In this section, we present computer simulation examples to show the detection perfor- mance and the complexity of the proposed multiuser detector for QPSK symbols. We assume the simulation channel is perfect power control with AWGN, where the users em- ploy randomly generated spreading codes. We choose Mb = 15 and Nu = 300. The
Single-user BER performance is obtained by theoretical calculation. Fig. 5.1 shows the BER performance of the DCD-BTN-M detector. The number of users is K = 4, the spreading factor is SF = 4. It can be seen that the performance is poor. Therefore, the DCD-BTN-M detector is not suited for the small system size.
Fig. 5.2 shows the bit error rate (BER) performance of the proposed multiuser detector in comparison with MMSE detector in the scenario of K = 40 and SF = 63. It shows that
CHAPTER 5. THE DCD-BTN-M DETECTOR FOR M-PSK SYMBOLS 83 0 2 4 6 8 10 12 14 10−4 10−3 10−2 10−1 100 SNR,dB BER N=1, c=1 N=1, c=2 N=1, c=3 N=1, c=4 N=1, c=5 MMSE
Single−user BER (approx.)
Figure 5.2:The effect of the constant c on BER performance of the DCD-BTN-M detector when N = 1 in the scenario of K = 40, SF = 63, Mb= 15.
MMSE detector is inferior to the proposed detector. The simulation results also show the effect of the constant c on the BER performance of the proposed detector. It shows that when N = 1, the increase of c can slightly improve the BER performance of this proposed detector at high SNRs. The performance cannot be further improved when c > 4. When
c = 4, the difference in the performance compared to the single user bound is 1.5 dB at
BER of 10−4.
Fig. 5.3 shows the effect of the number of Tikhonov iterations N and the constant c on the BER performance of the proposed detector in the scenario of K = 40, SF = 63. When c varies from 1 to 4, increase in N can slightly improve the BER performance of the proposed detector at high SNRs. The symbol error rate (SER) performance in Fig. 5.4 and the group detection error (GDE) performance in Fig. 5.5 also show this.
Fig. 5.6 shows the complexity of the proposed detector in the scenario of K = 40 and SF = 63. It can be seen that when N = 4, this detector with c = 4 significantly reduces the complexity compared to that with c = 1. When N = 1, the detector with c = 4 has lower average complexity than that with c = 1, and also has a lower worst-case complexity at
CHAPTER 5. THE DCD-BTN-M DETECTOR FOR M-PSK SYMBOLS 84 0 2 4 6 8 10 12 14 10−4 10−3 10−2 10−1 100 SNR, dB BER
Single−user BER (approx.) c=1,N=4
c=1,N=1 c=4,N=1 c=4,N=4
Figure 5.3: BER performance of the DCD-BTN-M detector in the scenario of K = 40, SF = 63, Mb = 15.
low SNRs.
Fig. 5.7 shows the BER performance of the proposed multiuser detector in comparison with MMSE detector in the highly loaded scenario of K = 60 and SF = 63. It shows that MMSE detector is inferior to the proposed detector. Increase in N cannot significantly improve the performance of this detector. Fig. 5.8 and Fig. 5.9 show the SER and GDE performance of the proposed detector, respectively. At SER = 10−4, this proposed de-
tector has approximately 2 dB difference to the single user bound. Increase in N cannot significantly improve the detection performance of proposed detector. Fig. 5.10 shows that the complexity of this proposed detector linearly increases with the increase of N. We also can see that this proposed detector with c = 4, and N = 1 has almost constant complexity when SNR > 8 dB.
CHAPTER 5. THE DCD-BTN-M DETECTOR FOR M-PSK SYMBOLS 85 0 2 4 6 8 10 12 14 10−6 10−5 10−4 10−3 10−2 10−1 100 SNR, dB SER Single−user c=1,N=4 c=1,N=1 c=4,N=1 c=4,N=4
Figure 5.4:SER performance of the DCD-BTN-M detector in the scenario of K = 40, SF = 63, Mb = 15.
5.5 Conclusions
In this chapter, we further exploit the DCD-BTN detector and propose the DCD-BTN- M detector for M-PSK symbols. Numerical results show that the DCD-BTN-M detector is suitable for detection of the complex-valued symbols and provides better detection performance in comparison with the MMSE detector. The type of constrained used in the DCD-BTN-M detector is most suitable for M-PSK constellation. It can also be used for QAM symbols. However, for QAM symbols, this constrained is not tight enough. Therefore, for QAM symbols, the detection performance can be worse than that for M- PSK symbols.
CHAPTER 5. THE DCD-BTN-M DETECTOR FOR M-PSK SYMBOLS 86 0 2 4 6 8 10 12 14 10−4 10−3 10−2 10−1 100 SNR, dB
Group Detection Error
c=1,N=4 c=1,N=1 c=4,N=1 c=4,N=4
Figure 5.5: GDE performance of the DCD-BTN-M detector in the scenario of K = 40, SF = 63, Mb = 15.
CHAPTER 5. THE DCD-BTN-M DETECTOR FOR M-PSK SYMBOLS 87 0 2 4 6 8 10 12 14 1 2 3 4 5 6 7 8x 10 4 SNR, dB Number of additions Worst−case c=1,N=4 Average c=1,N=4 Worst−case c=1, N=1 Average c=1,N=1 Worst−case c=4, N=1 Average c=4, N=1 Worst−case c=4, N=4 Average c=4, N=4
Figure 5.6: The complexity of the DCD-BTN-M detector in the scenario of K = 40, SF = 63, Mb = 15.
