Abstract:
Methods and apparatus, including computer program products, are provided for polar noise shaping. In one aspect there is provided a method. The method may include receiving a first error signal representative of a first noise including a first quantization noise carried by a quadrature signal; receiving a second error signal representative of a second noise including a second quantization noise carried by an in-phase signal; and determining one or more bits in a polar domain, wherein the one or more bits cancel a portion of the first noise and the second noise represented by the first error signal and the second error signal. Related apparatus, systems, methods, and articles are also described.

Description:
FIELD 
       [0001]    The subject matter described herein relates to wireless communications. 
       BACKGROUND 
       [0002]    When a signal is converted from a floating point to a fixed point signal, the conversion may be performed before a digital-to-analog converter. The difference between the floating point input signal and the fixed point output signal represents an error and, in particular, quantization error, which may also be referred to as quantization noise. In radio transmitters, this quantization noise is conventionally attenuated right after the digital-to-analog converter by analog filters before the signal is up-converted into radio frequency. Rather than use analog filters, some transmitter technologies may transmit fixed point radio frequency signals including quantization noise. 
       SUMMARY 
       [0003]    Methods and apparatus, including computer program products, are provided for polar noise shaping. 
         [0004]    In one aspect there is provided a method. The method may include receiving a first error signal representative of a first noise including a first quantization noise carried by a quadrature signal; receiving a second error signal representative of a second noise including a second quantization noise carried by an in-phase signal; and determining one or more bits in a polar domain, wherein the one or more bits cancel a portion of the first noise and the second noise represented by the first error signal and the second error signal. 
         [0005]    In some variations, one or more of the features disclosed herein including the following features can optionally be included in any feasible combination. The method may further include combining, in the polar domain, the one or more bits with the amplitude signal and the phase signal to cancel the portion. The combining may include subtracting. Two sigma delta modulators may determine from the first error signal and the second error sigma, the one or more bits. The two sigma delta modulators may include two parallel sigma delta modulators, wherein the two parallel sigma delta modulators each have a feedback gain adaptively chosen according to at least the amplitude signal, the phase signal, and one or more signs of the two parallel sigma delta modulators outputs. The feedback gain may be chosen so that it is proportional to a rectangular domain change equivalent of least significant bit changes of the amplitude signal and the phase signal. One of the gain levels may be chosen from the one or more gain levels, so that it provides a high gain in the two parallel sigma delta modulators. The two sigma delta modulators may have different non-even quantizer levels. The non-even quantizer levels may be adaptively chosen according to at least the amplitude signal, the phase signal, and the one or more signs of the two parallel sigma delta modulators outputs. The non-even quantizer levels may be chosen, such that the non-even quantizer levels may be proportional to rectangular domain change equivalents of one or more least significant bits changes of the amplitude signal and the phase signal. The first and second noise may be due in part to at least one of a regular or an irregular step size of quantized polar domain signals. 
         [0006]    The above-noted aspects and features may be implemented in systems, apparatus, methods, and/or articles depending on the desired configuration. The details of one or more variations of the subject matter described herein are set forth in the accompanying drawings and the description below. Features and advantages of the subject matter described herein will be apparent from the description and drawings, and from the claims. 
     
    
     
       DESCRIPTION OF THE DRAWINGS 
         [0007]    In the drawings, 
           [0008]      FIG. 1  depicts an example of a polar noise shaper, in accordance with some example embodiments; 
           [0009]      FIG. 2  depicts an example of a simulated plot of the cancelation of quantization noise provided by the polar noise shaper, in accordance with some example embodiments; 
           [0010]      FIG. 3  depicts another example of a polar noise shaper, in accordance with some example embodiments; 
           [0011]      FIG. 4  depicts an example of a two-dimensional sigma delta modulator, in accordance with some example embodiments; 
           [0012]      FIG. 5A  depicts an example of rectangular domain to polar domain mapping, in accordance with some example embodiments; 
           [0013]      FIG. 5B  depicts an example process for determining a least significant bits which can be used to cancel noise including quantization noise and the like, in accordance with some example embodiments; 
           [0014]      FIG. 6  depicts another example of a polar noise shaper, in accordance with some example embodiments; 
           [0015]      FIG. 7  depicts another example of a two-dimensional sigma delta modulator, in accordance with some example embodiments; 
           [0016]      FIG. 8  depicts an example process for polar noise shaping, in accordance with some example embodiments; 
           [0017]      FIG. 9  depicts an example of a user equipment, in accordance with some example embodiments; and 
           [0018]      FIG. 10  depicts an example of a network node, in accordance with some example embodiments. 
