In this chapter, we have derived an analytical expression for the PPM signal in an UWB channel characterized by the cluster effect and highly dense frequency selective fading. Furthermore, we have demonstrated that the time-switched transmit diversity combined with the template-based pulse detection can improve the performance of the PPM based UWB system.
Through analysis and simulations, we have the following two major re-marks:
• Although multiple transmit or receive antennas cannot deliver diver-sity gain for the UWB system in the strict sense (i.e., improving the slope of BER v.s. SNR), multiple transmit antennas can improve the system performance in the manner of reducing signal variations. Thus, transmit antennas can be used to reduce receiver complexity since the number of fingers of a Rake receiver in the UWB system can be very high.
• Multiple receive antennas can provide higher antenna array combining gain. Because the transmitted power in the UWB system is extremely low, multiple receive antennas techniques can be an effective approach to improve the performance from the view point of coverage extension.
Table 4.1: System Parameters
The UWB pulse width 1 ns
The sampling time (time bin) 1 ns
Simultaneous arrival path number n A modified Poisson process.
μH 2/3
μL 1/3
Average resolvable path power Exponential decay.
γ −5 dB
β 0.025
The PDF of the received signal power Gamma distribution.
The diversity schemes
1) no diversity, Tx1-Rx1, 2) receive diversity, Tx1-Rx2, 3) transmit diversity, Tx2-Rx1, 4) transmit diversity, Tx1-Rx4,
5) MIMO, Tx2-Rx2.
The modulation schemes PPM
The frame number f 2
The RAKE finger number L 10, 30, 50, 100, or 200 The delay time δ associated with PPM 1 ns
Figure 4.1: The diversity schemes: a) no diversity, b) receive diversity, and c) time-switched transmit diversity.
0 0.5 1 1.5 2 2.5 x 10−7 0
0.2 0.4 0.6 0.8 1 1.2 1.4
Time (second)
Amplitude (normalize to the first path)
Figure 4.2: An example of the UWB channel response in the time domain.
0 50 100 150 200 250 4
5 6 7 8 9 10 11 12 13 14
Rake Finger Number (L)
SNR (dB)
simulation (Receive Diversity) analysis (Receive Diversity) simulation (No Diversity) analysis (No Diversity) simulation (Transmit Diversity) analysis (Transmit Diversity)
Figure 4.3: Analytical and simulation results for the SNR of the PPM signals over the UWB channel with multiple transmit and receive antennas.
0 50 100 150 200 250 101
102
Rake Finger Number (L)
Variance
Receive Diversity (simulation) Receive Diversity (analysis) No Diversity (simulation) No Diversity (analysis) Transmit Diversity (simulation) Transmit Diversity (analysis)
Figure 4.4: Analytical and simulation results for the variance of the PPM signals over the UWB channel with multiple transmit and receive antennas.
40 60 80 100 120 140 160 180 200 220 240 101.1
101.2 101.3 101.4 101.5
Rake Finger Number (L)
Variance
ρ = 0 (simulation) ρ = 0 (analysis) ρ = 1/3 (simulation) ρ = 1/3 (analysis) ρ = 2/3 (simulation) ρ = 2/3 (analysis) ρ = 1 (simulation) ρ = 1 (analysis)
Figure 4.5: Effect of spatial correlation of transmit diversity on the variance of the PPM signals over the UWB channel.
−7 −5 −3 −1 1 3 5 7 9 10−4
10−3 10−2 10−1
Eb/N0 (dB)
BER
Tx1 Rx1 L50 f2 δ1 Tx2 Rx1 L50 f2 δ1 Tx1 Rx2 L50 f2 δ1 Tx2 Rx2 L50 f2 δ1 Tx1 Rx4 L50 f2 δ1
Figure 4.6: The BER simulation results for the different diversity schemes in the PPM UWB system. Here, Tx and Rx represent the transmit and the receive antenna numbers, respectively, L represents the RAKE finger number, f represents the frame number, and δ represents the modulation index with PPM.
