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RADIO COMMUNICATIONS

Incorporating Specific Absorption Rate Constraints into Wireless Signal Design Bertrand M. Hochwald, David J. Love, Su Yan, Patrick Fay, and Jian-Ming Jin

ABSTRACT

Bertrand M. Hochwald and Patrick Fay are with the University of Notre Dame. David J. Love is with Purdue University. Su Yan and Jian-Ming Jin are with the University of Illinois at Urbana-Champaign. This work was supported in part by the National Science Foundation under grant CCF1141868.

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Portable wireless devices used in close proximity to the human body have transmitter power constraints that are dictated in part by regulatory limits on a form of electromagnetic exposure called specific absorption rate (SAR). SAR, measured in Watts per kilogram, is a measure of electromagnetic energy absorption by the body, which can cause the heating of tissue. Some portable wireless devices sold today operate near the accepted human SAR limit. This article examines how SAR constraints can be incorporated into wireless signal design for multiple transmitters. A SAR constraint, although related to a power constraint, differs sufficiently that signals designed specifically for the constraint are needed. Although it is well known that multiple transmitters subject only to a power constraint can improve the link performance of a wireless system compared to a single transmitter, it is not clear when the device is also subject to a SAR constraint: how to model the constraint; whether performance advantages still exist; and how to realize any advantages. In this article, we introduce SAR constraints and discuss the SAR measurement, simulation, and modeling process. We then show how to incorporate the SAR constraint into system performance analysis and code design. We show how SAR codes use multiple transmit antennas to get good combined farfield error performance and near-field SAR performance, improving handset transmitter performance in the critical uplink of a communication system.

INTRODUCTION AND MOTIVATION During transmission, a portable wireless device exposes the human body to electromagnetic radiation, and the amount of near-field exposure that is experienced by a user is regulated. In the United States, the FCC establishes and governs the testing methodologies and exposure limits for electromagnetic radiation generated from devices. Many other countries have similar regulatory agencies that address electromagnetic radiation (e.g., the European Union has Comité Européen de Normalisation Électrotechnique — CENELEC). One common measure of exposure is called specific absorption rate (SAR). SAR,

0163-6804/14/$25.00 © 2014 IEEE

typically measured in Watts per kilogram, is a measure of the rate of energy absorption in a volume of human tissue in the presence of an electromagnetic field. Many wireless systems are limited in performance by the abilities of portable terminals because of their limited size, battery, processors, and transmission power. In particular, the uplink performance in a cellular system from the mobile to the base station is often weak because of the limited transmitter power of a portable phone. In fourth-generation (4G) systems such as WiMAX and Long Term Evolution (LTE), a typical transmitter power for a portable device is 23 dBm. However, this transmitter power is not chosen because power amplifiers with higher output power, good efficiency, and long battery life do not exist. Rather, this choice is a result of the fact that some portable cellular devices from a variety of manufacturers operate near their SAR limit with 23 dBm power, and higher transmitter powers risk the device exceeding this limit. Hence, the SAR constraint acts as a power constraint in devices with a single transmitting element. Since the uplink is generally a limiting factor in a wireless communication network deployment, improvements to the uplink in systems such as LTE are receiving special attention. One such potential improvement is a requirement for portable devices to support up to four transmitter chains operating in the same band [1]. Fifthgeneration wireless systems are considering using multiple transmit chains in the millimeter-wave band. However, it is unclear how, in a SAR-limited device, these multiple transmitters should be used to realize good uplink performance. Improvements in uplink performance can only come with transmission techniques that account for their effect on SAR. Standard space-time techniques are designed with power constraints in mind; these codes are not necessarily SARfriendly. The relationship between how multiple transmitters are used to communicate with a receiver in the far field and their effect on SAR in the near field therefore requires investigation. We argue that two or more low-power transmitters can improve device uplink performance while maintaining, or even reducing, SAR vs. a single transmitter, but only if proper modeling and coding are employed. Standard space-time multiple-transmitter or beamforming techniques

IEEE Communications Magazine • September 2014


do not suffice; new codes and techniques are needed. We overview electromagnetic exposure, SAR testing, measurement, and simulation. We present a model for SAR for multiple transmitters that allows the SAR constraint to be combined with the standard transmit power constraint, thus putting them on an equal footing. We show how transmission strategies, called SAR codes, may be designed to simultaneously maximize farfield performance while controlling near-field SAR. Uplink performance gains of 3 dB in SARconstrained devices are readily obtained using SAR codes vs. standard single-antenna or spacetime techniques.

