Email: see http://www.ntnu.edu/iet/staff ... factor, load modulation, massive MIMO, antenna coupling. ... e.g. [2], and it is commonly referred to as massive MIMO.
Load Modulated Massive MIMO Ralf R. M¨uller∗† , Mohammad A. Sedaghat† and Georg Fischer‡ ∗ Institute
for Digital Communications Friedrich-Alexander Universit¨at Erlangen-N¨urnberg, Erlangen, Germany Email: see http://www.idc.lnt.de/en/mitarbeiter/hochschullehrer/prof-dr-ing-ralf-mueller/ † Department of Electronics and Telecommunications The Norwegian University of Science and Technology, Trondheim, Norway Email: see http://www.ntnu.edu/iet/staff ‡ Lehrstuhl f¨ ur Technische Elektronik Friedrich-Alexander Universit¨at Erlangen-N¨urnberg, Erlangen, Germany Email: see http://www.lte.techfak.uni-erlangen.de/wir-ueber-uns/mitarbeiter/index.shtml/georg-fischer.shtml
Abstract—We propose a new hardware architecture for costand size-effective implementation of massive MIMO transmitters based on load modulation that is fully compatible with standard receiver architectures. With load modulation, a massive MIMO transmitter can be driven by a single power amplifier operating at constant envelope. The various data streams are modulated onto the antennas elements by varying the complex impedances of the various antenna circuits at symbol rate. The law of large numbers ensures that the common power source is matched to the parallel concatenation of the various antenna circuits, if the number of antenna elements is very large. For 100 antenna elements that are supposed to transmit Gaussian-like signals, e.g. due to OFDM modulation and/or precoding, the crest factor is only 1.2 dB at a clipping probability of 0.1%. In that case, load modulation reduces the average consumed power and the amplifier peak power by 49% and 79%, respectively, as compared to classical distributed amplifiers with voltage modulation. Furthermore, one class F amplifier can be used to replace 100 class A/B amplifiers. Mutual antenna coupling need not be addressed by a physical matching network, but can be mitigated dynamically by digital signal processing in baseband without additional hardware. This allows for closer antenna spacing as in architectures with distributed amplifiers. Index Terms—multi-antenna systems, power amplifier, crest factor, load modulation, massive MIMO, antenna coupling.
I. I NTRODUCTION
= W
L W Antenna
9 W
5
Fig. 1.
General model of RF-circuitry.
at the access point, multiuser interference can be overcome regardless of the powers and number of the interfering users. The two main obstacles to the implementation of massive MIMO systems are the hardware costs and the physical size of the antenna array1 . Load modulation offers the opportunity to reduce both costs and size of massive antenna transmitters. This is detailed in the subsequent Sections IV and V, respectively, after the concept of load modulation has been introduced in Section II and related work has been discussed in Section III. A summary with outlook is given in Section VI. II. L OAD M ODULATION The purpose of radio-frequency (RF) circuitry is to create a current on an antenna element that is proportional to the signal s(t) to be transmitted. If we model the transmitter as shown in Fig. 1, the current on the antenna is given by
In [1], a multiple antenna system was proposed that mimics the idea of spread-spectrum. By massive use of antenna elements, it can cope with minimal signal processing effort. Like a large processing gain that can be realized in a spreadspectrum system by massive use of radio spectrum, a large array gain is realized by a massive use of antenna elements. This system design has recently attracted much attention, see e.g. [2], and it is commonly referred to as massive MIMO. Its advantage over the old spread-spectrum idea lies in the fact that antennas can be manufactured in arbitrarily high numbers, while radio spectrum is limited. Since the array gain grows unboundedly with the number of antenna elements
with V (t) denoting the voltage at the amplifier, Z(t) denoting the complex impedance of the circuit, and R denoting the resistance of the antenna. In standard RF hardware, the circuit impedance is kept constant and the voltage is formed proportional to the transmit signal. This is called voltage modulation in the sequel. The
The project HARP acknowledges the financial support of the Seventh Framework Program for Research of the European Commission under grant number 318489.
1 Pilot contamination [3] has also been regarded as a serious problem of massive MIMO systems. However, recent progress, e.g. [4], [5], has alleviated this issue.
i(t) =
V (t) Z(t) + R
(1)
!
= W = W
9 W
=N W
L W L W
LN W
The single RF transmitter
5
. . .
Baseband block
5
io 2
Load Modulator
5
PA
. . .
ic R
v0 cos(ω t) Fig. 2.
io1
Load Modulator
Load modulation for massive MIMO.
