Expansión de capacidades

In this section, we present SINR and spectral efficiency results for the proposed coordinated RZF scheme. We plot these results against the average received cell- edge SNR, ρ0, obtained by substituting the link distance equal to Rc in (7.2)

given by ρ0 = E



10 log10 P010(ησSF/10)/N0



, where the noise power N0 = 1

and η _{∼ N (0, 1). It is important to mention that increasing ρ}0 also increases

the SNR at the users. The increase in ρ0 also increases interference to the

users (in the same or neighboring cells). Figure 7.3 shows the average SINR performance of the coordinated RZF scheme with perfect CDI and limited feed- back based RVQ CDI. The approximate expected SINRs derived in (7.21) and (7.41) are plotted (in the linear scale) in Fig. 7.3 for perfect CDI and RVQ CDI with various numbers of feedback bits. It is observed that the approximations of the expected SINR with perfect CDI matches the average simulated spec- tral efficiency, however the expected SINR approximation (7.41) with an RVQ codebook shows a small deviation relative to the simulated average SINR at ρ0

values. The average cell-edge spectral efficiency for C = 2 and C = 3 cells with K = 2 cell-edge users is shown in Fig. 7.4, where each BS has nt= 6 antennas.

Denoting the cell-edge spectral efficiency by Cedge, the average cell-edge spectral

efficiency simulations are performed using E [Cedge] = E " _K X k=1 log₂(1 + SINRk,c) # , (7.54)

7.6. NUMERICAL RESULTS AND DISCUSSION 120 ρ 0 (dB) -6 -4 -2 0 2 4 6 8 10 E [ SINR k,c ] 0 5 10 15 20 25

Average SINR Simulations, Perfect CDI Expected SINR (7.23), Perfect CDI Average SINR Simulations, RVQ CDI Expected SINR (7.43), RVQ CDI

B_k,c,c = B_k,c,j = 20

B_k,c,c = B_k,c,j = 15

B_k,c,c = B_k,c,j = 10

Figure 7.3: The average SINR for the kth _{user in the c}th _{cell, with C = 2 cells}

and K = 2 users where each BS has nt = 4 antennas with Bk,c,c = Bk,c,j = 20,

15 and 10.

where SINRk,c is given in (7.5) and the users are located in the cell-edge area.

Therefore we refer to (7.54) as the average cell-edge spectral efficiency of the cell. This is plotted against different ρ0 values in Fig. 7.4. The single cell

MU system gives superior average cell-edge spectral efficiency compared to the other scenarios, due to the absence of ICI. However, when ICI is present, the average cell-edge spectral efficiency with the non-coordinated RZF precoding scheme suffers high losses and the performance gap increases compared to the single-cell case, as ρ0 increases. For the coordinated RZF scheme, we consider

two cases: 1) only 2 out of 3 cells coordinate and 2) all 3 cells coordinate. In Fig. 7.4, we consider two regularization parameters for the coordinated RZF case 2: ζc and ζcopt.

The coordinated RZF case 2 with ζopt

c achieves better average cell-edge spec-

tral efficiency compared to the coordinated RZF case 1 (with ζc) and the non-

coordinated RZF scheme. The coordinated RZF schemes with both cases 1 and 2 outperform the coordinated ZF [128] scheme. However, for ρ0 < 2 dB and

ρ0 < 3 dB with case 1 and case 2, respectively, it is noted in Fig. 7.4(a) that the

coordinated RZF schemes with ζc are not effective and the non-coordinated RZF

scheme is more effective, as the former leverages the benefit of fewer channels being orthogonalized while precoding, thus leading to a stronger signal power. The same reasoning is applicable to the proposed coordinated RZF case 1 which yields better performance than the proposed coordinated RZF case 2, for ρ0 < 8

dB, with the same number of antennas at the BS (i.e., nt= 6). In Fig. 7.4(b),

we plot the same cases as Fig. 7.4(a) with nt = 8 antennas at the BS. We

observe that for ρ0 >−4 dB, the proposed coordinated RZF schemes using ζk

ρ

0 (dB)

-7 -2 3 8 13

Average cell-edge spectral efficiency (bps/Hz)

2 4 6 8 10 12 14 Single-cell RZF, ζ c, no ICI No Coord. RZF, ζ_c, C = 3 Coord. RZF b/w 2 cells, ζ_c, C = 3 Coord. ZF [132] b/w 3 cells, C = 3 Coord. RZF b/w 3 cells, ζ_c, C = 3

Coord. RZF b/w 3 cells, ζopt_c , C = 3

(a) nt= 6

ρ

0 (dB)

-7 -2 3 8 13

Average cell-edge spectral efficiency (bps/Hz)

2 4 6 8 10 12 14 16 Single-cell RZF, ζ c, no ICI No Coord. RZF, ζ c, C = 3 Coord. RZF b/w 2 cells, ζ_c, C = 3 Coord. ZF [132] b/w 3 cells, C = 3 Coord. RZF b/w 3 cells, ζ_c, C = 3

Coord. RZF b/w 3 cells, ζopt_c , C = 3

(b) nt= 8

Figure 7.4: The average cell-edge spectral efficiency with C = 3 cells for K = 2 users.

proposed RZF case 2 with ζopt

c is higher than all the other scenarios. There-

fore, by comparing Fig. 7.4(a) and Fig. 7.4(b), we note that the coordination gain can be obtained over the non-coordinated RZF method, for a range of ρ0

values by either increasing nt, such that nt > CK, or by using an effective

regularization parameter (here, ζopt

7.6. NUMERICAL RESULTS AND DISCUSSION 122

7.6.3

Performance of Adaptive Bit Allocation Scheme