5.5 Properties of the Optimal STF Block Codes
5.6.3 Effect of Number of Transmit Antennas Jointly En-
En-coded (M = 3)
Figure 5.5 shows the effect of number of transmit antennas jointly encoded on the BER for CM1, CM2, CM3, and CM4 for the optimal STF block codes for the M = 3 and Ni = 2 case. The modulation is BPSK. The sub-figures (a), (b), and (c) correspond to the cases Nt = 2, 3, and 4, respectively. As the same in the M = 2 case, when the number of channel model increases, the BER decreases. However, unlike the M = 2 case which has diversity order of 2, the M = 3 case has diversity order of 2 for the Nt = 2 and CM
= 1, 2, Nt = 3 and CM = 1 cases. The diversity order equals to 3 for other cases. This can be seen both from Fig. 5.5 and Table 5.3. Moreover, as the number of transmit antennas Nt increase, the BER decreases. Thus, the optimal STF block codes in the M = 3 case improve the BER performance when Nt increases. In the M = 2 case, this phenomenon does not occur. On the other hand, compared with the M = 2 case, the M = 3 case has better BER performance. Hence, increasing the number of subcarriers which are jointly encoded also improves the BER performance.
5.6.4 Effect of Number of Transmit Antennas Jointly Encoded (N
t) for Four Subcarriers Jointly En-coded (M = 4)
Figure 5.6 shows the effect of number of transmit antennas jointly encoded on the BER for CM 1 ∼ 4 for the optimal STF block codes for M = 4 and Ni = 2. Figs. 5.6(a) and 5.6(b) show the BER for Nt = 23, respectively.
Like the M = 3 case, the BER decreases as CM or Nt increase. Different CM have different diversity orders. The M = 4 case also has better BER performance than the M = 3 case does.
5.6.5 BER Comparison with STF Codes in [1] and [2]
Figure 5.7 shows the BER comparison of our code with Chusing’s code [2]
and Zhang’s code [1] for the M = 4, Ni = 2, Nr = 1, Nt = 2 case in the IEEE 802.15.3a UWB channel model CM4. We can see that the diversity gains of the three codes are the same, but our code has better BER performance than Chusing’s and Zhang’s codes do. At BER = 10−4, the coding gain between our code and Chusing’s code is about 8 dB and the coding gain between our code and Zhang’s code is about 1 dB.
5.7 Conclusions
In this chapter, we study the BER-minimized STF block codes design for the MIMO highly frequency-selective block fading channels. We consider the IEEE 802.15.3a UWB channel model. Based on the BER analysis under the aforementioned environment in [19], we provide a BER-minimized design criterion, an efficient searching algorithm for the optimal STF block codes,
and optimal BER performance curves. Among our proposed optimal STF block codes, we find that almost all of them need nonlinear operations in the encoder. Thus it is necessary to consider nonlinear codes when we design the optimal STF block codes for the MIMO-OFDM systems under the IEEE 802.15.3a UWB channel model. When the number of subcarriers M which are jointly encoded is equal to two and the number of transmit antennas Nt is 2 ∼ 4 or M = 3, Nt = 4, the optimal STF block codes for all the IEEE 802.15.3a UWB channel models CM 1 ∼ 4 can be found according to the proposed code search algorithm in the above considered cases. When 1) M = 3, Nt= 2∼ 3, and 2) M = 4, Nt= 2∼ 3, there does not exist optimal STF block codes for all the four UWB channel models. We also find that the BER decreases as CM increases, i.e., our optimal STF block codes provide better BER performance when the channel fading is more severe. On the other hand, increasing the number of transmit antennas does NOT improve the BER performance for the MIMO-UWB systems when M = 2. This is similar to the case of the uncoded MIMO-UWB systems but opposite to the STBC case. However, increasing the number of received antennas improves the BER performance for the MIMO-UWB systems. This is similar to the STBC case. We also find that the diversity order is different for different CM in the M = 3∼ 4, Nt= 2∼ 3 cases. Compared with other STF codes [1,2]
for multiband UWB-MIMO communication systems, our code has about 1 and 8 dB coding gain at BER = 10−4, respectively.
Information Bits b1b2
STF Block Encoder
OFDM Modulator
IEEE 802.15.3a UWB Channel
Output Bits ML STF Block Decoder
OFDM Demodulator
»¼
« º
¬ ª
22 21
12 11
d d
d
d d11
d21
d12
d22
Figure 5.1: The system block diagram.
1 2 3
5 4 6
7
8
9
10
11
12 13 14
15
16
(a)
1 2 3
5 4 6
7
8
9
10
11
12 13 14
15
16
(b)
(c)
Figure 5.2: Illustration of our proposed efficient searching algorithm for the optimal STF block codes for two subcarriers jointly encoded, two transmit antennas jointly encoded, and two input information bits for each codeword.
We search complete graphs with four vertices subject to the largest m metrics.
(a) m = 1. (b) m = 2. (c) m = 3.
