas the modulations of interferences i1 and i2 can be either 16QAM or QPSK and are unknown to the receiver. A
3GPP-Algorithm 1 Modified SQRD Algorithm
specified punctured turbo code of code rate R = 1/2 and codeword length1920 bits is adopted [10]. Under a 15 × 128 block interleaver, 480 16-QAM symbols are received at the receiver, in which the 8-iteration Max-Log-MAP decoder is used for turbo decoding.
It is assumed that the channel coefficients can be perfectly estimated. Only the slow fading scenario is considered; hence, the parameter Lmax is set to be 0.2.
We first examine the impact on the correctness of modulation classifications in Fig.
4.5. The exact modulation schemes of the interference sources i1 and i2 are 16QAM and QPSK, respectively. For the incorrect modulation judgement of interference, two situations are thus examined. The modulation scheme of i1 is wrongly declared as QPSK, and that of i2 is wrongly decided to be 16QAM. We can then observe from Fig. 4.5 that any one incorrectly judgement on interference modulation scheme can seriously jeopardize the system performance, where the resultant BLERs decrease at a
16 16.5 17 17.5 18 18.5 19 10−4
10−3 10−2 10−1 100
SNR
BLER
i1 QPSK i
2 QPSK i1 16QAM i2 16QAM i1 16QAM i
2 QPSK
Figure 4.5: Comparison of BLERs between correct and erroneous declarations of mod-ulation scheme for interferences
very low speed as the SNR grows.
Next, we investigate the modulation classification errors when only one RE is used.
The modulation schemes of i1 and i2 are set as {16QAM, 16QAM}, {QPSK, 16QAM}, {QPSK, QPSK} in the left, middle, and right subfigures of Fig. 4.6 respectively.1
Similar to those examined in Fig. 4.6, we shows the modulation classification error for one RE in Fig. 4.7, where the modulation schemes of of i1 and i2 are now randomly chosen with equal probability from QPSK and 16QAM. Figure 4.7 again confirms that high-order modulations are favored in decision, particularly at the low SNR region.
Next, we examine the thresholds for unfair voting when taking N = 8 and N = 16 REs in Figs. 4.8 and 4.9, respectively. The interference modulation scheme to be compared is the modified GLRT in [14]. Note that since the number of total votes is an even number, we set the thresholds Vbias to be also even as for example setting Vbias= 0
1It can be verified that the simulation result for the modulation scheme of i1and i2being{16QAM, QPSK} is identical to that of i1 and i2 being{QPSK, 16QAM}. Therefore, we omit such case in Fig.
4.6.
16 16.5 17 17.5 18 18.5 19
Figure 4.6: Modulation classification errors. The modulation schemes of i1 and i2 are set as {16QAM, 16QAM}, {QPSK, 16QAM}, {QPSK, QPSK} from left to right in the three subfigures, respectively.
is equivalent to setting Vbias = 1, setting Vbias = 2 is equivalent to setting Vbias = 3, etc. In order to reduce the modulation classification error, we determine the threshold according to
minVbias{max{Pr(QPSK|16QAM), P (16QAM|QPSK)}}.
We then found that Vbias = 2 and Vbias = 6 achieve the above minimization values respectively for N = 8 and N = 16.
After identifying the Vbias, we next compare the performance of unfair voting with that of the modified GLRT [14]. In Fig. 4.10, the incorrect modulation classification error rates respectively using unfair voting and the modified GLRT are illustrated for both N = 8 and N = 16. In Fig. 4.11, the average complexity per receive antenna and the number of paths stored during the modulation classification stage are presented.