ELECTROMAGNETIC RADIATION AND SPECIFIC ABSORPTION RATE Devices sold in the United States, and many countries abroad, are tested for the intensity of their induced RF exposure to ensure compliance with regulatory standards for maximum user exposure to non-ionizing electromagnetic fields. The gold standard for regulatory compliance is SAR measurement, expressed in power per unit mass [2]. Devices that emit levels below accepted thresholds are considered safe for use by the public in an uncontrolled environment. SAR is a measure of electromagnetic power density and subsequent absorption of electromagnetic radiation. It is expressed as SAR = sE2/r, where s is the conductivity of the tissuesimulating material (Siemens per meter), E is the total root mean square (RMS) field strength (Volts per meter), and r is the mass density of tissue-simulating material (kilograms per meter cubed). SAR is measured with the device operating in its intended manner at full transmit power (“worst case” setting). Since the electric field is generally not spatially uniform, SAR is averaged over a volume of tissue, either one gram or 10 grams. Depending on the nature of the source, the E field is also generally not constant in time, and short-term time averaging is done by a probe. The measured average value is compared to a threshold to determine compliance. The threshold enforced is a function of the device usage; higher limits are allowed for occupational usage with controlled exposure. The “partial body” threshold for the general population and uncontrolled exposure [3] is  SAR £ SAR0 = 1.6 W/kg.

(1)

This threshold applies, for example, to the head and torso. Limits in other countries are similar (e.g., CENELEC enforces 2 W/kg for partial body measured over 10 grams for partial body exposure). A SAR measurement requires specialized equipment, including mannequins, electrolytes, and robotically controlled probes, with the device operating at full power while the probe searches for worst-case field measurements. Although all consumer transmitting devices must obey human exposure limits, SAR testing generally applies to devices meeting the portable classification in that they can be carried on a person and are used


within 20 cm of the body. Devices such as cellular phones, wireless routers, wireless USB sticks, and smart WiFi cameras are considered portable since they are often held close to the head, clipped to the waistline, or stored in a handbag or pocket. Reliable simulations of SAR are also widely available. For example, the CST Studio Suite is an industry-standard tool for a wide range of microwave and radio frequency applications and has been approved by the FCC to comply with draft recommended practices for computational SAR techniques. CST Studio employs a finitedifference time-domain (FDTD) method to calculate the SAR in human tissues. According to the FCC guidelines [2], the simulation results from an FDTD calculation may be used as part of the test reports submitted for equipment authorization that requires SAR evaluation. The threshold SAR0 in Eq. 1 must be obeyed by the device at all times. SAR testing requires the device to be held in a variety of typical operating conditions (or “gestures”) by a non-conducting holder, near a mannequin head or torso, while a field probe makes measurements. The worst case measurement is compared with SAR0 to determine if the device passes. The operating condition that leads to the worst case SAR depends on the industrial design of the wireless device and placement of amplifiers, shields, and types of antennas. The threshold SAR 0 is not dependent on the number of transmitting elements.

Although all consumer transmitting devices must obey human exposure limits, SAR testing generally applies to devices meeting the portable classification in that they can be carried on a person and are used within 20 cm of the body. Devices such as cellular phones, wireless routers, wireless USB sticks, and smart WiFi cameras are considered portable.

SAR AND MULTIPLE TRANSMITTERS Survey articles (e.g., [4]) summarize the evolution of antenna designs that have the goal of reducing SAR in mobile phones. These reports emphasize antennas such as the planar monopole (PMA) and planar inverted-F antenna (PIFA) that developed as phones became smaller and antennas were mounted within the device. The PIFA antenna in particular has beneficial SAR characteristics since this antenna tends to direct energy toward the back of the phone away from the head. Some advanced techniques include ferrite loading, auxiliary parasitic elements, and the use of metamaterials and high-impedance surfaces such as artificial magnetic conductors, with the goal of “trapping” energy that might otherwise be directed toward the person [5]. Early steps toward studying SAR when using multiple in-band transmitters in a portable device include [6], where a planar diversity antenna with horizontal and vertical polarization modes is examined and its SAR computed. Other examples of diversity antennas include [7]. In [8] it is shown that certain phases in a phased array have SAR 10 dB lower at 1.8 GHz for two transmitters vs. a single transmitter. A study in [9] shows how SAR behaves as a function of phase difference between two antennas at 1.9 GHz, where certain phases mitigate SAR and others enhance it. Other examples of analysis of SAR with multiple antennas include [10, 11]. These studies generally analyze and model typical gestures for worst case SAR, and their results are with respect to this gesture. However, largely unexploited to date is how to formulate a model for SAR and integrate the model into the operation of a wireless communication system

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8

SAR meas SAR model Single Tx

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SAR (W/kg)

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Figure 1. Data and model of SAR vs. q. The solid data curve is obtained using CST Studio Suite 2011, with each of the two antennas driven with 0.5 W of power at 1.8 GHz. The SAR reaches it maximum at q  p. The equivalent single-antenna SAR transmitting 1 W is 4.92 W/kg, indicated by the dash-dotted line. The model (dashed line) is taken from Eq. 2.

