ANÁLISIS DE COSTOS BÁSICOS A COSTO DIRECTO

Figure 4.9: (a) Non-reciprocity estimation normalized MSE and (b) system spectral eﬃciency

vs. input reflection coefficients variance (σ2_rc) for different values of sparsity thresholdD with

N = 100, Mtot=K = 20, τu=τd=Mtot,ρu= 0 dB,ρd= 20 dB,Tcoh= 250.

Figure 4.10: System spectral eﬃciency vs. the number of scheduled UEs (K) for N = 100,

Mtot=K, D = 1, τu=τd=Mtot,ρu= 0 dB,ρd= 20 dB,σrc2 =−20 dB, Tcoh= 250.

Figure 4.11: System spectral efficiency vs. input reflection coefficients variance (σ2

N = 100, Mtot=K = 20, D = 1, τu=τd=Mtot,ρu= 0 dB,ρd= 20 dB,Tcoh= 250.

ANÁLISIS DE COSTOS BÁSICOS A COSTO DIRECTO

Here, the performance of channel non-reciprocity estimation and mitigation framework

is evaluated and compared to two other existing schemes in the literature, namely the

direct-path based Least Squares (LS) known as “Argos” [97] and the generalized neighbor

LS [96]. Both LS-based methods rely on downlink pilots to compensate the transceiver

56

Chapter 4. Analysis and Mitigation of Channel Non-Reciprocity in Massive MIMO

Systems

non-reciprocity in the UE side while employing mutual coupling between the BS antennas

to estimate and mitigate BS transceiver non-reciprocity. It should be noted that the

conventional method of sending downlink pilots in which the number of sent pilots is

equal to the number of antennas in the BS side is not feasible in massive MIMO context.

Thus, here we take advantage of the method proposed in [66] for massive MIMO systems,

in which the number of downlink pilots can be τ

≥ M

. As mentioned earlier, exact

number of such pilots used in the simulations is τ

= M

.

In order to quantify the accuracy of BS and UE sides’ transceiver non-reciprocity estima-

tion, the normalized MSE metric is employed which is deﬁned as

δ

=

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎩

C − ˆC

||C||

,

for BS side

diag (A) − diag

ˆ

A

||diag (A)||

,

for UE side.

(4.55)

The example simulation scenario consists of 20 single-antenna UEs where the BS is

assumed to estimate channel non-reciprocity in 4 iterations over C

= 10 neighboring

subcarriers. The convergence aspects of the channel non-reciprocity estimation method,

which resulted into having 4 as the number of iterations of choice, is covered in details

in [P1]. In pilot signaling stage, uplink and downlink SNRs are assumed to be ˜ρ

= 0

dB and ˜ρ

= 10 dB, respectively, while for the two LS-based methods, the coupling SNR

between two neighboring antennas is 80 dB [96]. The entries of channel non-reciprocity

matrices are drawn based on the channel non-reciprocity model introduced in [77]. Based

on such modeling, in this example, variances of diagonal elements in F

, F

, B

,

and B

, shown in (2.21), are set to−20 dB while the power of elements in M

and

M

is controlled by input reﬂection coeﬃcients which have the variance σ

[77]. The

antenna layout follows the one in Figure 4.1 and the carrier frequency is assumed to be

f

= 3.5 GHz.

The impacts of sparsity threshold on the channel non-reciprocity estimation normalized

MSE and the system spectral eﬃciency is evaluated and visualized in Figure 4.9. Here,

the baseline system settings are followed while the x-axis represents varying σ

. In

this respect, Figure 4.9a shows the normalized MSE of BS and UE sides’ transceiver

non-reciprocity estimation. Based on the results, highest accuracy in UE transceiver

non-reciprocity estimation is achieved when D = 0, i.e., only the diagonal elements of

_{C − ˆ}_C

_{diag (A) − diag}

_{, F}

_{, B}

_,

_{, shown in (2.21), are set to}_{−20 dB while the power of elements in M}

_and

_{is controlled by input reﬂection coeﬃcients which have the variance σ}