1 2 3 4 5 6 7 8 9 10 11 10−4
10−3 10−2 10−1
Eb/N0 (dB)
BER
Tx1 Rx1 L10 f2 δ1 Tx2 Rx1 L10 f2 δ1 Tx1 Rx1 L30 f2 δ1 Tx2 Rx1 L30 f2 δ1 Tx1 Rx1 L50 f2 δ1 Tx2 Rx1 L50 f2 δ1 Tx1 Rx1 L100 f2 δ1 Tx2 Rx1 L100 f2 δ1 Tx1 Rx1 L200 f2 δ1 Tx2 Rx1 L200 f2 δ1
Figure 4.7: The BER simulations of the PPM UWB system with the different RAKE finger numbers, where Tx and Rx represent the transmit and the receive antenna numbers, respectively, L represents the RAKE finger number, f represents the frame number, and δ represents the modulation index with PPM.
Chapter 5
BER-Minimized
Space-Time-Frequency Codes for MIMO Highly
Frequency-Selective
Block-Fading Channels
In this chapter, we present bit error rate (BER)-minimized space-time-frequency (STF) block codes for multi-input multi-output (MIMO) highly frequency-selective block-fading channels. We consider the IEEE 802.15.3a ultra-wide band (UWB) channel models (CM) 1–4. Based on a new STF block codes design criterion with the objective of minimizing BER, we develop an ef-ficient searching algorithm for the design of the optimal STF block codes which maximize the coding gain. For 128 subcarriers with two subcarriers jointly encoding with 2–4 transmitting antennas, we find that the optimal STF block codes for all the IEEE 802.15.3a UWB channel models CM 1–
4 can be found. Furthermore, the designed STF block codes outperform the recently published high-rate full-diversity STF codes [1] by 1 dB. Last, the proposed STF codes can be decoded by maximum likelihood decoding approach, which is simpler than the sphere decoding principle used in [1].
5.1 Motivation
The space-time-frequency (STF) coding is a technique which provides error control ability in multi-input multi-output (MIMO) systems, which are usu-ally combined with the orthogonal frequency-division multiplexing (OFDM) technology. The main purpose of using the STF coding is to achieve the full diversity gain. For example, in [1], the authors proposed STF codes which achieve the diversity gain of NtNrKL, where Nt is the number of transmit antennas, Nr is the number of receive antennas, K is the number of indepen-dent fading blocks in one codeword, and L is the number of taps of channel impulse response (CIR) between any pair of transmit and receive antennas.
The space diversity, time diversity, and frequency diversity are NtNr, K, and L, respectively.
However, in a highly frequency-selective fading channel, the number of taps of CIR could be very large. For example, in the IEEE 802.15.3a UWB channel model [98], the number of taps of CIR is infinity theoretically and about 1000 to 2000 practically. Thus, it is difficult to achieve the full fre-quency diversity under the highly frefre-quency-selective fading channel. Thus, it motivates us to turn to a more fundamental problem: How to design BER-minimized STF codes for MIMO highly frequency-selective block-fading channels? Here the block-fading channel is defined as follows: The channel remains the same within one fading block and is independent from one block
to another one [1].
The difficulties of design BER-minimized STF block codes for the MIMO highly frequency-selective block-fading channels can be discussed in three aspects. Note that we take the IEEE 802.15.3a UWB channel model as an example in this chapter.
1. First, the IEEE 802.15.3a channel model has four different sets of pa-rameters, named CM1, CM2, CM3, and CM4. For different channels, we have to design different codes to reflect the channel characteristics.
One challenging issue arises: Is there a universal code which is opti-mal for all the four channel models CM 1 ∼ 4 for given numbers of subcarriers and transmit antennas?
2. As the numbers of subcarriers and transmit antennas increase, the num-ber of all possible codes becomes astronomical. Thus, the second chal-lenge is to search the optimal codes efficiently.
3. Because traditional STF coding methods focus on linear codes, it will be challenging to examine if there exist nonlinear optimal STF block codes.
To our best knowledge, the design of STF block codes for the MIMO-OFDM systems under the IEEE 802.15.3a channel models considering all the three aforementioned challenges has not been seen in the literature.