network with receivers in the far field. We show an example wherein SAR and far-field wireless communication performance measures are integrated into one system model. It is well known that if multiple transmitters are used judiciously, there are significant farfield reliability and throughput advantages over a single transmitter. Importantly, these communication system advantages are derived with the transmitters subject to a sum-power constraint. SAR, however, is a measure of power per unit mass and therefore does not directly measure the total output power of a device. Hence, for a given total output power, SAR may be decreased by distributing the power over a larger tissue volume. One potential SAR benefit of using multiple transmitters derives from the fact that multiple transmitting elements are physically separated, hence providing an opportunity to decrease the power per unit mass. However, this qualitative effect must be supplemented with a model for the SAR constraint as a function of the transmitted signal vector. We show that the sum-power constraint and SAR constraint, although related, are different enough to require substantial advances in the modeling, analysis, and design of communication techniques to maximize the performance of portable wireless devices.

MODELING SAR WITH MULTIPLE TRANSMITTERS Manufacturers work hard to separate transmitting antennas as much as possible from each other on a given device, but this is becoming increasingly difficult as devices get smaller and

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slimmer while the number of radios gets larger. Restrictions on antenna placements in portable devices are generally very severe. Transmitting elements are typically confined to specific areas of the printed circuit board where they interfere as little as possible with other circuitry, and only a few square centimeters may be available. Devices such as USB dongles are so small that antenna spacings of less than 1/10 of a wavelength need to be accommodated. We must assume that antennas operating on a single carrier frequency on a portable device are close enough that they interact significantly. Consider a two-antenna system transmitting with equal power from each antenna, but with a phase shift of q between the two antennas. With two antennas transmitting 1.8 GHz signals, SAR was simulated using the CST Studio Suite 2011 Microwave Studio as a function of the phase difference q between antenna 2 and antenna 1 (there is no SAR dependence on common phase). The model of the head and hand includes typical skin, bone, and human tissue conductivity and absorption layers. The model of the phone uses typical industrial design, plastic, shields, and form factor. The phone was held relative to the head in a common gesture. Some results are plotted in Fig. 1, where the SAR and total radiated power are shown. In the figure, the SAR that results from transmitting 0.5 W per antenna (1 W total) oscillates approximately sinusoidally as a function of q, reaching a minimum of close to 3 W/kg at q  p/4 and a maximum of 7.5 W/kg at q  p. Simulation also shows that the equivalent SAR for a single antenna transmitting 1 W is 4.92 W/kg, drawn as the dashed line in the figure. Although these SAR values are much greater than the limit, SAR0 = 1.6 W/kg, this is a result of the 1 W of power delivered to the antennas continuously; power amplifiers for commercial portable devices generally output approximately 23 dBm (200 mW) for 3G (CDMA) and 4G (WiMAX, LTE) technologies, and 33 dBm (2W) for GSM. GSM transmission has 1/8 time-slotted duty cycle, effectively reducing its average output power to 24 dBm.

SAR MODELS The qualitative dependence of SAR on q in Fig. 1 has also been observed by others, such as [9], which contains a similar figure for a two-antenna system operating at 1.9 GHz. A model for the dependence in Fig. 1 is SAR(q) = P(s1+s2 cos(q + q0)), where s1, s2 are positive real parameters, P is the total power supplied to the two antennas, and q0 is a phase offset. In our case, P = 1 W, s1  5.3, s 2  2.1, and q 0  p, as determined by a least squares fit on the measured data. The result is shown in Fig. 1. In the case of the data collected in [9], s1  5, s2  3, and q0  2p/3. Since P is in units of Watts, s1 and s2 have units kg–1. We explain the SAR model as follows. The electric field from two coupled antennas at a point r is ⎡ x1 E(r ) = ⎡⎣ E1 (r ) + γ E2 (r ) E2 (r ) + γ *E1 (r ) ⎤⎦ ⎢ ⎢⎣ x2

⎤ ⎥ ⎥⎦



where E i (r) is the three-dimensional electric field from antenna i = 1, 2 generated by a unit excitation (we use bold to denote vectors), xi is the excitation of antenna i, and g indicates coupling from antenna 1 to antenna 2; the medium is assumed to be reciprocal so that coupling from antenna 2 to antenna 1 is the conjugate g*. Let x = [x1 x2]T. Since SAR is proportional to the averaged E2(r) = E*(r) ⋅ E(r) over a volume V, we obtain Eq. 1, where SV is defined to be a SAR matrix for the volume V. For a given gesture or operating condition of the device, the measuring probe scans for the V that leads to the largest SAR(x) for a given x. Denote this volume V ; we have observed that V depends strongly on the gesture but not strongly on x. By construction, S V is positive semidefinite conjugate-symmetric, and Eq. 2 shows how to compute the SAR for a two-antenna excitation x. The entries of S V can be estimated, for example, using a least squares fit to measured SAR V (x) for various known excitations x. In the notation that follows, we drop the dependency of S V on V  , with the understanding that S depends on the gesture or operating condition of the phone. However, as we explain, a SAR constraint can be imposed on the transmitted signal without needing to know the realtime gesture or operating condition of the device. Note that we can easily recover the — cosine dependence in SAR(q) by letting x =  jq T P[1 e ] . When x is an information-bearing signal in a communication system, it is time-varying on the SARV (x ) ∝

