“…Therefore, the resulting effective DL and UL channels are not reciprocal, which is known as channel non-reciprocity problem in TDD systems [4], [5]. As shown in [6], [7], channel non-reciprocity has two main sources, one is the frequencyresponse (FR) mismatches between transmitter and receiver chains of any individual transceiver, and the other one is the difference in the mutual coupling effects between the antenna elements in antenna array based devices in transmitting and receiving modes.…”
Section: Introductionmentioning
confidence: 99%
“…The estimation of channel non-reciprocity in TDD based MIMO systems has also been addressed in various works [3], [4], [6], [10], [11]. These studies can be divided into three main categories: The first two refer to such methods which are performed in BS using a reference antenna and are called "selfcalibration" methods [3], [4], [6], [10].…”
Section: Introductionmentioning
confidence: 99%
“…These studies can be divided into three main categories: The first two refer to such methods which are performed in BS using a reference antenna and are called "selfcalibration" methods [3], [4], [6], [10]. These two categories can be further differentiated based on the availability of additional circuitry.…”
Section: Introductionmentioning
confidence: 99%
“…These two categories can be further differentiated based on the availability of additional circuitry. The third category refers to over-the-air (OTA) methods in which BS transmits pilot signals to UEs and receives back properly precoded signals from UEs [6], [11] to facilitate nonreciprocity estimation.…”
Section: Introductionmentioning
confidence: 99%
“…As novel contributions, we consider a massive MIMO system model which incorporates both FR mismatch and mutual coupling mismatches unlike many of the works that consider only FR mismatch, such as [3], [4], [6], [10], [11] or works that focus on more classical small scale MIMO systems [6], e.g., 2-4 BS antennas.…”
Abstract-In this paper, we study the estimation of channel non-reciprocity in precoded time division duplexing based massive multiple-input multiple-output (MIMO) systems. The considered channel non-reciprocity model covers both the frequencyresponse and the mutual coupling mismatches between the transmitter and the receiver chains of a massive MIMO basestation (BS). Based on the assumed non-reciprocity model, it is shown that the effective downlink channel can be decomposed as a product of the uplink channel and another sparse matrix, referred to as the BS transceiver non-reciprocity matrix. Stemming from such modeling, we then propose an efficient estimator of the BS transceiver non-reciprocity matrix exploiting its sparse nature, combined with an appropriate formulation of the associated overthe-air pilot-signaling. The mean-squared error performance of the overall corresponding estimation method is finally evaluated using extensive computer simulations which indicate that the nonreciprocity characteristics can be estimated efficiently and accurately, thus potentially facilitating large system-level performance gains in multi-user massive MIMO systems.
“…Therefore, the resulting effective DL and UL channels are not reciprocal, which is known as channel non-reciprocity problem in TDD systems [4], [5]. As shown in [6], [7], channel non-reciprocity has two main sources, one is the frequencyresponse (FR) mismatches between transmitter and receiver chains of any individual transceiver, and the other one is the difference in the mutual coupling effects between the antenna elements in antenna array based devices in transmitting and receiving modes.…”
Section: Introductionmentioning
confidence: 99%
“…The estimation of channel non-reciprocity in TDD based MIMO systems has also been addressed in various works [3], [4], [6], [10], [11]. These studies can be divided into three main categories: The first two refer to such methods which are performed in BS using a reference antenna and are called "selfcalibration" methods [3], [4], [6], [10].…”
Section: Introductionmentioning
confidence: 99%
“…These studies can be divided into three main categories: The first two refer to such methods which are performed in BS using a reference antenna and are called "selfcalibration" methods [3], [4], [6], [10]. These two categories can be further differentiated based on the availability of additional circuitry.…”
Section: Introductionmentioning
confidence: 99%
“…These two categories can be further differentiated based on the availability of additional circuitry. The third category refers to over-the-air (OTA) methods in which BS transmits pilot signals to UEs and receives back properly precoded signals from UEs [6], [11] to facilitate nonreciprocity estimation.…”
Section: Introductionmentioning
confidence: 99%
“…As novel contributions, we consider a massive MIMO system model which incorporates both FR mismatch and mutual coupling mismatches unlike many of the works that consider only FR mismatch, such as [3], [4], [6], [10], [11] or works that focus on more classical small scale MIMO systems [6], e.g., 2-4 BS antennas.…”
Abstract-In this paper, we study the estimation of channel non-reciprocity in precoded time division duplexing based massive multiple-input multiple-output (MIMO) systems. The considered channel non-reciprocity model covers both the frequencyresponse and the mutual coupling mismatches between the transmitter and the receiver chains of a massive MIMO basestation (BS). Based on the assumed non-reciprocity model, it is shown that the effective downlink channel can be decomposed as a product of the uplink channel and another sparse matrix, referred to as the BS transceiver non-reciprocity matrix. Stemming from such modeling, we then propose an efficient estimator of the BS transceiver non-reciprocity matrix exploiting its sparse nature, combined with an appropriate formulation of the associated overthe-air pilot-signaling. The mean-squared error performance of the overall corresponding estimation method is finally evaluated using extensive computer simulations which indicate that the nonreciprocity characteristics can be estimated efficiently and accurately, thus potentially facilitating large system-level performance gains in multi-user massive MIMO systems.
Theory is the first term in the Taylor series expansion of practice. Thomas Cover 5 1.2 Signal distributions Table 1.1 Constellation minimum distancesConstellation d min M -PSK 2 sin π M Square M -QAM 6 M −1 M -ary phase shift keying (M -PSK), where s m = e j2π m M +φ0 m = 0, . . . , M − 1 (1.1) with φ 0 an arbitrary phase. Because of symmetry, the points are always equiprobable, p m = 1/M for m = 0, . . . , M − 1. Special mention must be made of binary phase-shift keying (BPSK), corresponding to M = 2, and quadrature phase-shift keying (QPSK), which corresponds to M = 4. Square M -ary quadrature amplitude modulation (M -QAM), where the in-phase and quadrature components of s independently take values in the set 3 2(Nonsquare M -QAM constellations also exist, and they are employed regularly in wireline systems, but seldom in wireless.) Although making the points in a M -QAM constellation equiprobable is not in general optimum, it is commonplace. Note that, except for perhaps an innocuous rotation, 4-QAM coincides with QPSK.
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