3.4 Complexity Analysis and Simulation Results
3.4.2 Simulation Results
M(K-Q)!K!
. Finally, the com-plexity of the bit-loading algorithm is O
K
In this subsection, we evaluate the performance of the non-orthogonal precoding scheme and compare it with the performance of the orthogonal precoding scheme (using the low complexity algorithm) described in chapter 2.
The performance of the non-orthogonal precoding scheme and the orthogonal pre-coding scheme for downlink transmissions with different channel matrix rank value is shown in Fig. 3.1 ∼ Fig. 3.3 respectively. The average power is normalized by that of the single-user case, i.e., when a single user has access to all eigenchannels and all subcarriers. We define the average power ratio at BER=B as :
PB = 10 log10
Pavg,B
Pavg,10−5,single
(3.11)
where Pavg,B represents the average transmit power for a given modulation scheme at BER=B and Pavg,10−5,singlerepresents the average transmit power for the single user case at BER=10−5.
We assume the number of the antenna at the BS and the MS are the same. The antenna number is from 3 to 5. Each entry of the channel matrix is i.i.d. zero-mean, unit-variance complex Gaussian The system has eight different modulation modes, BPSK, QPSK, 8QAM, 16QAM, 32QAM, 64QAM, 128QAM and 256 QAM, respectively. For simplicity, we assume that the required data rate and BER are the same for all users.
We can notice that when the rank of the channel matrix is 3, the performance of the non-orthogonal precoding scheme is about 1 dB worse than the orthogonal precoding
scheme. However, when we increase the rank to 4 and 5, the performance of the non-orthogonal precoding scheme is better than the non-orthogonal precoding scheme by 0.7 and 1.8 dB, correspondingly.
The reason for this phenomenon is that for the rank 3 case, we provide 2 orthog-onal eigenchannels and 2 orthogorthog-onal eigenchannels on each subcarrier in the non-orthogonal precoding scheme. However, in the non-orthogonal precoding scheme, we pro-vide 3 orthogonal eigenchannels on each subcarrier in total. This means that for the non-orthogonal precoding scheme, we ”sacrifice” 33% of the orthogonal eigenchannels to get Q non-orthogonal eigenchannels (in this case, Q=2). However, the gain of the non-orthogonal eigenchannels is not enough to compensate the loss of the orthogonal eigenchannels. For rank 4 and rank 5 cases, 25% and 20% of the orthogonal eigen-channels are sacrificed. This implies that when the rank of the MIMO channel matrix is increased, the impact of sacrificing the orthogonal eigenchannels is reduced. But for each case, we still provide Q non-orthogonal eigenchannels to users for the non-orthogonal pre-coding scheme. Therefore, when the rank of the MIMO channel matrix is increased, the advantage of the non-orthogonal pre-coding scheme will begin to appear.
In Fig. 3.4 and 3.5, the performance is not improved as we increase the value of Q. This contradicts the intuition that the larger Q provides more eigenchannels (with interference) than smaller Q. This is because the bit-loading algorithm used in the non-orthogonal precoding scheme is not guaranteed optimal. The optimalty is destroyed by loading the bits to the non-orthogonal eigenchannel. Therefore, the result of the bit-loading algorithm used in the non-orthogonal precoding scheme may be the local optimal solution instead of global optimal solution. Thus, increasing the value of Q will not insure the better performance.
−4 −2 0 2 4 6 8 10 10−5
10−4 10−3 10−2 10−1
BER
Average Power Ratio (dB)
Orthogonal precoding scheme Non−orthogonal precoding scheme
Figure 3.1: Average power ratio per user for a MIMO-OFDM downlink; 32 subcarriers, 128 bits per OFDM symbol, 4 users, rank=3.
−4 −2 0 2 4 6 8 10
10−5 10−4 10−3 10−2 10−1
BER
Average Power Ratio (dB)
Orthogonal precoding scheme Non−orthogonal precoding scheme
Figure 3.2: Average power ratio per user for a MIMO-OFDM downlink; 32 subcarriers, 192 bits per OFDM symbol, 4 users, rank=4.
−4 −2 0 2 4 6 8 10 10−5
10−4 10−3 10−2 10−1
BER
Average Power Ratio (dB)
Orthogonal precoding scheme Non−orthogonal precoding scheme
Figure 3.3: Average power ratio per user for a MIMO-OFDM downlink; 32 subcarriers, 240 bits per OFDM symbol, 4 users, rank=5.
−4 −2 0 2 4 6 8 10
10−5 10−4 10−3 10−2 10−1
BER
Average Power Ratio (dB)
Q=2 Q=3
Figure 3.4: Average power ratio per user for a MIMO-OFDM downlink; 32 subcarriers, 144 bits per OFDM symbol, 4 users, rank=3.
−4 −2 0 2 4 6 8 10 10−5
10−4 10−3 10−2 10−1
BER
Average Power Ratio (dB)
Q=2 Q=3
Figure 3.5: Average power ratio per user for a MIMO-OFDM downlink; 32 subcarriers, 192 bits per OFDM symbol, 4 users, rank=4.
Chapter 4
Resource Allocation for MIMO Systems with Codebook-based Precoding
The precoding schemes we considered so far require complete channel state informa-tion to achieve full performance gain. In a frequency-division duplex system, however, full channel state information must be conveyed through a feedback channel. This is not very efficient and practical due to the number of channel coefficients that needed to be quantized and sent back to the transmitter over limited bandwidth control channels.
Precoding schemes for spatial multiplexing systems with limited feedback capacity is more feasible in real-world applications [11]-[12]. The basic idea is that the transmit precoder is chosen from a finite set of precoding matrices, called the codebook, known to both the receiver and the transmitter. The receiver chooses the optimal precoder from the codebook as a function of the current channel state information and sends the binary index of this (precoder) matrix to the transmitter over a feedback channel. In this chapter, we discuss the resource optimization problem for codebook-based MIMO-OFDMA systems.