1 V

∫V E

2

• Since SAR £ SAR0 is enforced by the FCC for all operating conditions of the device, our requirement is no more arduous than the FCC requirement. In other words, even if the device is often used in a low-SAR manner away from the human body, such as while a person is texting, the device must always obey the worst case constraint. • The SAR matrices S 1 , …, S L are determined offline during SAR testing. Similar to the power constraint, the SAR constraint does not vary with time or usage of the device. • The matrices S1, …, SL capture and summarize the effects of antenna choices, board layout, industrial design, and operating frequency. Hence, the SAR matrices are strong functions of the device model, but they do not vary from device to device within a given model. • Studies have shown that among the standardized gestures tested, there is usually a “worst case” gesture that is readily found and clearly dominates the SAR of other gestures [13], such that tr(S kQ) ≥ tr(S lQ) for all l = 1, …, L and positive semidefinite Q. We denote the corresponding worst-case SAR matrix simply as S. The matrix model formulation for SAR in Eq. 2 also fits well when there are more than two transmit antennas. Figure 2 shows three antennas in a clam shell phone operating at 1.8 GHz, all driven with equal excitation such that 1 W total power is delivered to the antennas.

1 V

order of microseconds corresponding to the symbol rate of the communication system. Because SAR probes are time-averaging, it becomes more meaningful to measure SAR as a function of average x rather than instantaneous x. We define Q = E(xx*) as the covariance of the transmitted signal where the expectation operator E(⋅) denotes averaging, and write the SAR constraint as SARS(Q) = E(x*Sx) = tr(SQ) £ SAR0 where tr(⋅) denotes matrix trace. This equation can be compared with the commonly used power constraint E||x||2 = tr(Q) £ P. Both the power and SAR constraints should be enforced.

WORST CASE ANALYSIS: DEVICE UNAWARE OF REAL-TIME OPERATING CONDITION Let S 1,S 2, …, S L represent a sequence of SAR matrices corresponding to L > 1 different, often standardized, testing gestures (e.g., [12]) of the device against the head or torso, with and without a supporting hand holding the device. The SAR constraint then becomes max l=1,…,L tr(S l Q) £ SAR0. This is a worst case constraint on Q, and may seem overly restrictive and difficult to enforce, but:


in portable devices are generally very severe. Transmitting elements are typically confined to specific areas of the printed circuit board where they interfere as little as possible with other circuitry, and only a few square centimeters may be available.

(2)

(r ) d r

⎡ 2 (E1 (r ) + γ E2 (r ))* ⋅ (E2 (r ) + γ *E1 (r )) E1 (r ) + γ E2 (r ) *⎢ x 2 ∫V ⎢ * * E2 (r ) + γ *E1 (r ) ⎢ (E2 (r ) + γ E1 (r )) ⋅ (E1 (r ) + γ E2 (r )) ⎣  x * SV x

=

Restrictions on antenna placements

⎤ ⎥ ⎥ x dr ⎥ ⎦

Some values of relative phase are shown simulated along with a least squares fit of the SAR matrix and the corresponding surface plot generated by the matrix. Because of space limitations, the SAR matrix is not presented here. The small distance between the simulated values (black stems) and the surface plot indicates a good model approximation.

INTEGRATING SAR CONSTRAINTS INTO COMMUNICATION AND INFORMATION THEORY Most existing models and capacity calculations with multiple antennas enforce only simple power constraints. These models apply to the downlink of a communication system, where the base station is the transmitter, and a SAR constraint does not generally apply. On the uplink, where a portable device is the transmitter, the models, capacity calculations, and code designs must incorporate the SAR constraint in addition to the power constraint. We now touch on capacity and coding considerations with a SAR constraint.

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The SAR spatial averaging effect of the 8

Alamouti code and spatial multiplexing

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intuitively holds SAR (W/kg)

because the phase offset between the two transmit anten-

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nas is uniformly distributed. This means

high SAR are not avoided, and combi-

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that symbol combi-

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nations with phase offsets that have a low SAR are not preferred.