       
    
    
       [0019]    Like labels are used to refer to same or similar items in the drawings. 
       DETAILED DESCRIPTION 
       [0020]      FIG. 1  depicts an example of a radio frequency transmitter  100  including a modem  110  (for example, a Cartesian floating point modem and the like), a radio frequency (RF) power digital-to-analog converter (DAC)  199 , and an RF polar shaper  150 . The RF power DAC may perform a direct conversion of signal  112 A-B as in-phase (I) and quadrature phase (Q) signals into radio frequency signal. The input  112 A may represent a high bit count quantized version or floating point version of the in-phase signal, while input  112 B may represent a high bit count quantized version or floating point version of the quadrature phase signal. A rectangular-to-polar quantizer (RTPQ)  116  may then convert rectangular signals  112 A-B to lower bit count polar form before modulation and transmission via antenna  180 . 
         [0021]    The RF power DAC (digital-to-analog converter) may be used to transmit RF signals with the capability to choose bandwidth, carrier frequency, and/or multiple carriers flexibly, on the fly in a power efficient transmitter. However, RF power DACs may not have a conventional baseband, which can include for example baseband filtering and the like. Instead, the RF DAC brings the quantized, digital bits  118 A-B to the antenna interface port  180 , where these bits are converted directly into RF signal power for transmission via an antenna. As such, RF power DACs may operate in polar form, wherein a digitally controlled clock phase carries phase information and has amplitude bits that modulate clock amplitude. Because RF power DACs may not have conventional baseband analog processing, RF DACs may not allow for any baseband analog filtering to filter out noise, such as quantization noise and the like, from the signal before transmission. This quantization noise in the digital data at  118 A-B and  118 A-B may thus be transmitted, making it difficult for some receivers to receive relatively, weak signals in the presence of the quantization noise. 
         [0022]    Sigma delta modulation may be used to push the quantization noise away from frequencies where a transmitted signal(s) of interest may be found. However, conventional sigma delta modulation may present problems that can make them ill-suited with respect to out-of-band noise. Specifically, some radios, such as cellular radios and the like, may be allowed to have noise where the desired signal resides, but out-of-band frequencies may be kept clean to allow reception of weaker signals. Moreover, in polar transmitters, cleaning a frequency band from noise in a phase branch or an amplitude branch does not necessarily result in substantial noise reduction in the out-of-band ( 00 B) frequencies. 
         [0023]    In some example embodiments, the subject matter disclosed herein may provide a polar noise shaper  150  to modulate one or more least significant bits of the amplitude (A) signal and the phase (P) signal in order to cancel the quantization noise from the RF signal or band of interest traversing the RF power DAC. The one or more least significant bits are likely where the noise, such as quantization noise and the like, resides. Accordingly, modulation of these one or more least significant bits may be used to cancel the noise. For example, polar noise shaper  150  may modulate only the least significant bits of signals  118 A-B by adding a −1 least significant bit (LSB), a 0 or +1 LSB to these signals  118 A-B to cancel the noise including quantization noise. 
         [0024]    Although some of the examples refer to modulating a single least significant bit of an amplitude signal and a single least significant bit of a phase signal, additional bits may be modulated as well to cancel (for example, reduce, shape, suppress, filter, and the like) the noise including quantization noise and the like. 
         [0025]    The quantized digital signals  118 A or  118 B may, in some example embodiments, have a certain resolution, such as for example 8 bits of resolution. This 8-bit resolution may be sufficient for the desired RF signal quality, but out-of-band ( 00 B) noise level may require closer to about for example 22 bits or more. Given that RF power DACs are highly oversampled, the bits are generally constant over many clock cycles of the RF power DAC. The polar noise shaper  150  may modulate (for example, change, manipulate, and the like) some of least significant bits in a way that cancels the noise/quantization noise and that does not substantially affect the RF signal/band of interest. 
