7.3 Link Outage and Coverage Performance Analysis
7.5.2 Effects of Transmission Power and Number of Antennas on Coverage 130
Figures 7.8 and 7.9 show the coverage performance versus the number of users K for various scheduling schemes in the case of N = 32 under different PT and M values, respectively. For comparison with COSA, we also show the coverage performance of FOSA by simulations.
5 10 15 20 25 30 600
700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
Number of users (K)
Coverage (meters)
COSA FOSA COUS Random
M = 4
Line: simulation Mark: analysis
M = 2
Figure 7.8: Reliable coverage versus number of users for different scheduling algorithms under M = 2 and M = 4. Parameters: N = 32, PT = 0 dBW, noise power σ2 = −103 dBm, g0 = −32 dB, µ = 4, Pout = 0.1 and γth= 6 dB.
From both figures, the random scheduling algorithm does not take advantage of multiuser diversity even though it achieves fairness among users. The results of COUS show that the coverage performance can be improved by utilizing multiuser scheduling. However, the improvement is not significant compared to the schemes, COSA and FOSA, which simul-taneously exploit multiuser selection and subchannel assignment. Additionally, the reliable coverage increases as K increases and the proposed COSA can provide the best coverage performance than FOSA, COUS and random scheduling. Note that the gain of COSA over FOSA indicates the subchannel-oriented assignment is better than user-oriented assignment
5 10 15 20 25 30 600
700 800 900 1000 1100 1200 1300 1400
Number of users (K)
Coverage (meters)
COSA FOSA COUS Random
Line: simulation Mark: analysis
PT = 0 dBW PT =3 dBW
Figure 7.9: Reliable coverage versus number of users for different scheduling algorithms under PT = 0 dBW and PT = 3 dBW. Parameters: N = 32, M = 4, noise power σ2 = −103 dBm, g0 = −32 dB, µ = 4, Pout = 0.1 and γth = 6 dB.
in terms of maximizing reliable coverage.1
Based on Fig. 7.8, a MIMO-OFDM system with a smaller number of antennas M can be easier to hold the desired link quality under a larger serving area. As the number of antennas increases (or decreases) from M1 to M2, the resulting coverage have constantly (independent
1For different objective and constraints, the two assignments may result in different performance results.
For example, in the spatial multiplexing based MIMO-OFDM systems, the user-oriented assignment can outperform subchannel-oriented assignment subject to maximizing capacity and per user priority constraint [124]. The details will be presented in Chapter 8.
10 20 30 40 50 60 70 80 90 100 0
10 20 30 40 50 60
Number of users (K)
G(N, K) (%)
N=32 N=128
COSA (joint multiuser and frequency diversity)
COUS (only multiuser diversity) N=32
N=128 Coverage gain of COUS and COSA over random scheduling (independent of M)
Figure 7.10: Coverage gain G in percentage of COUS and COSA over random scheduling under µ = 4, Pout = 0.1 and various K values. According to (7.37) and (7.38), the gains are independent of number of antennas M.
of K) reduced (or enlarged) ratio for both COUS and COSA as follows:
÷M1
M2
¸2/µ
− 1
!
× 100% in percentage . (7.44)
For example in Fig. 7.8, under arbitrary K value, the reliable coverage of both COUS and COSA reduce 29.29% as M = 2 increases to M = 4.
Similarly, based on Fig. 7.9, when the available transmission power is α-fold of PT, the reliable coverage of COUS and COSA increase (α1/µ− 1) × 100% in percentage. For example in Fig. 7.9, the coverage increases 18.92% for both COUS and COSA when the transmission power is doubled from PT = 0 dBW to PT = 3 dBW.
K = 10 K = 20 K = 30 K = 50 K = 100 0
0.2 0.4 0.6 0.8 1 1.2 1.4
Number of users (K)
Coverage ratio η
coverage extension coverage
shrinkage Random
COUS COSA
Figure 7.11: Coverage ratio η of various scheduling schemes to SISO under N = 32, M = 2, µ = 4, Pout = 0.1 and various K values.
7.5.3 Coverage Gain and Extension from Multiuser and Frequency Diversity
In this section, we illustrate numerical results to quantify the benefit of jointly multiuser scheduling and subchannel assignment on coverage performance in term of the coverage gain and coverage extension discussed in Section 7.4.2 and 7.4.3, respectively. Based on (7.37) and (7.38), Fig. 7.10 shows the gains GCOUS and GCOSA under various K values with N = 32 and 128. Take N = 32 as an example, the gain of COUS over random scheduling is merely up to 15% with multiuser diversity only. However, the gain of COSA over random scheduling can significantly raise to 57% under taking advantage of joint multiuser and frequency diversities. In addition, there are smaller coverage gains GCOUS and GCOSA under
Table 7.1: Coverage performances with different scheduling schemes normalized to SISO system.