Figure 2. Three antennas in a clam shell phone simulated next to a human head, including the least squares model fit of SAR matrix S with equal excitation of all antennas and 1 W total transmitted power. Black vertical stems show simulated SAR using CST Studio Suite at pairs (q1, q2), where q1 is the relative phase of antennas 2 and 1, and q2 is the relative phase of antennas 3 and 1. The surface plot shows SAR as modeled by a SAR matrix.

SAR CODES Using standard tools in information theory as applied to multiple-antenna channels, we may formulate a SAR-constrained capacity [14], where the traditional power constraint is augmented with a SAR constraint corresponding to the worst case SAR matrix. This capacity requires knowledge of the SAR matrix S, but does not require real-time knowledge of how the device is being held. Similarly, code designs to achieve this capacity will require knowledge of S, but no knowledge of how the device is being held. The capacity represents a fundamental performance limit for a SAR-constrained device. The inverse equation is also meaningful. The minimum SAR needed to achieve an error-free rate of r b/channel use is denoted SARmin(S, r). Standard space-time codes that have been proposed for multiple-antenna power-constrained channels generally are not optimum for SAR-constrained channels. Two examples help show why. The Alamouti code is a popular downlink code used extensively in the 4G standards for two transmitters sending two symbols. The symbols are generally chosen independently from standard phase shift keying (PSK) or quadrature amplitude modulation (QAM) constellations. The space-time encoding of these two symbols impacts the SAR. Alamouti employs a phase reversal technique between the first and second encoded channel uses. This results in an averaging of the SAR between the two antennas. If the model used for a clam shell phone is applied, the time-averaged SAR for the Alamouti code (for 1 W total transmitter power) exhibits spatial averaging and has SAR(Alamouti) = 5.3 W/kg. A similar phenomenon happens with spatial multiplexing, where elements of the transmitted vector are chosen from inde-

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pendent constellations for all units of time. Each possible phase offset symbol combination is counterbalanced by a phase reversed symbol combination. Therefore, we again get a spatial averaging and SAR(spatial mult.) = 5.3 W/kg. As noted earlier, simulation shows that the SAR for a single-antenna system operating with 1 W of power is 4.92 W/kg. Hence, the twoantenna SAR for the Alamouti and spatial multiplexing codes is around 0.4 dB higher than a single antenna with the same output power. So while there are well-known far-field performance advantages to these two-antenna codes vs. a single antenna, in a SAR-limited device this higher SAR removes 0.4 dB from the advantage. The SAR spatial averaging effect of the Alamouti code and spatial multiplexing intuitively holds because the phase offset between the two transmit antennas is uniformly distributed. This means that symbol combinations with phase offsets that have a high SAR are not avoided, and combinations with phase offsets that have a low SAR are not preferred. We can therefore improve the SAR-constrained performance by using codes that emphasize phase offsets with a low SAR (e.g., those shown in the lower part of the SAR curve in Fig. 1). Restricting the range of the phase offset q between the two antennas is equivalent to choosing the signal sent on the first antenna x 1 and the signal sent on the second antenna x 2 in a jointly-constrained manner, rather than choosing them independently. These constrained transmissions represent a step in transmitting along the eigenvectors of small SAR in Eq. 2. However, there is a fundamental trade-off between restricting the range too severely to reduce SAR, and having the ability to create codewords with good “distance” properties [14]. An example of a two-antenna SAR code is



Codeword

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Bit assignment

000

001

110

111

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110

010

011

x1

1

j

–j

–1

1

j

–j

–1

x2

ejp/3

jejp/3

–jejp/3

–ejp/3

e–jp/3

je–jp/3

–je–jp/3

–ejp/3

Table 1. List of values of x1 and x2 for eight codewords chosen so that q is constrained to be ±p/3.

Systematic Design, Decoding Complexity, Bit Assignments, and Many Antennas — The SAR code presented in the previous section was designed using the SAR curves in Fig. 1. We note that even with the performance advantages of these codes over standard space-time codes, there is a still a gap of approximately 3 dB to the lowest possible SAR shown in Fig. 3 as SARmin(S,1.5). Better codes are needed to close this gap, since 3 dB is too much to leave unex-