1. solution Our circuit impedance can be perfectly
ioN
Load Modulator
advantage is that the matched to the antenna, such that no power is reflected ! The single back into the amplifier. The disadvantage, however, is theRF transmitter Fig. 3. Load modulation with circulator. large back-off that is required to drive the♦ amplifier, What as is the power efficiency? detailed in Section IV. Furthermore, mutual coupling can lead to mismatch for close element spacing in multiple antenna L D L D transmitters, cf. Section V. With load modulation, we refer to a circuitry where V (t) L is a sinusoid of fixed amplitude and phase while the circuit impedance Z(t) is chosen such that D 1
1
3
3
2
3
1 Z(t) + R
(2)
is proportional to the complex baseband representation of the transmit signal s(t). The advantage of load modulation is that the amplifier is a simple high-power oscillator. However, load modulation may suffer from severe mismatch of the circuit to the antenna impedance. For this severe disadvantage, load modulation is not used in state-of-the-art transmitter hardware. For massive antenna arrays, however, the mismatch of load modulation can be made the smaller the larger the number cos(ω t) of antenna elements. In that case, a common powerv0amplifier creates a sinusoid that feeds the parallel concatenation of N antenna circuits, cf. Fig. 2. The admittance seen by the voltage source N X 1 Y (t) = (3) Z (t) + R n=1 n is the sum of the admittances of all antenna circuits. The single power source is equivalent to N parallel power sources each of which seeing the average admittance Y (t)/N . Despite the individual impedances Zn (t) + R varying significantly, the law of large numbers ensures that the larger the number of antennas N , the smaller the variation of the average admittance Y (t)/N . For N = 100 antenna elements, the power reflected back to the amplifier is negligible for most combinations of data signals s1 (t), . . . , sN (t). In order to protect the power amplifier from reflected waves, that occur in rare events of unfavorable combinations of data signals, a circulator is applied that re-directs this power to heat a resistor by the current ic in Fig. 3.
Load Modulator
io1
Fig. 4. Implementation of a load modulator by a T–network of 3 variable capacitors and 3 fixed inductors. i Load Modulator
o2
The load modulators can be implemented in various ways. PA In the following, we will discuss two options, which we . consider the most ipromising. c . The first R implementation is analog by means of varactor . diodes, cf. Fig. 4. A T– or Π–network of variable capacitors is sufficient to implement all complex loads that cover most data signals within the complex unit circle [6]. For a single antenna transmitter, load modulation at a data rate of i1.2 Gbit/s oN Load has already been demonstrated in a prototype [7] utilizing Modulator Schottky diodes. More, recently load modulated transmitters were reported in [8]. Due to the nonlinearity of varactor diodes, either oversampling or post-filtering has to be applied. The second implementation is digital by networks of pindiodes. With 64k integrated pin-diode switches, one out of 216 predefined loads can be chosen. Given the fast decay of digital hardware costs, even higher resolution than 16 bit accuracy seems possible. Furthermore, accuracy can be improved by shaping of the quantization noise and passive post-filtering by means of surface acoustic wave (SAW) filters. This implementation has the advantage that it does not require any D/A-converters. Only a level-shifter is required to connect digital baseband to the pin-diode switches. However, a power loss around 1/2 to 2 dB (depending on carrier-frequency) caused
1. High peak-to-average power ratio (PAPR) signals ( 8dB − OFDM) need highly linear power amplifier (e.g., A/B clas 2. Poor power efficiency
III. R ELATED W ORK Load modulation is most common and has been known for long in context of radio-frequency identification (RFID) tags based on backscattering [9]. This is near-field communication at short distance and conceptually very different from cellular communications aiming for high data rates and mobility. The concept of load modulation for far-field communications dates back to [10]. The idea that load modulation can make particular sense for MIMO transmitters is not entirely new, either. The idea of creating a multiplexing gain by changing antenna impedances was pioneered in [11]. In that work, the power source was still voltage modulated and, galvanically, only connected to a single antenna element, called the active one. The other antenna elements, called the passive ones, were (due to close vicinity) inductively fed by the current in the active antenna. The actual currents in the passive antennas were steered by changing their loads. This design was not aimed towards massive MIMO, but to implement a classical MIMO transmitter very compactly and at reduced cost. Its main drawback is that it is not fully compatible with standard receivers for classical voltage-based modulation techniques. A proof-of-concept implementation can be found in [12]. A prototype that evolved from that concept is reported in [13]. A detailed overview on various methods of load modulation for MIMO systems can be found in [14]. Constant envelope transmitters for massive MIMO systems were first proposed in [15]. In contrast