Notably, the number of paths stored can be regarded as an index of memory storage required for the proposed algorithm. We can see from the two figures that the modified GLRT outperforms the proposed unfair voting in classification error rate; however, the superiority in classification error rate of the modified GLRT is obtained at the cost of a
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0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
SNR
Modulation Classification Error Rate
Pr( 16QAM | QPSK ) Pr( QPSK | 16QAM )
Figure 4.7: Modulation classification error. Modulation schemes of i1 and i2 are ran-domly chosen from QPSK and 16QAM.
higher complexity and higher storage requirement. The high complexity of the modified GLRT is due to that it checks the metrics of all possible hypotheses. In the scenario we simulated, the modified GLRT needs to examine the four cases of i) i1 ∈ QPSK and i2 ∈ QPSK, ii) i1 ∈ 16QAM and i2 ∈ QPSK, iii) i1 ∈ QPSK and i2 ∈ 16QAM, and iv) i1 ∈ 16QAM and i2 ∈ 16QAM. In addition, to determine the ML path as well as the ML path’s metric for each hypothesis, the SESD algorithm should be executed four times.
During this process, all information for each candidate path needs to be stored. For the above reasons, the modified GLRT requires a much higher complexity and storage requirement than our proposed unfair voting.
We would like to add at the end of this discussion that the complexity and the num-ber of paths required to be stored for the modified GLRT are actually proportional to the number of hypotheses, while those of the proposed unfair voting, are only propor-tional to Ni (i.e., the number of interferences), where the number of hypotheses grows exponentially as Ni increases.
In this thesis, we only consider QPSK and 16QAM as candidate modulation schemes
16 17 18 19 10−4
10−3 10−2 10−1 100
SNR
Pr(QPSK|16QAM)
Vbias=0 Vbias=2 Vbias=4
16 17 18 19
10−4 10−3 10−2 10−1 100
SNR
Pr(16QAM|QPSK)
Vbias=0 Vbias=2 Vbias=4
Figure 4.8: Classification errors for different Vbias subject to N = 8
for intereferences. If 64QAM is additionally considered, then the complexity of the GLRT may grow dramatically and become impractical.
On the other hand, the performance gap in Fig. 4.10 regarding Pr(16QAM|QPSK) may look huge; however, Figure 4.12 indicates that the simulated BLERs of the modified GLRT and the proposed unfair voting are not that deviated. We may accordingly conclude that the proposed unfair voting can achieve similar performance to the modified GLRT with a much smaller complexity and its simplicity in implementation makes it a suitable candidate for hardware implementation.
16 17 18 19 10−4
10−3 10−2 10−1 100
SNR
Pr(QPSK|16QAM)
Vbias=0 Vbias=2 Vbias=4 Vbias=6 Vbias=8
16 17 18 19
10−4 10−3 10−2 10−1 100
SNR
Pr(16QAM|QPSK)
Vbias=0 Vbias=2 Vbias=4 Vbias=6 Vbias=8
Figure 4.9: Classification errors for different Vbias subject to N = 16
16 17 18 19 10−4
10−3 10−2 10−1 100
SNR
Pr(QPSK|16QAM)
Unfair Voting, N=8, Vbias=2 Unfair Voting, N=16, Vbias=6 Modified GLRT, N=8 Modified GLRT, N=16
16 17 18 19
10−4 10−3 10−2 10−1 100
SNR
Pr(16QAM|QPSK)
Unfair Voting, N=8, Vbias=2 Unfair Voting, N=16, Vbias=6 Modified GLRT, N=8 Modified GLRT, N=16
Figure 4.10: Modulation classification error rate for unfair voting and the modified GLRT
16 17 18 19 5
10 15 20 25 30 35 40
SNR
Average Complexity Per Receive during Modulation Classification Stage
Unfair Voting, N=8, V bias=2 Unfair Voting, N=16, Vbias=6 Modified GLRT, N=8 Modified GLRT, N=16
16 17 18 19
10 20 30 40 50 60 70 80 90
SNR
Number of Paths stored during Modulation Classification Stage
Unfair Voting, N=8, V bias=2 Unfair Voting, N=16, Vbias=6 Modified GLRT, N=8 Modified GLRT, N=16
Figure 4.11: Average complexity and the numbers of paths stored during the modulation classification stage
16 16.5 17 17.5 18 18.5 19 10−3
10−2 10−1
SNR
BLER
Unfair Voting, N=8, V
bias=2 Unfair Voting, N=16, V
bias=6 Modified GLRT, N=8 Modified GLRT, N=16
Figure 4.12: Block error rate of the modified GLRT and the proposed unfair voting