SAR code versus 1-Tx and 2-TX space-time coes, 1.5 bits/channel-use

100

10-1

Bit error rate

given in Table 1, and its performance is presented in Fig. 3. This code has 8 codewords representing 3 bits. Also shown in the figure are three additional performance curves corresponding to the Alamouti code, unconstrained spatial multiplexing, and single-antenna transmission. To ensure equal information rates for all the codes, the Alamouti code chooses x1 and x2 from 8-PSK constellations, spatial multiplexing chooses x1 from quadrature PSK (QPSK) and x2 from BPSK, and the single-antenna transmission is 8-PSK. All the codes in the figure are simulated on the narrowband channel model for two receive antennas. Additionally, all the performance curves use an outer turbo code with rate 1/2 and 8000-bit block length. The effective information rate for all the codes is then 1.5 b/channel use. The channel is allowed to change rapidly from symbol to symbol, simulating the effect of a time-varying channel and a channel interleaver. The additive noise in all cases has unit variance, and the transmitter power P is varied to create the performance curves. The resulting SAR is computed and displayed on the x-axis. The performance curves therefore capture the far-field error rate at a receiver vs. the near-field generated SAR at the transmitter. Also shown is the result of solving SAR min (S, r) for r = 1.5 b/channel use. We remark on the relative performance of these codes. The single-antenna code has the worst performance, even though its SAR, for given amount of transmitter power, is slightly lower than the Alamouti or spatial multiplexing code with the same amount of power. Thus, the far-field performance advantages of Alamouti and spatial multiplexing outweigh the near-field SAR disadvantages. The Alamouti code outperforms spatial multiplexing by a slim margin. However, the SAR code has a 2.5 dB performance advantage over the Alamouti code. We see from Table 1 that the codewords were chosen to constrain q to be ±p/3. Figure 1 shows that for q = ±p/3 the SAR is very low. Hence, the SAR code takes advantage of its knowledge of the SAR model to choose the constrained x1 and x2.

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Figure 3. Bit error rates for single transmitter, Alamouti code, spatial multiplexing, and the SAR code of Table 1. In all cases, an outer turbo code with rate 1/2 is used, and the coded bit rate is 1.5 b/channel use. The receiver has two receive antennas, and the additive noise variance is unity. The transmitter power is varied, and the resulting SAR displayed on the xaxis. The line marked “capacity” equals SARmin(S, 1.5).

ploited. A systematic analysis of the distance properties of SAR codes is needed to design better codes. This analysis will become especially important for designing codes for more than two transmitters, where hand design becomes difficult. Since x 1 and x 2 are constrained by certain phase relationships in our SAR code examples, the demodulation and computation of log-likelihood ratios for these codes at the receiver may require examining all possible symbol combinations jointly. Decoding a SAR code would then generally be more complex and time-consuming than decoding its unconstrained space-time counterpart. In the pursuit of systematic code designs, we need to ensure that decoding complexity stays reasonable, especially as we consider codes for more than two antennas or high rates. The bit assignments in Table 1 are based on a distance analysis of the code. Since the symbols x1 and x2 have a constrained relationship in this SAR code, the distances between code symbols are nontrivial to analyze, and Gray coding becomes difficult.

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SAR coded beamforming vs. conventional beamforming for a system using a rate 1/4 turbo code with a 16-QAM constellation. The transmit power is varied to satisfy the imposed SAR constraint. Note that SAR coded beamforming provides more than 3.5 dB improvement over conventional beamforming.

SAR coded versus conventional beamforming, 1 bits/channel-use 100

Bit error rate

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FUTURE RESEARCH

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Figure 4. Bit error rates for SAR coded and SAR-unaware beamforming using a 16-QAM constellation and an outer rate 1/4 turbo code, yielding 1 b/channel use. The additive noise variance is unity. The transmitter power is varied, and the resulting SAR displayed on the x-axis. The line marked “capacity” equals SARmin(S, 1).

SAR CODES WITH CHANNEL INFORMATION AT THE TRANSMITTER SAR considerations with transmitters that adapt to instantaneous far-field channel conditions are especially important [15]. To illustrate this, consider a simple two-antenna phase controlled beamformer, which can be expressed as a two-dimensional vector — — of the form f(q) = (1/ 2 )[1 ejq]T where the 1/ 2 factor indicates that the total power is divided equally between the two transmitters. The beamforming vector f(q) that is not SAR-aware sets the phase offset equal to the q bf that maximizes the receive signal-to-noise ratio (SNR). The SAR incurred from beamforming is clearly dependent on the value of q chosen, which is typically chosen as a function of the channel conditions. The worst case beamformer phase offset in Fig. 1 is qwc  p and has more than two times more SAR than the best case. Since the FCC requires the device to be put into the mode that yields worst case SAR readings during testing, any beamforming scheme that ignores the beamformer direction dependence of SAR must choose a low enough transmitter power to ensure that the maximum exposure limit passes regulatory scrutiny for qbf = qwc. Therefore, a portable beamforming device that does not exploit the SAR model in Eq. 2 may be constrained to have unusually low transmit power to pass the worst case regulatory requirements. The key to making a beamformer with high transmit power is incorporating the SAR constraint into its design and operation. An optimal beamformer is one that maximizes receive SNR while maintaining SAR compliance. We refer to a beamforming technique optimizing the capacity subject to SAR constraints as SAR coded beamforming. Figure 4 shows the performance of