to this work, the authors of [15] proposed distributed amplifiers, i.e. one per antenna element. For their proposal, it is irrelevant whether voltage or load modulation is used. The authors achieved constant envelope signals by modifying the precoders at the transmitter side. The drawback of their work is the need for an increased number of antennas to obtain a similar array gain as in classical systems. Furthermore, the constant envelope is constrained to discrete time so far. Current continuous-time implementations either use pulse-shaping giving up constant envelope or create out-of-band radiation due to phase jumps. How to overcome this problem is currently under investigation [16]. Base-band controlled load fluctuations can also be used for de-modulation of MIMO signals by means of a single RFchain [17]. However, the concept is very different form the
Theoritical efficiency of an amplifier in class A/B with 8dB crest factor
80 Maximum power ~ eff.=78% 70
60 Power efficiency (%)
by the SAW filters is to be tolerated. Classical voltage modulation and the proposed implementation of load modulation are only two different alternatives to create the same wave field on air. The same receiver can be used irrespective of whether the transmit signal is created by the proposed load modulation or standard MIMO transmitters based on classical voltage modulation. As a result, the use of load modulation does not imply any loss with respect to theoretical performance bounds set by information theory. Given nowadays amplifier technology, however, the power efficiency (including amplifier losses) of load modulation is significantly higher than the power efficiency of voltage modulation, as to be shown in Section IV. This holds irrespective of the targeted data rate.
Average power
50
40 Crest factor=8dB 30
20
10
0 0
Fig. 5.
20
40 60 Output power (%)
80
100
Power efficiency vs. back-off for class A/B amplifiers.
transmitter technology and exceeds the scope of this paper. IV. C OST R EDUCTION With the cost of digital circuitry continuously dropping, analog hardware is the dominant cost of a massive MIMO transmitter. This holds in particular, if it is implemented in a distributed manner, i.e. a separate D/A-converter, a separate mixer, and a separate power amplifier for each antenna element. Separate power amplifiers must be driven at high back-off. In massive MIMO, irrespective of whether conjugate beamforming or zero-forcing is applied as strategy to focus radiated power, the transmit signals at individual antenna elements are Gaussian-like, as they are the (weighted) superpositions of a large number of random channel coefficients. At moderate clipping probabilities of 0.1% to 1%, a Gaussian signal results in a crest factor of 6.5 dB to 8.5 dB. The theoretical efficiency of class A/B amplifiers at given back-off b is given by [18] π√ η= b. (4) 4 At 8 dB crest factor, the power efficiency is thus at most 31%, cf. Fig. 5. For load modulated MIMO with a common power amplifier the crest factor is greatly reduced due to the averaging effect of the parallel antenna circuits. For independent2 complex Gaussian data signals sn (t) and N antenna elements, the output power is χ2 -distributed with 2N degrees of freedom. 2 Note that even for fully correlated data to be transmitted, the antenna signals sn (t) are statistically independent across antennas, if the channel coefficients are independent of each other and conjugate beam-forming is used.
10
V(t)
9 8
−4
10
Z1(t) Z2(t)
clipping probability
i1(t) i2(t) ZR
crest factor [dB]
7 6
ZN (t)
5
i N(t)
10−3
4 −2
3
Fig. 7.
10
V. S IZE R EDUCTION
2 1 0 0 10
Load modulation for coupled antennas.
1
10
2
# antennas
10
3
10
Fig. 6. Crest factor vs. the number of antenna elements that are fed by a common amplifier.
The crest factor reduction due to this averaging effect is depicted in Fig. 6. For N = 100 antenna elements, and 0.1% clipping, the crest factor is around 1.2 dB. There is no need to deploy linear class A/B amplifiers. Instead one can use a simpler class F amplifier. Constantly operating at peak power, it has an efficiency of 80 % [18]. Note, however, that the crest factor is not 0 dB, but 1.2 dB. This means that 24% of the output power is reflected by the antennas and converted to heat by the circulator current ic in Fig. 3. The overall efficiency including the circulator current is thus 61%. Given a total radiated power of 189 mW, we would either need N = 100 distributed class A/B amplifiers consuming 6.1 mW each for voltage modulation or a single common class F amplifier consuming 310 mW for load modulation. We conclude that voltage modulation consumes approximately twice as much energy as load modulation does. Savings are even more pronounced with respect to hardware costs. The class A/B amplifiers need to be designed for 8 dB back-off yielding 12 mW peak power for each of them. The common class F amplifier is operating at peak power all the time. The peak power is the radiated power plus the loss due to the circulator current, i.e. 249 mW. Although, the common amplifier replaces N = 100 distributed amplifiers, its peak power is not 100 times, but only 21 times higher. This will save twofold on hardware costs: both due to the cheaper type of amplifier and the 5 times lower aggregate peak power. Finally, discretized load modulators do not require any D/A converters.
