3.4 Complexity Analysis and Simulation Results
4.3.2 The Power Loading Scheme
In the previous subsection, we assume that the total power of user k is equally distributed to the all substreams on the subcarriers assigned to the user k and perform dynamic subcarrier assignment to extract the diversity gain of multiuser MIMO-OFDMA systems.
In this subsection, we consider the dynamic power loading to further enhance the overall system performance.
As discussed in section 4.2, our goal is to minimize the average BER. In [26], the author had derived how to obtain the optimum power allocation for minimizing BER in muticarrier systems. Now we follow the method proposed in [26] to get the optimal power loading for the codebook based MIMO-OFDMA systems.
Since the subcarrier assignment has been done in previous subsection and we allow at most one user to transmit signals on each subcarrier, there is no co-channel interference and therefore the multiuser power loading is then decoupled into single user case. That is, we can deal with the power allocation for each user individually.
The BER for the nth substream on the mth subcarrier is generally a function of the corresponding power and GNR (gain to noise ratio), like (4.6). Because (4.6) is a convex function with respect to the power pmnk, we can use the Lagrange multiplier method with the total power constraint. The Lagrangian function of user k may be expressed as
J (Pk11k, Pk12k, . . . , Pk
where k1 ∼ kck is the subcarrier index assigned to the user k and λkdenotes the Lagrange multiplier. By differentiating (4.10) with respect to pktnk and setting it to zero, we obtain a set of equations as
1
But (4.12) still depends on the Lagrange multiplier λk. So we take (4.12) into the user’s
power constraint
1.5GNRktnkln(0.3GNRc ktnk
kN(2b−1) )
Thus, the corresponding power can then be computed. It is noted that if some sub-streams’ power is negative after the computation, it means that the GNRs of these substream are too low and these substreams should not be allocated any power in order not to deteriorate the overall performance. In such case, we should exclude these sub-streams and do the Lagrange multiplier method again until the power of all subsub-streams are not negative.
4.4 Complexity Analysis and Numerical Results
4.4.1 Computational Complexity Analysis
In this subsection, we analyze the complexity of the subcarrier assignment algorithm and the power loading algorithm.
For the subcarrier assignment algorithm, the complexity of step 2 is O(KN log2N + M Klog2K +M log2M ), and for step 3 the complexity is O(M K), so the total complexity of the subcarrier assignment algorithm is O(KN log2N +M Klog2K +M log2M +M K)≈ O(M Klog2K). And for the power loading algorithm, the complexity is O(N M ).
4.4.2 Numerical Results
Selected simulated performance of the proposed RA algorithm are presented in this sub-section. First the performance of the subcarrier assignment algorithm for the codebook based MIMO-OFDAM systems is shown in Fig. 4.1 ∼ 4.4. For Fig. 4.5 ∼ 4.6, we evaluate the performance of the proposed power-loading algorithm.
We assume each Hmk is a 4× 2 (4 antennas at the BS and 2 antennas at each MS) matrix for 2 substream codebook 4×3 (4 antennas at the BS and 3 antennas at each MS)
matrix for 3 substream codebook with i.i.d. zero-mean, unit-variance complex Gaussian entries. The system’s modulation mode is BPSK. For simplicity, we assume that the required data rate are the same for all users. The codebook used here is from 802.16e standard.
In Fig. 4.1 and Fig. 4.2, we compare the subcarrier assignment algorithm for the ZF receiver with fixed subcarrier assignment scheme. From the figures we can find that the performance of the dynamic subcarrier assignment is better than fixed subcarrier assignment by almost 4dB at BER=10−2 for the 2 substream case and more than 4dB at BER=10−2for the 3 substream case. The same result can also be found when the MMSE receiver is used (Fig. 4.3 and Fig. 4.4). The performance of the dynamic subcarrier assignment is better than fixed subcarrier assignment by 3dB at BER=10−2 for the 2 substream case and 2.5 dB at BER=10−2 for the 3 substream case.
For the dynamic power loading algorithm, we compare the performance of it with the equally power distributed system. We consider three different scheme:fixed subcarrier assignment without codebook precoding, fixed subcarrier assignment with codebook precoding and dynamic subcarrier assignment with codebook precoding. Here we assume QPSK modulation is used. In Fig. 4.5, using the dynamic power loading algorithm will provide nearly 1.5dB gain at BER=10−2over the equally power distributed system in the fixed subcarrier assignment without codebook precoding environment. In Fig. 4.6, the dynamic power loading algorithm also achieves approximately 1dB gain at BER=10−2 in the fixed subcarrier assignment with codebook precoding environment. Finally, in Fig.4.7, the dynamic power loading algorithm is superior to the equally power distributed system in the dynamic subcarrier assignment with codebook precoding environment by more than 1.5dB at BER=10−4.
These figures (Fig. 4.5∼ 4.7) also show that the improvement of the dynamic power-loading algorithm is more obvious in the fixed subcarrier assignment without codebook precoding environment. This is because that without precoding, the variation of the
channel condition is much larger. Simulation results show that the variance of GNR is reduced by almost 50% after precoding. Therefore, the performance gain offered by the power-loading algorithm is smaller in the other two cases.