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The research challenges of incorporating SAR constraints into wireless signal design involve four areas: modeling and validation, capacity analysis, design of SAR codes, and standardization. The models for SAR, including SAR matrices, need further vetting across different devices, frequencies, and numbers of transmitter antennas. The capacity and minimum SAR expressions for systems with and without transmit channel state information do not appear to have simple closed-form solutions, and further analyses on the relative weighting of the SAR constraint vs. the power constraint are needed. SAR codes yield substantial performance improvements over standard space-time or single-antenna codes, but systematic design approaches are needed. In order to be viable for cellular systems, SAR codes need to be standardized, including the ability to adapt to devicespecific parameters. In the coming years, designers of portable wireless devices face the pressure of improving device spectral efficiency, where the challenge is particularly acute on the uplink. Even with technological improvements in batteries and amplifiers, designers cannot simply increase the transmitter power of these devices due to the need to maintain compliance with electromagnetic exposure limits. SAR-aware transmission techniques such as SAR codes are needed to get the best transmission performance from devices subject to SAR constraints.

REFERENCES [1] C. Park et al., “Evolution of Uplink MIMO for LTEAdvanced,” IEEE Commun. Mag., vol. 49, Feb. 2011, pp. 112–21. [2] FCC, “Evaluating Compliance with FCC Guidelines for Human Exposure to Radiofrequency Electromagnetic Fields,” tech. rep. OET Bull. 65, Suppl. C, ed. 01-01, June 2001. [3] IEEE Std C95.1-2005, “IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields, 3 kHz to 300 GHz,” 2005. [4] C. Rowell and E. Y. Lam, “Mobile-Phone Antenna Design,” IEEE Antennas and Propagation Mag., vol. 54, no. 4, Aug 2012, pp. 14–34. [5] R. Gomez-Villanueva, H. Jardon-Aguilar, and R. L. y Miranda, “State of the Art Methods for Low SAR Antenna Implementation,” Proc. 4th Euro. Conf. Ant. and Prop., Barcelona, Spain, Apr. 12–16, 2010. [6] M. Douglas, M. Okoniewski, and M. Stuchly, “A Planar Diversity Antenna for Handheld PCS Devices,” IEEE Trans. Vehic. Tech., vol. 47, no. 3, Aug 1998, pp. 747–54. [7] S. Ko and R. Murch, “Compact Integrated Diversity Antenna for Wireless Communications,” IEEE Trans. Antennas and Propagation, vol. 49, no. 6, June 2001, pp. 954–60. [8] M. Mangoud et al., “SAR Reduction for Handset with Two-Element Phased Array Antenna Computed Using Hybrid Mom/FDTD Technique,” Elect. Lett., vol. 35, no. 20, 30 Sept. 1999, pp. 272–75. [9] K. Chim, K. Chan, and R. D. Murch, “Investigating the Impact of Smart Antennas on SAR,” IEEE Trans. Antennas and Propagation, vol. 52, May 2004, pp. 1370–74.



[10] J. Moustafa et al., “SAR Measurements for Several Two Elements Phased Antenna Array Handsets,” Proc. Euro, Conf. Ant, and Prop., Mar. 2009, pp. 2201–04. [11] F. Ferrero et al., “Phased Two-Element PIFA for Adaptative Pattern in UMTS Handsets,” Proc. IEEE Int’l. Wksp. Antenna Technology, Mar. 2009. [12] IEEE Std 1528-2003, “IEEE Recommended Practice for Determining the Peak Spatial-Average Specific Absorption Rate (SAR) in the Human Head from Wireless Communications Devices: Measurement Techniques,” June 2003. [13] U. Chandupatla et al., “Evaluation of SAR in a Homogeneous Head Model for Clam-Shell Type Cellular Phones,” Proc. Int’l. Symp. Ant. and Prop. Soc., Miami, FL, July 2006, pp. 2105–08. [14] B. M. Hochwald et al., “SAR Codes,” Proc. Info. Theory and App. Wksp., San Diego, CA, Feb 2013, pp. 1–9. [15] B. M. Hochwald and D. J. Love, “Minimizing Exposure to Electromagnetic Radiation in Portable Devices,” Proc. Info. Theory and App. Wksp., San Diego, CA, Feb 2012, pp. 255–61.

