Multi-Cell

In this part, the impacts of UE transceiver FR mismatch on the performance of multi-cell

MIMO networks are evaluated for both centralized and decentralized precoding schemes

while σ

2

B

= σ

2M

= σ

2D

= 0. As an example, we consider a scenario where there are two

quad-antenna BSs each supporting 3 dual-antenna UEs which leads to having 6 UEs in

total in the network. Frequency flat Rayleigh fading channel is chosen as the propagation

environment between each BS and UE pair. The average path-loss between a BS and its

associated UEs is assumed to be 0 dB, while the same parameter is chosen to be 3 dB

for the non-associated UEs which are supported by other BSs. The considered scenario

represents a case in which all the UEs are close to cell edges. The number of iterations

for in-cell optimization in strategy B for the faster convergence is chosen to be 15.

Figure 3.6 demonstrates the impacts of UE transceiver FR mismatch on the average

achievable sum-rate for each BS where the number of iterations is assumed to be 30.

As shown, with UE transceiver FR mismatch being σ

_F2

=−20 dB, there is essentially

no performance degradation in the centralized precoding scheme. Whereas, there is

substantial loss in sum-rate when decentralized precoding is used. In general, strategy

A is found to be more sensitive to UE transceiver non-reciprocity compared to strategy

B. It can be partially justified by the fact that impact of transceiver non-reciprocity in

the UE side is related to inter-cell interference in strategy B, while, in strategy A, the

Figure 3.7: Relative per BS achievable sum-rate degradation vs. level of FR mismatch in the

UE side. There are two BSs, each one is equipped with 4 antennas and serves 3 dual-antenna UEs.

impacts of UE transceiver non-reciprocity depends on all the interference sources and

even the useful signal.

Finally, we evaluate the impacts of transceiver FR mismatch in the UE side on relative

achievable sum-rate degradations in Figure 3.7. As illustrated, with high downlink SNR,

even with extremely high values of UE transceiver FR mismatch (σ

2

F

= 0 dB), the

centralized precoding scheme has negligible performance degradation. Whereas, with

lower downlink SNR values, there is clear performance degradation with relatively high

levels of UE transceiver FR mismatch, i.e., σ

2

F

>

−10 dB. On the other hand, the

performance of decentralized precoding schemes is certainly impacted even by small levels

of UE transceiver FR mismatch and high SNR values. In this example scenario, in order

to achieve performance close to the one in ideal reciprocal case the maximum level of

transceiver FR mismatch at the UE side should be around−40 dB with strategy A, and

around−30 dB with strategy B. Such low levels of FR mismatches are in general very

hard to maintain in practical transceivers without efficient calibration procedures.

Analysis and Mitigation of

Channel Non-Reciprocity in

Massive MIMO Systems

In this chapter we extend the channel non-reciprocity analysis and mitigation studies to

massive MIMO systems based on the publications [P1] – [P5]. The impacts of FR and

mutual coupling mismatches on the performance of precoded TDD single-cell scenario is

first analyzed based on the work in [P2] and [P3] where closed-form analytical expressions

are derived for effective SINRs and the corresponding achievable sum-rates. In particular,

[P2] investigates the channel non-reciprocity problem with multi-antenna UEs under

imperfect CSI, i.e., without assuming perfect effective uplink channel estimation. Then,

based on the analysis and depending on the availability of downlink pilots, [P4] proposes

two different algorithms to efficiently estimate the level of BS transceiver non-reciprocity at

the UE side which allows the network to schedule BS transceiver non-reciprocity calibration

rounds more efficiently. An algorithm is then proposed in [P5] to estimate BS transceiver

non-reciprocity parameters. Finally, considering the more generic case of having imperfect

uplink CSI, [P1] proposes a framework in which transceiver non-reciprocity impacts in

both BS and UE sides are estimated and mitigated. In this framework, owing to the

proposed pilot signaling scheme, BS and UE sides’ transceiver non-reciprocity matrices

are first estimated and then used in the proposed channel non-reciprocity aware precoder

to achieve performance close to that of ideal reciprocal channels.

4.1

Background and Prior Art

Due to the large potential of massive MIMO systems, there have been numerous studies

focusing on such networks and their performances during the past few years, e.g., [58, 62,

72 – 75, 93 – 95] and references therein. Most of the massive MIMO studies in the literature,

including [58, 62, 72 – 75, 93 – 95], have assumed UEs to be single-antenna devices as BSs

can employ the available extra degrees of freedom offered by massive MIMO systems to

reduce the required complexity of UEs [95]. However, in practice, most of the current

38

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

Systems

generation UEs are equipped with more than one antenna. This would allow the network

to have higher per UE data rate. Another common assumption in many massive MIMO

studies, e.g., [58, 62, 75, 93, 94], is the use of statistical properties of precoded downlink

channels to acquire downlink CSIs required for detection purposes at the UE side. This

is in contrast to the small-scale MIMO system scenario where UEs rely on pilot symbols

sent from the BS side for estimating the effective precoded downlink channel for data

decoding [66].

The impacts of channel non-reciprocity on the performance of TDD massive MIMO systems

are discussed in [72 – 75]. In particular, [73] considers BS transceiver FR mismatch as

the only source of channel non-reciprocity while [74, 75] take also FR mismatch at the

UE side into account. The effects of mutual coupling mismatch in the BS side are then

discussed in [72] where UEs are assumed to have ideal reciprocal transceivers. [72, 74]

have focused on evaluating the impacts of channel non-reciprocity on ZF precoded TDD

massive MIMO systems, whereas [73, 75] also considered MRT precoding scheme. All

the mentioned works, i.e., [72 – 75], have considered perfect uplink channel estimation

and thus do not provide any insight on the joint impacts of channel non-reciprocity and

imperfect CSI in TDD networks.

The channel non-reciprocity mitigation works mentioned in Chapter 3, e.g., [71, 76, 77,

77, 81 – 85] are mainly developed to be applied in small-scale MIMO systems where the

number of antennas in a given BS is relatively small. In general, such methods cannot be

directly applied on massive MIMO systems as their implementations and computational

complexities grow with the number of antennas in the BS side. In this respect, [96 – 99]

have focused on designing channel non-reciprocity compensation methods which are

feasible for massive MIMO system use. In [96 – 99], each BS performs self-calibration

where pilots signals are sent from a chosen reference antenna in the BS and received

from all other antennas in the same BS. Such methods do not require additional circuitry

to be developed in the BS side. On the other hand, they only focus on mitigating

FR mismatches in the BS side while neglecting mutual coupling mismatches and also

transceiver non-reciprocity in the UE side.

4.2

General Assumptions

As mentioned in Chapter 2, each data stream is assumed to be allocated to one antenna

in the UE side in case of having ZF or MRT precoding schemes. Since the only con-

sidered precoding schemes in this chapter are ZF and MRT, {m, M

k

, M

total

} are used

interchangeably with {q, Q

_k

, Q

_total

}, for notational simplicity. In this chapter, the signal

models are written for a given antenna in the UE side, e.g., the m-th antenna in the UE

side, as opposed to a given stream in a given UE, e.g., the q-th stream in the k-th UE.

Furthermore, since each antenna has its own data stream, there is no special receiver

processing as the ones in common multi-antenna receivers. A common massive MIMO

assumption is also used throughout this chapter where the effective uplink channel matrix,

G, has i.i.d.

CN (0, 1) elements [58, 61, 62, 66]. As shown in [100], with increasing number

of antennas, such assumption very accurately models the behavior of practical massive

MIMO measurements.

In document Analysis and Mitigation of Channel Non-Reciprocity in TDD MIMO Systems (Page 48-52)