Chapter Summary

In this chapter, we have investigated the issue of applying the fading mitigation based an-tenna technique for the multiuser scheduling system through a capacity analysis. A unified capacity formula connecting multiuser diversity from multiple users, antenna diversity from multiple antenna systems and fading parameter from Nakagami channel models is estab-lished. With a set of parameter changes, the new capacity expression is powerful to inter-pret the interaction between the multiuser scheduling system and various fading mitigation based antenna techniques. As a result, it is concluded in this chapter that it may not be a good strategy for utilizing the diversity-based antenna technique in the multiuser scheduling system due to the following two main reasons. First, the channel damping effect resulting from using the diversity-based antenna technique is intrinsically harmful to the multiuser scheduling system where large channel fluctuations are preferred. Second, from the multiuser MIMO point of view, since the user population has contributed a large amount of multiuser diversity gain, the additional antenna diversity coming from the diversity-based antenna scheme can then only add to limited capacity benefit. In the next chapter, we will move

to consider another category of multiple antenna techniques, i.e. the multiplexing-based antenna technique, for their application in the multiuser scheduling system.

Chapter 4

Throughput Enhancement Based Antenna Techniques for Multiuser Scheduling Systems

This chapter studies the benefit of combining the throughput enhancement based (or mul-tiplexing based) antenna technique with the multiuser scheduling system from both the perspectives of cell coverage extension and system capacity improvement. For a point-to-point MIMO system, recent studies have revealed that the remarkable capacity gain resulting from the spatial multiplexing MIMO system may come at the sacrifice of degrading link re-liability. This tradeoff between antenna multiplexing gain against antenna diversity gain may translate into smaller coverage areas. In this chapter, we will demonstrate that using the scheduling technique can effectively replenish the diversity-deficient spatial multiplexing MIMO system with multiuser diversity. In particular, we will introduce a novel schedul-ing scheme, called the strongest-weakest-normalized-subchannel-first (SWNSF) schedulschedul-ing, which requires only limited amount of feedback. Analysis and results will indicate that the SWNSF scheduling can significantly increase the coverage of the multiuser MIMO system while further improving the system capacity.

4.1 Channel Model

Consider a multiuser MIMO system where a base station with N_t transmit antennas serves K downlink users each of which is equipped with N_r receive antennas. We assume that the

spatial multiplexing method is used for data transmission between the base station and any target user. For clarifying the effect of multiuser scheduling on the supplement of diversity gain, we assume N_t = N_r = N since in this case all the degrees of freedom in the MIMO system are exhausted for multiplexing gain [3]. Thus, the link between the base station and each individual user constitutes an N × N MIMO system. Let xk and y_k be the N × 1 transmit and receive signal vectors for user k, respectively, G_k the N × N channel matrix between the base station and user k, and n_k the N × 1 spatially white noise vector with E[n_kn^H_k] = σ²_nI. Thus, the link between x_k and y_k is related by [89]

y_k = G_kx_k+ n_k =√

g_kH_kx_k+ n_k , (4.1)

where g_kdepicts the large-scale (local average) behavior of the channel gain, and H_kcaptures the channel fading characteristics. For user k at a distance of r_k from the base station, g_k can be generally represented by [24]

10 log₁₀(g_k) =−10µ log10(r_k) + g₀ [dB] , (4.2)

where µ is the path loss exponent and g₀is a constant subject to certain path loss models. For the N×N normalized channel matrix Hk, we assume that every entry of H_kis independent, circular-symmetric complex Gaussian random variable CN (0, 1), meaning that the real and imaginary parts of each entry have uncorrelated Gaussian distributions with zero mean and variance 1/2. The total transmit power at the base station is constrained by P_t, i.e.

E[x^H_kxk]≤ Pt.

With the link model defined in (5.1), the ergodic capacity (nats/sec/Hz) of an open-loop MIMO system with equal power allocation among transmit antennas is given by [1]

C_k= E



log det

 I + ρ_k

NH_kH^H_k 

(4.3)

where

ρ_k= P_tg_k/σ_n² = (P_t/σ²_n) r^−µ_k 10^g0/10 (4.4)

is the average receive signal-to-noise ratio (SNR) of user k. By applying the singular value decomposition (SVD) to H_k of (4.3), C_k can be also represented by

C_k = N

i=1

E

 log

 1 + ρ_k

Nλ_k,i 

, (4.5)

where{λk,i}^Ni=1 are the eigenvalues of the Wishart matrix HkH^H_k for user k. Without loss of generality, we arrange{λk,i}^Ni=1 in the decreasing order so that λ_k,N ≥ λk,N−1 ≥ · · · ≥ λk,1 ≥ 0¹. Comparing to the ergodic capacity of the single-input-single-output (SISO) system, the ergodic capacity of an open-loop MIMO channel is enhanced by forming n parallel subchannels, each of which has effective output SNR γ_k,i= ρ_kλ_k,i/N at the receive antenna.

In this thesis, we refer to the link capacity as the ergodic capacity of the information theory.

In addition to the link capacity, let’s examine the link outage probability of the MIMO system because it reflects how reliable a MIMO channel can support the corresponding capacity. For the SISO system, a common definition of link outage is the probability that the receive SNR is less than a predetermined value γth, i.e. P_out = Pr{γ < γ^th} [88]. Based on the insight from [14], the link outage for the spatial multiplexing MIMO system can be generalized as follows. By noting that all the subchannels of the spatial multiplexing MIMO system are used for independent data transmissions in parallel, the link outage for the spatial multiplexing MIMO system can be defined as the event when the receive SNR of any subchannel is less than γth. That is, for any user k,

P_out^k = Pr{γk,1 < γth ∪ γk,2 < γth · · · ∪ γk,N < γth}

= 1− Pr

min∀ i {γk,i} = γk,1 ≥ γ^th

= Pr{γk,1 < γth} . (4.6)

Intuitively, the weakest subchannel with the lowest SNR in the MIMO system dominates the outage probability performance since the weakest subchannel is most likely to incur trans-mission errors. By writing (4.6) as Pr{γk,1 ≥ γ^th} = 1 − Pout^k , (4.6) can be also interpreted

1It is shown in [95] that the random Wishart matrixH_kH^H_k hasN distinct eigenvalues with probability one.

as that all the receive SNR in subchannels of the MIMO system are required to be greater than γth with the probability of (1−Pout^k ). In Section 4.3, we will relate (4.6) to the resulting cell coverage.