         [0026]      FIG. 2  depicts example spectrum plots  200  of simulated results, in accordance with some example embodiments. The transmitted signal  212  represents a signal when processed by the polar noise shaper  150 , which provides one or more least significant bits to cancel the quantization noise carried by the signal  212 . The effect of the cancelation within a frequency, F, is shown at  216 . The noise reduction at  216  may be reduced in other portions of the spectrum as well (for example, by varying the clock frequency and resonator frequency response). In contrast, spectrum of an RF DAC without polar noise shaping is depicted by  210 . It can be seen that the polar noise shaper may be used to reduce the noise at the frequency band, F  216 , when compared to the level at  210 . 
         [0027]      FIG. 3  depicts an example implementation of the polar noise shaper  150 , in accordance with some example embodiments. 
         [0028]    The polar noise shaper  150  may have inputs  302 A-D and outputs  304 A-B. 
         [0029]    Input  302 A may be coupled to quadrature phase (Q) signal  112 B, and input  302 B may be coupled to an in-phase (I) signal  112 A. Input  302 D may be coupled to the amplitude (A) signal  118 A, and input  302 C may be coupled to phase (P) signal  118 B. Output  304 A may couple to a subtractor  322 A, where output  304 A is combined with amplitude (A) signal  118 A to form amplitude output  390 A, and output  304 B may couple to a subtractor  322 B, where output  304 B is combined with phase (P) signal  118 B to form phase output  390 B. 
         [0030]    The polar noise shaper  150  may, as noted, modulate one or more least significant bits of signals  118 A-B, which are generated by rectangular-to-polar converter quantizer (R2PQ)  116 . The modulation may, for example, comprise adding a +1 LSB, a 0, and/or a −1 LSB to quantized digital data  118 A-B in order to shape a reduction in noise including the quantization noise. 
         [0031]    Input signals  302 A-B may couple to combiners  316 A-B (for example, a subtractor). Combiners  316 A-B may also couple to rectangular signals  314 A-B, which represent input signals  302 C-D after conversion to polar form by polar-to-rectangular converter  312 . When rectangular signals  314 A-B are subtracted at  316 A-B, the signals  318 A-B represent an error between the signal before and after rectangular-to-polar converter quantizer (R2PQ)  116 . The outputs  318 A-B represent the quantization noise (or error) for the quantization occurring at rectangular-to-polar converter quantizer  116 . 
         [0032]    The signals  318 A-B (or errors) may be provided as input to a two-dimensional sigma delta modulator  310  (labeled 2DΣM), in accordance with some example embodiments. Two-dimensional sigma delta modulator  310  may also receive as input polar signals  302 C-D (which may be the same or similar to signals  118 A-B) generated by rectangular-to-polar converter quantizer  116 . 
         [0033]    The two-dimensional sigma delta modulator  310  may be considered two-dimensional in the sense that the two branches of sigma delta modulator  310  may not be considered to operate individually but instead operations may be influenced by the output of both modulators. 
         [0034]    The noise, such as quantization noise and the like, caused by quantization may be measured and provided at  318 A-B to the two-dimensional sigma delta modulator  310  to allow the two-dimensional sigma delta modulator  310  to generate output  304 A-B, so that when combined  322 A-B with polar signals  118 A-B, the noise/quantization noise of signals  118 A-B is canceled when transmitted via antenna port  180  and a corresponding antenna. 
         [0035]    The two-dimensional sigma delta modulator  310  may determine the values of generated output  304 A-B based on both domains. Specifically, polar noise shaper  150  including the two-dimensional sigma delta modulator  310  may receive inputs from both the rectangular (or I-Q) domain (for example, inputs  302 A-B) and polar domain (inputs  302 C-D). In this way, although the determination of the noise/quantization noise cancelation is in the rectangular domain at  310 , the cancelation signal  304  belongs to coordinates in the polar domain. 