Spacing antenna elements closely leads to electromagnetic coupling between them, i.e. the current in one element induces currents in adjacent elements and vice versa. This leads to antenna currents that are correlated with each other. Furthermore, antenna coupling affects the impedances of the individual antenna elements and leads to mismatch of distributed power sources driving them. In that case, sophisticated analog multi-port matching networks are needed to mitigate mutual coupling. These networks implement an N × N impedance matrix with N denoting the number of antennas. In practice, this impedance matrix is dominated by the diagonal. However, the closer the antenna elements are spaced, the more offdiagonal elements of the matrix are relevant and need be implemented. Alternatively, mutual coupling can be avoided by distant antenna spacing. Aiming for size reduction, distant spacing is not an option, thus, we need to find efficient ways to deal with mutual coupling. Load modulated massive MIMO offers several advantages over voltage modulated massive MIMO with respect to mutual coupling. For close antenna spacing, the generic structure of load modulated MIMO shown in Fig. 2 transforms into the structure shown in Fig. 7 where ZR denotes the N × N impedance matrix of the antenna array. As the power source is scalar, the matching network degenerates to an N × 1 vector of load modulators leaving the block structure of Fig. 3 unaffected by mutual coupling. Mutual coupling does affect the currents at the individual antenna elements in an unwanted manner, though. Due to linearity of the antennas, this effect can be described by a linear matrix transform of the current vector i(t) = [i1 (t), i2 (t), . . . , iN (t)].
(5)
This unwanted linear transform can be easily equalized by premultiplication of the digital baseband signal with the inverse matrix. In voltage modulated massive MIMO systems, such a pre-multiplication is possible, too. The pre-multiplication, however, only solves the problem of linear signal distortion by mutual coupling. It does not solve the issue of antenna
mismatch. To overcome antenna mismatch, voltage modulated transmitters require a multi-port matching network, load modulated transmitters simply utilize the law of large numbers. While in theory there is no limit on the directivity of a given antenna aperture [19], implying that there is no theoretical lower limit to the size of a massive MIMO array, robustness puts constraints on array miniaturization, in practice. Superdirective antennas are anything but robust. The larger the ratio of directivity and size, the more sensitive they are with respect to small changes of permittivity or permeability within their vicinity. Load modulated massive MIMO offers the possibility of dynamic antenna decoupling. Uplink pilot data can be utilized to measure the instantaneous coupling matrix of the array and combat the deviations from its desired values by adapting the loads on the antenna elements. Fluctuations of permittivity or permeability can be tracked and mitigated in a similar manner as multitpath fading is treated in mobile communications. This will greatly improve the robustness of highly directive arrays with small aperture and allow for the implementation of massive arrays with element spacings significantly below half a wavelength. The existence of such MIMO arrays has been known for long, see e.g. [20], [21]. Having them robust, is a feature promised by load modulation. VI. S UMMARY AND O UTLOOK Load modulation offers several advantages for the implementation of massive MIMO systems. It reduces the cost of hardware implementation, reduces the power consumption, enables smaller array size, and promises dynamic adaptation to fading in the near-field of the transmitter. Load modulation can be implemented in several ways. The most promising one seems to be digital by means of pindiode networks. It gives digital baseband signal processing full control over both the radio-frequency data-bearing signals and the impedances and scattering factors of the RF-antenna circuitry. It pushes the interface between digital and analog hardware further towards the antenna connector and opens for RF-adaptation by baseband algorithms. R EFERENCES [1] T. L. Marzetta, “How much training is required for multiuser MIMO?” in Fortieth Asilomar Conf. on Signals, Systems, & Computers, Pacific Grove, CA, USA, Oct. 2006. [2] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, and F. Tufvesson, “Scaling up MIMO: Opportunities and challenges with very large arrays,” IEEE Signal Processing Magazine, vol. 30, no. 1, pp. 40–60, Jan. 2013.
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