BIOGRAPHIES BERTRAND M. HOCHWALD [F] ([email protected]) received his undergraduate education from Swarthmore College, Pennsylvania. He received his M.S. degree in electrical engineering from Duke University, Durham, North Carolina, and his M.A. degree in statistics and Ph.D. degree in electrical engineering from Yale University, New Haven, Connecticut. From 1986 to 1989 he worked for the Department of Defense, Fort Meade, Maryland. After completing graduate school he was a research associate and visiting assistant professor at the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign. In September 1996, he joined the Mathematics of Communications Research Department at Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey, where he was a Distinguished Member of Technical Staff. In 2005 he joined Beceem Communications, Santa Clara, California, as their chief scientist, and in 2009 as vice-president of systems engineering. He served concurrently as a consulting professor in electrical engineering at Stanford University, Palo Alto, California. In 2011, he joined the faculty at the University of Notre Dame as Freimann Professor of Electrical Engineering. He has served as an Editor for several IEEE journals, and given plenary and invited talks on various aspects of signal processing and communications. He has co-invented several well-known multiple-antenna techniques, including a differential method, linear dispersion codes, and multi-user methods. His papers have been listed by Thomson ISI as most-cited in multiple years. DAVID J. LOVE ([email protected]) received his B.S. (with highest honors), M.S.E., and Ph.D. degrees in electrical engineering from the University of Texas at Austin in 2000, 2002, and 2004, respectively. Since August 2004, he has been with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana, where he is now a professor and recognized as a University Faculty Scholar. He has served as an Editor for IEEE Transactions on Communications, an Associate Editor for IEEE Transactions on Signal Processing, and as a Guest Editor for special issues of the IEEE Journal on Selected Areas in Communications and the EURASIP Journal on Wireless Communications and Networking. He has received numerous awards including the IEEE Transactions on Vehicular Technology Jack Neubauer Memorial best paper award and a 2013 IEEE GLOBECOM best paper award. His research interests are in the design and analysis of communication systems and MIMO array processing.He is recognized as a


Thomson Reuters Highly Cited Researcher and named to the Thomson Reuters list of “The World’s Most Influential Minds: 2014.” SU YAN ([email protected]) received his B.S. degree in electromagnetics and microwave technology from the University of Electronic Science and Technology of China (UESTC), Chengdu, in 2005 and his M.S. degree in electrical and computer engineering from the University of Illinois, Urbana-Champaign in 2012, where he is currently working toward a Ph.D. degree in electrical engineering. He was the recipient of the Best Student Paper Award presented by the IEEE Chengdu Section in 2010, and the Best Student Paper Award (First Place Winner) presented at the 27th International Review of Progress in Applied Computational Electromagnetics (ACES), Williamsburg, Virginia, in 2011. He was also the recipient of the Yuen T. Lo Outstanding Research Award presented by the Department of Electrical and Computer Engineering, University of Illinois at UrbanaChampaign, in 2014. His current research interests include nonlinear electromagnetic problems, electromagnetic scattering and radiation, numerical methods in computational electromagnetics, especially finite element methods, integral equation based methods, fast algorithms, and preconditioning techniques. P ATRICK F AY ([email protected]) is currently a professor in the Department of Electrical Engineering at the University of Notre Dame, Indiana. He received a Ph.D. in electrical engineering from the University of Illinois, Urbana-Champaign in 1996 after receiving a B.S. in electrical engineering from Notre Dame in 1991. He joined the faculty at the University of Notre Dame in 1997. His research interests include the design, fabrication, and characterization of microwave and millimeter-wave electronic devices and circuits, as well as high-speed optoelectronic devices and optoelectronic integrated circuits for fiber optic telecommunications. His research also includes the development and use of micromachining techniques for the fabrication of microwave and millimeter-wave components and packaging. His educational initiatives include the development of an advanced undergraduate laboratory course in microwave circuit design and characterization. He was awarded the Department of Electrical Engineering’s IEEE Outstanding Teacher Award in 1998–1999.

The research challenges of incorporating SAR constraints into wireless signal design involve four areas: modeling and validation, capacity analysis, design of SAR codes, and standardization. The models for SAR, including SAR matrices, need further vetting across different devices, frequencies, and numbers of transmitter antennas.

J IANMING J IN ([email protected]) received B.S. and M.S. degrees in applied physics from Nanjing University, China, in 1982 and 1984, respectively, and his Ph.D. degree in electrical engineering from the University of Michigan, Ann Arbor, in 1989. He joined the University of Illinois, UrbanaChampaign in 1993 and is currently the Y. T. Lo Chair Professor of Electrical and Computer Engineering and director of the Electromagnetics Laboratory and Center for Computational Electromagnetics. He has authored and coauthored over 200 papers in refereed journals and 20 book chapters. He also authored The Finite Element Method in Electromagnetics (Wiley, 1st ed. 1993, 2nd ed. 2002), Electromagnetic Analysis and Design in Magnetic Resonance Imaging (CRC, 1998), and Theory and Computation of Electromagnetic Fields (Wiley, 2010); and co-authored Computation of Special Functions (Wiley, 1996), Fast and Efficient Algorithms in Computational Electromagnetics (Artech, 2001), and Finite Element Analysis of Antennas and Arrays (Wiley, 2008). His current research interests include computational electromagnetics, scattering and antenna analysis, electromagnetic compatibility, high-frequency circuit modeling and analysis, bioelectromagnetics, and magnetic resonance imaging. He was elected by ISI as one of the world’s most cited authors in 2002.

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