N = 1 N = 32
The spatial multiplexing based OFDM systems K = 20 K = 50 K = 20 K = 50
M = 1 SISO 1 1 1 1
M = 2 Random scheduling 0.707 0.707 0.707 0.707
M = 2 SWNSF COUS 1.515 1.647 0.791 0.806
M = 2 in [30] COSA (in [30]) (in [30]) 1.006 1.070
M = 3 Random scheduling 0.577 0.577 0.577 0.577
M = 3 SWNSF COUS 1.237 1.345 0.646 0.658
M = 3 in [30] COSA (in [30]) (in [30]) 0.821 0.874
higher frequency selectivity condition, i.e. the results of N = 128 in Fig. 7.10.
Figure 7.11 shows the coverage ratios η of random scheduling, COUS, and COSA to the SISO system according to (7.40), (7.41), and (7.42) under N = 32 and M = 2. Clearly, with multiple antennas M = 2, the coverage performance is reduced compared to a SISO system, i.e. only 0.707-fold achievable coverage of a SISO system. With multiuser and subchannel assignment, the reduced coverage can be compensated. Although we can find the K value satisfies (7.43) such that COUS can fully compensate the coverage shrinkage due to multiple antennas, the value of K is usually extremely large. For example in Fig. 7.11, the theoretical K satisfies (7.43) is 3.45664 × 1015. However, COSA can fully compensate the coverage shrinkage issue and further achieve extra coverage extension as K ≥ 20. This example shows again the value of joint exploiting multiuser and frequency diversities on the spatial multiplexing based MIMO-OFDM systems.
Finally, we present Table 7.1 to illustrate the improvement on reduced coverage by scheduling under K = 20, 50 and M = 2, 3. This table is an extended result for [30]
which shows the coverage shrinkage ratio of the spatial multiplexing based MIMO system to SISO system, i.e. N = 1. In Table 7.1, we further show the coverage performance under the MIMO-OFDM systems, i.e. N = 32. The reliable coverage of the SISO system is normalized to unity. We find that the shrinking coverage due to split transmission power can be easier compensated (or even achieving extra coverage extension) for a low-frequency selectivity system.
Chapter 8
Capacity Enhancement for Multiuser MIMO-OFDM Systems
In this chapter, we investigate the resource allocation issue in a spatial multiplexing based multiuser MIMO-OFDM system. Different from Chapter 7, we focus on designing a sched-uler to adaptively assign resource among users under different requirements and channel conditions. The key issue is the allocation of subchannels and power among users to share the system. Previous literature mainly focus on maximizing capacity but ignore the intrinsic coverage shrinkage and link reliability degradation problems in a MIMO system. Particu-larly, we formulate a system with better link reliability under a proportional rate requirement among users. To alleviate the complexity of jointly optimal subchannel and power allocation, we at first propose two suboptimal subchannel allocation algorithms, namely, user-oriented and subchannel-oriented allocations. We next propose a low-complexity power allocation method.
8.1 System Model and Problem Formulation
8.1.1 Modeling and Assumption
Identical to Chapter 7, we consider a spatial multiplexing-based MIMO-OFDM downlink system as shown in Fig. 1.5. There are MT transmit antennas at the base station and MR receive antennas at each of all K users. For simplicity, we consider the case MT = MR= M for achieving full multiplexing gain. The total bandwidth of each subchannel is assumed to be smaller than the channel coherent bandwidth. Assume that the length of the cyclic prefix (CP) in the OFDM system is greater than the length of the discrete-time baseband channel impulse response so that the frequency-selective fading channel indeed decouples into a set of parallel frequency-flat fading channels. With channel information feedback from users, the scheduler at the base station performs adaptive resource allocation scheduling including
subchannel and power allocations based on available information and rate requirements among users.
The same with (7.1), the equivalent MIMO transmission model between the base station and user k at n-th subchannel is
yk,n =√
gkHk,nxk,n+ nk,n,
where xk,n and yk,n denote the M × 1 transmit and receive signal vectors for user k, respectively. The matrix Hk,n represents the corresponding flat and independent faded M × M channel matrix, and the vector nk,n be M × 1 spatially white noise vector with E[nk,nnHk,n] = σ2IM. The large-scale channel gain gk captures the path loss effect as mod-elled in (7.2).