In this section, we evaluate the performance of STC-OFDM systems by simulation. In the simulations, we choose a 16-state space-time trellis coded QPSK with two transmit antennas. The OFDM-1 modulation format is employed. The OFDM has 256 sub-carriers.
During each OFDM frame, a block of 512 information bits is encoded to generate two coded QPSK sequences of length 256, each of which is interleaved and OFDM modulated on 256 sub-carriers. The two modulated sequences are transmitted from two transmit antennas simultaneously. In the trellis encoder, we require that the initial and the final states of each frame are all-zero states. This can be done by setting the last four bits of the input block to be zero. Considering the tail bits of the trellis encoder and the guard interval of the OFDM modulation, the bandwidth efficiency of the STC-OFDM system is
η=2×256 296×508
512 =1.72 bits/s/Hz (8.40)
8.6.1 Performance on A Single-Path Fading Channel
A single-path fading channel is conceptually equivalent to a quasi-static frequency- nonselective fading channel [5]. In Fig. 8.5, the performance of the STC-OFDM on a single- path fading channel is shown. In the simulation, one receive antenna is employed. Since nT = 2, nR = 1, and Lp = 1, the scheme achieves a diversity gain of LpnTnR = 2.
The figure shows that no benefit can be obtained with OFDM on a quasi-static frequency- nonselective fading channel. Also, interleavers cannot improve the code performance, since the channel is quasi-static.
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10−3 10−2 10−1 100
SNR (dB)
Frame Error Rate
16−state, STC−OFDM 16−state, STC
Figure 8.5 Performance of STC-OFDM on a single-path fading channel
Performance Evaluation of STC-OFDM Systems 259
5 10 15 20 25
10−4 10−3 10−2 10−1 100
SNR (dB)
Frame Error Rate
16−state, with INT 16−state, without INT
Figure 8.6 Performance of STC-OFDM on a two-path equal-gain fading channel with and without interleavers
8.6.2 The Effect of The Interleavers on Performance
Figure 8.6 shows the performance comparison for the 16-state STC-OFDM scheme on a two-path equal-gain fading channel with and without interleavers in the transmitter [10].
The delay between the two paths is 5às. It is obvious that the random interleavers help to improve the code performance significantly. At the FER of 10−2, the STC-OFDM with interleavers is 3.8 dB better than the scheme without interleavers.
8.6.3 The Effect of Symbol-Wise Hamming Distance on Performance
Figure 8.8 shows the performance of two STC-OFDM schemes on a two-path equal-gain fading channel [10]. The delay between the two paths is 5à s. The first scheme is a 16-state space-time trellis coded QPSK, whose symbol-wise Hamming distance is 3. The other scheme is a 256-state space-time trellis coded QPSK, which is modified based on the conventional optimum rate 2/3, 256-state trellis coded 8-PSK scheme on flat fading channels with single transmit antenna [12]. In this modification, the original 8-PSK mapper is split into two QPSK mappers and the original rate 2/3 8-PSK scheme for single transmit antenna is transformed into a rate 2/4 2×QPSK code for two transmit antennas as shown in Fig. 8.7 [10]. After the modification, the space-time code has the same symbol-wise Hamming distance as the original code. For the 256-state code, the symbol-wise Hamming distance is 6. Comparing the performance in Fig. 8.8, we can see that the 256-state code performs much better than the 16-state code due to a larger symbol-wise Hamming distance. At the FER of 10−2, the performance gain is about 4 dB. In this system, asnT =2, nR=1, andLp =2, the maximum possible diversity isLpnTnR =4. For the 256-state code, δH =6, which is larger thanLpnT =4, so that the diversity gain is LpnT. It can achieve the maximum
b1 b2
Rate 2/3 Trellis Encoder
v0 v1 v2
QPSK Mapper QPSK Mapper
x1 x2
Figure 8.7 An STTC encoder structure
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SNR (dB)
Frame Error Rate
16−state 256−state
Figure 8.8 Performance of STC-OFDM with various number of states on a two-path equal-gain fading channel
diversity of 4. However, for the 16-state code,δH =3, which is less thanLpnT =4, so the diversity gain is δHnR =3. This code cannot achieve the maximum diversity. Therefore, we can conclude that the symbol-wise Hamming distance of the code plays an important role in the STC-OFDM performance on frequency-selective fading channels.
8.6.4 The Effect of The Number of Paths on Performance
In this section, we briefly discuss the impact of the number of paths Lp on the system performance. Figure 8.9 depicts the performance of the 16-state STC-OFDM scheme on a two-path and six-path equal-gain fading channel. For the two-path channel, the delay between the two paths is 40 às. For the six-path channel, six paths are equally spread with the delay of 6.5 às between adjacent paths. The figure indicates that the code performance slightly improves when the number of paths increases.
Performance of Concatenated Space-Time Codes Over OFDM Systems 261
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10−4 10−3 10−2 10−1 100
SNR (dB)
Frame Error Rate
two−path six−path
Figure 8.9 Performance of STC-OFDM on various MIMO fading channels