0 2 4 6 8 10 12 14 16 18 20 10−5
10−4 10−3 10−2 10−1 100
Eb / N0 (dB)
Bit Error Rate
CM1 CM2 CM3 CM4
(a)
0 2 4 6 8 10 12 14 16 18 20 10−5
10−4 10−3 10−2 10−1 100
Eb / N0 (dB)
Bit Error Rate
CM1 CM2 CM3 CM4
(b)
0 2 4 6 8 10 12 14 16 18 20 10−5
10−4 10−3 10−2 10−1 100
Eb / N0 (dB)
Bit Error Rate
CM1 CM2 CM3 CM4
(c)
Figure 5.3: The effect of different number of transmit antennas jointly en-coded (Nt) on the BER for CM1, CM2, CM3, and CM4 for the optimal STF block codes for two subcarriers jointly encoded and two input information bits for each codeword. The modulation is BPSK. (a) Nt = 2. (b) Nt = 3.
(c) Nt= 4.
0 2 4 6 8 10 12 14 16 18 20 10−5
10−4 10−3 10−2 10−1 100
Eb / N0 (dB)
Bit Error Rate
Nr=1,CM1 Nr=1,CM2 Nr=1,CM3 Nr=1,CM4 Nr=2,CM1 Nr=2,CM2 Nr=2,CM3 Nr=2,CM4
Figure 5.4: The effect of number of receive antennas (Nr) on the BER for CM1, CM2, CM3, and CM4 for the optimal STF block codes for two sub-carriers jointly encoded, two input information bits for each codeword, and two transmit antennas jointly encoded. Nr = 1 and 2. The modulation is BPSK.
0 2 4 6 8 10 12 14 16 18 20 10−4
10−3 10−2 10−1 100
Eb / N0 (dB)
Bit Error Rate
CM1 CM2 CM3 CM4
(a)
0 2 4 6 8 10 12 14 16 18 20 10−4
10−3 10−2 10−1 100
Eb / N0 (dB)
Bit Error Rate
CM1 CM2 CM3 CM4
(b)
0 2 4 6 8 10 12 14 16 18 20 10−4
10−3 10−2 10−1 100
Eb / N 0 (dB)
Bit Error Rate
CM1 CM2 CM3 CM4
(c)
Figure 5.5: The effect of number of transmit antennas jointly encoded (Nt) on the BER for CM1, CM2, CM3, and CM4 for the optimal STF block codes for three subcarriers jointly encoded and two input information bits for each codeword. The modulation is BPSK. (a) Nt = 2. (b) Nt= 3. (c) Nt= 4.
0 2 4 6 8 10 12 14 16 18 20 10−4
10−3 10−2 10−1 100
Eb / N0 (dB)
Bit Error Rate
CM1 CM2 CM3 CM4
(a)
0 2 4 6 8 10 12 14 16 18 20 10−4
10−3 10−2 10−1 100
Eb / N 0 (dB)
Bit Error Rate
CM1 CM2 CM3 CM4
(b)
Figure 5.6: The effect of number of transmit antennas jointly encoded (Nt) on the BER for CM1, CM2, CM3, and CM4 for the optimal STF block codes for four subcarriers jointly encoded and two input information bits for each codeword. The modulation is BPSK. (a) Nt = 2. (b) Nt= 3.
0 2 4 6 8 10 12 14 16 18 20 10−4
10−3 10−2 10−1 100
Eb / N0 (dB)
Bit Error Rate
Chusing‘s Code Zhang‘s Code Our Code
Figure 5.7: The BER comparison of our code versus Zhang’s code [1] and Chusing’s code [2] for three subcarriers jointly encoded, two input informa-tion bits for each codeword, one receive antenna, and three transmit antennas jointly encoded in the IEEE 802.15.3a UWB channel model CM4. The mod-ulation is BPSK.
Chapter 6
Statistical Analysis of A
Mobile-to-Mobile Rician Fading Channel Model
Mobile-to-mobile communication is one of the important applications for the intelligent transport systems and mobile ad hoc networks. In these systems, both the transmitter and receiver are in motion, subjecting to the signals to Rician fading and different scattering effects. In this chapter, we present a double-ring with a LOS component scattering model and a sum-of-sinusoids simulation method to characterize the mobile-to-mobile Rician fading chan-nel. The developed model can facilitate the physical layer simulation for a mobile ad hoc communication systems. We also derive the autocorrelation function, level crossing rate (LCR), and average fade duration (AFD) of the mobile-to-mobile Rician fading channel and verify the accuracy by simula-tions.
6.1 Motivation
Mobility affects wireless networks significantly. In traditional cellular sys-tems, the base station is stationary and only mobile terminals are in motion.
However, in many new wireless systems, such as intelligent transport systems (ITS) and mobile ad hoc networks, a mobile connects directly to another mobile without the help of fixed base stations. Thus, how mobility affects a system of which both the transmitter and the receiver move simultaneously becomes an interesting problem.