         [0036]      FIG. 4A  depicts two-dimensional sigma delta modulator  310 , in accordance with some example embodiments. The two-dimensional sigma delta modulator  310  may receive as inputs error signals  318 A-B and polar signals  302 C-D. Error signals  318 A-B may be processed by sigma delta resonators  368 A-B, which provides its output to two-dimensional quantizer  365 . Two dimensional quantizer  365  also receives polar signals  302 C-D, and calculates one or more least significant bits  304 A-B that cancel chosen frequency component of the error signals  318 A-B at antenna port  180  (for example, when combined at  322 A-B and transmitted via antenna port  180 ). Because the least significant bit calculator  405  has the error signals and the polar domain information  302 C-D, the calculator is able to provide one or more least significant bits  304 A-B to cancel frequency components of the quantization noise (or error) at the antenna port  180  when combined at  322 A-B. 
         [0037]      FIG. 5A  illustrates the polar/rectangular calculation performed by least significant bit calculator  405 , in accordance with some example embodiments. 
         [0038]    In order to map the one or more least significant bits which will be used to cancel the quantization noise, these cancelation bits may be transformed into the polar domain. In the example of  FIG. 5A , one or more bits in the rectangular domain of I and Q may be mapped  550  into the polar domain as amplitude and phase signal  592 E. The least significant bit calculator  405  may also be configured to perform this mapping. For example, in  1  LSB case, least significant bit calculator  405  may map a given point in the I and Q domain  592 E to one of 8 possible polar amplitude combinations  592 A-D and F-I that are on a polar domain grid. These phase amplitude combinations  592 A-D and F-I represent the combinations yielded by varying phase LSB by 0, +1, or −1 and/or by varying the amplitude LSB by 0, +1, or −1. As described further with respect to  FIG. 5 , the least significant bit calculator  405  may select 1 of the 8 combination, so that the sign of the I/Q bit in the polar domain may be maintained. Moreover, the selection may maximize the I and Q distance (or gain), which is fed back at  410 A-B to sigma delta resonators  368 A-B. The sigma delta feedback gain may thus be changed according to phase, amplitude, and both resonators  368 A-B outputs. The two-dimensional sigma delta modulator  310  may select quantization levels according to a current location in both coordinate systems, namely rectangular and polar. 
         [0039]      FIG. 5B  depicts an example process for canceling a portion of the noise including quantization noise carried by the least significant bits, in accordance with some example embodiments. The description of  FIG. 5B  also refers to  FIGS. 3 and 5A . 
         [0040]    At  520 , sigma delta resonator  368 A may calculate from the received Q (quadrature) error signal  318 A a direction that the Q signal should go in to cancel noise at a given frequency, F. The notation dir Q =+ or − refers to either a positive direction or a negative direction. 
         [0041]    At  522 , sigma delta resonator  368 B may calculate from the received I (in-phase) error signal  318 B a direction the I signal (see, for example,  592 E at  FIG. 5A ) should go in to cancel noise at a given frequency, F. 
         [0042]    At  526 , the two-dimensional quantizer  365  may calculate from the current values of the polar domain amplitude and phase signal  302 C-D the closest 8 points  592 A-D and F-I, as shown at  FIG. 5A . This points represent the amplitude and phase signal varied in the rectangular domain, such as increasing or decreasing the value of amplitude (A) or phase (P) by a value of for example plus (+) 1 or minus (−) 1, which effectively moves the amplitude and phase signal among the 8 possible values  592 A-D and F-I. For example, the amplitude and phase signal  592 E when increased in amplitude only by +1 moves the signal to  592 B and when decreased by −1 moves the signal to  592 H, while moving in phase only by +1 moves the signal to  592 F and by −1 moves the signal to  592 D. Moreover, if amplitude and phase signal  592 E is varied in phase by −1 and amplitude by −1, the signal moves to  592 I. 
         [0043]    At  528 , two-dimensional quantizer  365  may calculate which 4 points out of the 8 points  592 A-D and F-I provide the biggest rectangular change or feedback signal  410 A-B by changing the least significant bits the amplitude and phase signals. These 4 points provide the highest feedback gain in the sigma delta modulator  310  for any possible output value combinations from  368 A and  368 B. 
         [0044]    At  538 , two-dimensional quantizer  365  may choose a pair that provides the biggest feedback gain and has a direction that cancels the noise including quantization noise. For example, the least significant bit(s), LSB P , for the phase signal and the least significant bit(s) of the amplitude signal LSB Q  may be provided as an output at  538 , which is feedback at  540  to the sigma delta resonators and forwarded, at  542 , to subtractors  322 A-B, where output  304 A may be subtracted from amplitude signal  118 A and output  304 B may be subtracted from phase signal  118 B. 
