Coverage Enhancement for Spatial-Multiplexing-Based MIMO OFDM

Spatial-Multiplexing-Based MIMO OFDM Systems by Joint Multiuser Scheduling and Subcarriers Assignment

In Chapter 4 we first extend the fairness-oriented subcarriers assignment algorithm (FOSA) from SISO OFDM to MIMO OFDM. Next we propose another low-complexity coverage-oriented subcarriers assignment algorithm (COSA). We demonstrate that COSA can achieve larger cell coverage of spatial-multiplexing based MIMO-OFDM systems than FOSA, while achieving almost the same fairness performance as FOSA.

With respect to COSA, we further derive an analytical expression form for link

out-age probability and cell coverout-age reliability by means of order statistics and Glivenko-Cantelli Theorem. Simulation results validate the accuracy of the analytical model and approximation method. We also present some numerical results to illustrate how the total transmit power, the number of antennas, the number of users, pass loss exponents, and various subcarriers assignment algorithms affect the cell coverage for the spatial multiplexing MIMO-OFDM system.

5.3 Suggestion for Future Work

For the future research of the thesis, we provide the following suggestions to extend our work:

• Compare the link quality and cell coverage for single-user OFDM-based spatial multiplexing systems with Space-Time-Frequency coded MIMO-OFDM system.

• Consider the uplink case and see how large the coverage reliability is for OFDM-based spatial multiplexing systems.

• To design a criterion to describe the tradeoff between cell coverage and fairness.

• Consider the time correlation between each time slot for each user, and see how the doppler effect could effect the cell coverage.

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2002.

Chapter 6 APPENDIX A

In Appendix A we discuss how to obtain the approximate value ω. To this end, we introduce a function called empirical distribution. The empirical distribution for an i.i.d. sequence {γ₁, ...γ_N} is a random variable defined as

Furthermore, based on Glivenko-Cantelli Theorem, we know that the random variable D_N = sup

γ∈R

|F_N(γ) − F (γ)| (6.5)

converges to 0 with probability 1 when the value of N is large. In other words, P r

is a much stronger statement, and sup means the supremum upper bound. Since IEEE 802.11a employs fast Fourier transform (FFT) with 64 carriers and IEEE 802.16 uses 256 carriers furthermore [26], we can assume that the value of N is very large. (7.6) can be written as

ω = N · F_N(γ_(ω)) ' N · F (γ_(ω))

' N · F (²(γ)) (6.7)

where ²(γ) is the expectation value of a function f (γ) in a variable γ, and

²(γ) =

By substituting (7.10) into (7.9), we obtain ω ' N · F³ ρn

where N_ω is an approximation integer value of ω.

57

Fig. 6.1: Illustration of the empirical distribution for an i.i.d. sequence.

APPENDIX B

In Appendix B we discuss how to obtain the approximate value ω. To this end, we introduce a function called empirical distribution. The empirical distribution for an i.i.d. sequence {γ₁, ...γ_N} is a random variable which is defined as

Furthermore, Glivenko-Cantelli Theorem says that the random variable D_N = sup

γ∈R

|F_N(γ) − F_k^∗_,n(γ)| (7.5) converges to 0 with probability 1 when the value of N is large. In other words,

P r

59 is a much stronger statement, and sup means the supremum upper bound. We assume that the value of N is large enough. (7.4) can be written as

ω = N · F_N(γ_k^∗_,(ω)) ' N · F_k^∗_,n(γ_k^∗_,(ω))

' N · F_k^∗_,n(²(γ_k^∗_,n)), (7.7) where ²(γ) is the expectation value of a function f (γ) in a variable γ, and

f_k^∗_,n(γ) = 1

where B(a, b) represents a Beta function. By substituting (7.9) into (7.7) w ' N_ω(N, K) =

N · Ã

1 − exp

à 1

B(K, 1)

K−1X

i=0

C_i^K−1(−1)^K−i 1 (K − i)²

!!_K ,

(7.10) where Nω(N, K) is an approximation integer value of ω.

61

Vita

Cheng-Wei Chiu was born in Taiwan in 1981. He received the B.S. degree in Electrical Engineering from National Central University in 2004. From July 2004 to June 2006, he works his Master degree in the Wireless Network Lab of the Department of Communication Engineering at National Chiao Tung University. His research interests are in the field of radio resource management.