0 1 2 3 4 5 6 7 8 9 10
10−4 10−3 10−2 10−1 100
BER
Eb/No
Fixed ZF Adaptive ZF
Figure 4.1: Average BER performance for the ZF receiver ; 128 subcarriers, 8 users, 2 substreams.
0 1 2 3 4 5 6 7 8 9 10 10−3
10−2 10−1 100
BER
Eb/No
Fixed ZF Adpative ZF
Figure 4.2: Average BER performance for the ZF receiver ; 128 subcarriers, 8 users, 3 substreams.
0 1 2 3 4 5 6 7 8 9 10
10−5 10−4 10−3 10−2 10−1 100
BER
Eb/No
Fixed MMSE Adaptive MMSE
Figure 4.3: Average BER performance for the MMSE receiver ; 128 subcarriers, 8 users, 2 substreams.
0 1 2 3 4 5 6 7 8 9 10 10−4
10−3 10−2 10−1 100
BER
Eb/No
Fixed MMSE Adaptive MMSE
Figure 4.4: Average BER performance for the MMSE receiver ; 128 subcarriers, 8 users, 3 substreams.
0 1 2 3 4 5 6 7 8 9 10
10−3 10−2 10−1 100
BER
Eb/No
Equally power distributed Dynamic power−loading
Figure 4.5: Average BER performance for the ZF receiver; fixed subcarrier assignment without codebook precoding ; 128 subcarriers, 16 users, 2 substreams.
0 1 2 3 4 5 6 7 8 9 10 10−3
10−2 10−1 100
BER
Eb/No
Equally power distributed Dynamic power−loading
Figure 4.6: Average BER performance for the ZF receiver ; fixed subcarrier assignment with codebook precoding ; 128 subcarriers, 16 users, 2 substreams.
0 1 2 3 4 5 6 7 8 9 10
10−5 10−4 10−3 10−2 10−1
BER
Eb/No
Equally power distributed Dynamic power−loading
Figure 4.7: Average BER performance for the ZF receiver ; dynamic subcarrier assign-ment with codebook precoding ; 128 subcarriers, 16 users, 2 substreams.
Chapter 5 Conclusion
The allocation of radio resources in a MIMO-OFDMA system is critical in maximiz-ing resource efficiency, system capacity, and mitigatmaximiz-ing interference. We have presented two SVD-based precoding schemes (orthogonal GS precoding and non-orthogonal pre-coding) that minimize the total consumed power while meeting various rate and SINR requirements. For the orthogonal (GS) precoding scheme, we propose two adaptive RA algorithms and provide simulation results that prove the effectiveness of both algorithms in both uplink and downlink scenarios. These two algorithms yield almost the same rel-ative performance when compared with the optimal solution. To further increase the spectrum efficiency, we extend our concern to non-orthogonal precoding schemes that guarantee zero or limited cochannel interference. An adaptive RA algorithm is proposed and its numerical performance is given. It is found that the lift of the orthogonal con-straint leads to improved performance when the rank of the channel matrix is sufficient.
We also consider the RA issue for spatial multiplexing systems with limited feedback (codebook based precoding) and present subcarrier assignment and power loading algo-rithms that minimize the average BER performance. The simulation results show that these dynamic RA methods do indeed yield low average BER performance.
Several remarks on possible extensions to our work are in order. Firstly, the proposed schemes can be further extended for use in a multi-cellular network with the transmit antennas distributed among several BS’. They are certainly viable candidate RA and
interference control schemes for networked MIMO systems. Secondly, the only perfor-mance criterion we consider is total power or average BER minimization. These criteria are often more suitable for uplink design when the transmit power is limited. For down-link communications, it is more desirable to maximize the total throughput and take the fairness issue into account. Thirdly, since the resource unit considered in our work is a single space-frequency subchannel, transmitting the overall RA information would re-quire a large control-channel bandwidth. Practical concern often implies a resource unit be made of multiple space-time-frequency subchannels. It would be desirable to provide modified RA solutions that take such a resource unit definition into account. Finally, the fairness concern is usually answered by implementing a proper scheduling. Such a scheduling has to consider the time-varying nature of the associated multiuser channel.
Therefore, a complete RA design needs to consider the channels’ time, frequency and space selectivities and invoke appropriate multiuser channel models accordingly.
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作 者 簡 歷
翁志倫，高雄市三民區人，1984 年生
高雄市立高雄高級中學 2000.9 ~ 2003.6 國立交通大學電信工程學系 2003.9 ~ 2007.6 國立交通大學電信工程學系研究所系統組 2007.9 ~ 2009.6
Graduate Course:
1. Random Process
2. Digital Signal Processing 3. Digital Communications 4. Coding Theory
5. Detection and Estimation Theory 6. Adaptive Signal Processing
7. Information Theory 8. Matrix Computations 9. Embedded System Design