CHAPTER 5. THE DCD-BTN-M DETECTOR FOR M-PSK SYMBOLS 88 0 2 4 6 8 10 12 14 10−4 10−3 10−2 10−1 100 SNR, dB BER c=4, N=1 c=4, N=2 c=4, N=3 MMSE
Single−user BER (approx.)
Figure 5.7: BER performance of the DCD-BTN-M detector in the scenario of K = 60, SF = 63, Mb = 15.
CHAPTER 5. THE DCD-BTN-M DETECTOR FOR M-PSK SYMBOLS 89 0 2 4 6 8 10 12 14 10−6 10−5 10−4 10−3 10−2 10−1 100 SNR, dB SER Single−user c=4, N=1 c=4, N=2 c=4, N=3
Figure 5.8:SER performance of the DCD-BTN-M detector in the scenario of K = 60, SF = 63, Mb = 15.
CHAPTER 5. THE DCD-BTN-M DETECTOR FOR M-PSK SYMBOLS 90 0 2 4 6 8 10 12 14 10−4 10−3 10−2 10−1 100 SNR, dB
Group Detection Error c =4, N =1
c =4, N =2 c =4, N =3
Figure 5.9: GDE performance of the DCD-BTN-M detector in the scenario of K = 60, SF = 63, Mb = 15.
CHAPTER 5. THE DCD-BTN-M DETECTOR FOR M-PSK SYMBOLS 91 0 2 4 6 8 10 12 14 2 3 4 5 6 7 8 9x 10 4 SNR, dB Number of additions Worst−case c = 4, N = 1 Average c = 4, N = 1 Worst−case c =4, N =2 Average c =4, N =2 Worst−case c =4, N = 3 Average c= 4, N =3
Figure 5.10: Complexty of the DCD-BTN-M detector in the scenario of K = 60, SF = 63, Mb = 15.
Chapter 6
Multiple Phase Detection of M-PSK
Symbols
Contents
6.1 Introduction . . . 92 6.2 Problem Formulation . . . 94 6.3 Phase Descent Search Algorithm . . . 94 6.4 Multiple Phase Decoder . . . 98 6.5 Simulation Results for MPD in Multiuser Detection . . . 99 6.6 Simulation Results for MPD in MIMO Detection . . . 105 6.7 MPD Implementation Issues . . . 107 6.8 Conclusions . . . 110
6.1 Introduction
In multiple-access CDMA systems, multiuser detection is capable of providing high de- tection performance [9]. However, the complexity of multiuser detectors that are capable of approaching the optimal performance is still a very important issue. For a small-size problem, sphere decoding achieves a nearly optimal performance [97], but becomes com- plicated when the size of the problem increases [98]. Semi-definite relaxation (SDR) has also been proposed and investigated for joint detection of a number of symbols with
Z. Quan, Ph.D. Thesis, Department of Electronics, University of York
92
CHAPTER 6. MULTIPLE PHASE DETECTION OF M-PSK SYMBOLS 93
M-PSK modulation [12]. Although, promising for multiuser detection, SDR is still com- plicated for practical implementation [99].
In the MIMO wireless systems, ML decoder offers performance advantages over sophisti- cated sub-optimal detectors [100, 101]. The sphere decoders using depth-first tree search can provide the optimal ML decoding performance, while retaining a lower complex- ity [102]. Branch and bound based ML decoders have also been proposed for implemen- tation of ML detectors [39]. However, the computational complexity of depth-first sphere decoders and branch and bound decoders rely on a careful choice of initial sphere radius; if the initial radius is too small, new search has to be restarted and redundant computations occur [103].
In this chapter, we propose a new technique, multiple phase decoder (MPD), for solv- ing the quadratic optimization problem. The MPD is based on a phase descent search (PDS) algorithm. The PDS algorithm is based on coordinate descent iterations, where coordinates are unknown symbol phases, while constraints the symbols to have a unit magnitude. The MPD is investigated for detection of M-PSK symbols in multiuser and MIMO systems. In the multiuser detection, the MPD can be applied to highly loaded scenarios and the numerical results show that the MPD can provide the near-optimal per- formance and allow low complexity. In the MIMO detection, the MPD exhibits more favorable performance/complexity characteristics and can be considered as a promising alternative to the sphere decoder for decoding in MIMO systems.
This chapter is organized as follows. In Section 6.2, the problem formulation is presented. In Section 6.3 proposes the phase descent search algorithm. Section 6.4 proposes the multiple phase detection for M-PSK symbols. Section 6.5 presents the simulation results of the multiple phase detection in multiuser, and the simulation results of the multiple phase detection in MIMO system are shown in section 6.6. Section 6.7 proposes the hardware implementation issues for the multiple phase detection. Section 6.8 concludes the chapter.
CHAPTER 6. MULTIPLE PHASE DETECTION OF M-PSK SYMBOLS 94
6.2 Problem Formulation
The multiuser and MIMO detection deal with the channel model can be considered to
z = Gh + n , (6.1)
where h, z are K × 1 vectors, G is a K × K symmetric positive definite matrix, n is a
K × 1 zero mean Gaussian random vector with variance σ2. The vector h can be found by ˆ h = arg min h∈AKkz − Ghk 2 = arg min h∈AK ¡ hHRh − 2<{θHh}¢. (6.2) We denote J(h) = hHRh − 2<{θHh} , (6.3)
the quadratic cost function, R = GHG, and θ = GHz. The ML detector provides the op-
timal detection performance. However the complexity of the ML detector is exponential in the constellation set A and the number of users K (in multiuser detection) or transmit antennas (in MIMO communications).