Performance Evaluation Under Channel Non-Reciprocity

The simulation scenario considered for evaluating the performance of ZF and MRT

precoded multi-user massive MIMO downlink transmission consists of K = 20 UEs while

T

_coh

= 250. The non-reciprocity matrices A and C are constructed based on their

essential statistical properties in Table 4.1. Since the UEs are assumed to be single-

antenna devices, off-diagonal entries of A are zero and thus σ

2

a_od

= 0. The variance of the

m-th diagonal element in A



, σ

2

amm

, is assumed to be equal for all the values of m and is

set to σ

2

a_d

. Next, for each channel non-reciprocity realization, the diagonal elements of A



and off-diagonal elements of C



are assumed to be i.i.d.

CN

0, σ

2 a_d



and

CN

0, σ

2 c_od



,

respectively. The diagonal elements of C



are assumed to have Gaussian distribution with

zero mean, variance set to σ

2

c_d

and cross-correlation equal to δ

c2_d

.

The spectral efficiency and relative SINR degradation of the example scenario are plotted

against downlink SNR in Figure 4.2 and Figure 4.3, respectively, where the lines are

representing the results based on the closed-form analysis and star markers,∗, are the

corresponding simulation results. The perfect alignment between analytical and simulation

results proves the accuracy of the closed-form analysis and the used approximations. As

can be seen in Figure 4.2 and Figure 4.3, the impact of non-reciprocity in the channel is

much more severe in high SNR region as the performance in low SNR region is mainly

limited by noise and not the channel non-reciprocity. While both precoding schemes,

namely ZF and MRT, are suffering from channel non-reciprocity mainly in high SNR

region, it is clear that ZF precoding scheme is much more sensitive to such non-idealities,

as expected based on the analysis in Section 4.3.4.

The impacts of increasing the number of BS antennas on the spectral efficiency are

evaluated in Figure 4.4. As can be seen, the results are perfectly inline with the implications

made by analytical asymptotic performance study in Section 4.3.3 where it was concluded

that under non-reciprocal channels i) both ZF and MRT precoded systems have a finite

achievable sum-rate saturation level; ii) the saturation level is identical for both precoding

schemes. The results clearly confirm that the spectral efficiency of both ZF and MRT

52

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

Systems

Figure 4.3: Relative SINR degradation vs. downlink SNR (ρd) forN = 100, Mtot=K = 20,

τu=Mtot,ρu= 0 dB.

Figure 4.4: System spectral efficiency vs. the number of antennas at BS (N) for Mtot=K = 20,

ρd= 20,τu=Mtot,ρu= 0 dB,Tcoh= 250. Saturation levels based on (4.21) are plotted in

green horizontal lines for the two indicated channel non-reciprocity parameter settings.

precoded systems saturate towards the value derived in Section 4.3.3. As discussed

earlier, increasing the number of antennas in the BS side, which increases the number

of non-reciprocal transceiver chains and antenna units, causes reduction in advantage

of ZF over MRT to the point that the performance of both systems saturates to the

same value. Note that as opposed to, e.g., pilot contamination [94] problem where the

performance saturation happens with having around 10

5

_{BS antennas [102], the number}

of BS antennas that causes performance saturation due to channel non-reciprocity is

around 10

3

or even lower which shows the practical relevance of the results.

In Figure 4.5, the optimal number of simultaneously scheduled single-antenna UEs is

calculated as a function of channel non-reciprocity for two example values of downlink

Figure 4.5: Optimal number of single-antenna UEs to maximize system spectral efficiency vs.

non-reciprocity level (σ2_a d=σ

2

c_d = channel non-reciprocity level, whileσ2c_od =δ2c_d = channel

non-reciprocity level−10 dB) for N = 100, Mtot=K = 20, ρd= 20,τu=Mtot,ρu= 0 dB,

Tcoh= 250.

SNR, namely, ρ

_d

= 20 dB, 0 dB. This optimal number of simultaneously scheduled

single-antenna UEs, K

_opt

, refers to the K which maximizes the spectral efficiency and

is derived by evaluating (4.10) for all the values of N≥ K ≥ 1. Based on the obtained

results, K

_opt

drops for both precoding schemes as the channel non-reciprocity level, and

subsequently interference in the UE side, increases. Such drops are more visible in high

SNR region, i.e., ρ

d

= 20 dB, while in low SNR region, i.e., ρ

d

= 0 dB, the performance is

limited mainly by the receiver thermal noise. Comparing ZF and MRT precoded systems,

such drops can be experienced in the case of MRT precoding scheme in fairly severe

non-reciprocity levels, e.g., σ

2

a_d

>

−15 dB, whereas ZF precoded systems suffer from

a significant drop already with moderate channel non-reciprocity levels, e.g.,

−30 dB

< σ

2

a_d

<−20 dB. It is interesting to note that as opposed to ideal reciprocal scenario,

the optimal number of simultaneously scheduled single-antenna for MRT is higher than

that of ZF for high SNR values under moderate channel non-reciprocity levels.

Figure 4.6 illustrates the maximum tolerable channel non-reciprocity level as function of

downlink SINR at the UE side based on the derived SINR expressions in (4.13) and (4.18).

The considered example scenario covers two downlink SNR values, namely, ρ

_d

= 20 dB, 0

dB. As an example point in the obtained results, in order to guarantee 15 dB for downlink

SINR at the UE side in ZF precoded system with ρ

d

= 20 dB, channel non-reciprocity

level cannot be higher than around−20 dB. Such analysis can be used in practical system

design and deployments, e.g., to calculate the required channel non-reciprocity calibration

levels for a given target downlink transmission performance, which proves the applicability

of the provided analytical results in practical systems.

In document Analysis and Mitigation of Channel Non-Reciprocity in TDD MIMO Systems (Page 65-67)