         [0045]      FIG. 6  depicts another example of the polar noise shaper  350 , in accordance with some example embodiments. The polar noise shaper  350  is similar to polar noise shaper  150  in some respects, but polar noise shaper  350  outputs are different. Rather than just outputting the least significant bits, polar noise shaper  350  outputs all of the bits (for example, most and least significant bits) of amplitude and phase signals  390 A-B, which have already been modulated to reduce the quantization noise. Moreover, the sigma delta resonators, in the example of  FIG. 6 , may not include quantizers. 
         [0046]      FIG. 7  depicts another example of multi-bit two-dimensional sigma delta modulator  710 , in accordance with some example embodiments. The two-dimensional sigma delta modulator  710  of  FIG. 7  is similar in some respect to the two-dimensional sigma delta modulator  310  of  FIG. 3  but a quantizer has been removed from the sigma delta resonators at  768 A-B and the quantization levels provided by two-dimensional quantizer  765  is increased. The multi-bit two-dimensional sigma delta modulator  710  may be used in implementations where the polar noise shaper modulates more than just the least significant bits, such as in the implementation of  FIG. 3 . 
         [0047]      FIG. 8  depicts a process  800  for polar noise shaping, in accordance with some example embodiments. 
         [0048]    At  805 , an error indication of quantization error in a quantized radio frequency signal may be received, in accordance with some example embodiments. The error indication may, in some example embodiments, comprise a quadrature phase error, such as quantization error  318 A and an in-phase error, such as in-phase error  318 B. 
         [0049]    At  810 , a determination may be made of one or more bits in the polar domain that represent an error of a quantized radio frequency signal in rectangular domain, in accordance with some example embodiments. For example, polar noise shaper  150 / 350  including two-dimensional sigma delta modulator may determine one or more least significant bits which when combined in the polar domain with the quantized phase and amplitude signals  118 A-B cancels the quantization noise at antenna port  180  at a given frequency band. These one or more least significant bits may be determined in the rectangular domain to provide the cancellation, but the location stays in the polar domain. Moreover, the sign of the correcting signal may be determined in rectangular domain, while the magnitude of the correction is determined by polar domain. 
         [0050]    At  815 , the one or more determined bits  304 A-B may be combined, such as subtracted in the polar domain with the bits of the quantized radio frequency signal  118 A-B, in accordance with some example embodiments. For example, the determined least significant bit  304 A for the amplitude signal may be subtracted at  322 A from the amplitude signal  118 A, and the determined least significant bit  304 B for the phase signal may be subtracted at  322 B from the phase signal  118 B. When this is the case, subtractors  322 A-B output signals  390 A-B with new phase and amplitude signals that produce noise cancellation when modulated and transmitted via  180  as shown for example at  FIG. 2  at  216 . 
         [0051]    Although the previous example describes cancelation using a single bit, the cancelation may, as noted, use additional bits as well. 
         [0052]    In some example embodiments, the polar noise shaper  150  may be used for predistortion. Predistortion may be used when power components are non-linear. Non-linearity creates noise, so polar noise shaper  150  may remove this noise as well. If the non-linearity is known, it can be corrected by including the error from nonlinearity in the error signal of the polar noise shaper, so that at a given frequency of interest the noise due to predistortion may be canceled. 
         [0053]      FIG. 9  illustrates a block diagram of an apparatus  10 , which can be configured as a user equipment, in accordance with some example embodiments. The user equipment may be implemented as a smart phone, mobile station, a mobile unit, a subscriber station, a wireless terminal, a tablet, a wireless plug-in accessory, or any other device with a short-range transceiver, such as Bluetooth, Bluetooth Low Energy, and the like. 
         [0054]    The apparatus  10  may include at least one antenna  12  in communication with a transmitter  14  and a receiver  16 . Alternatively transmit and receive antennas may be separate. 
         [0055]    In some example embodiments, the transmitter  14  may include, or be coupled to, polar noise shaper  150  disclosed herein, although the polar noise shaper may be used in other locations in a radio as well. 
         [0056]    For example, the polar noise shaper may be implemented by a processor, such as process  20  and/or a digital signal processor, and the like. The apparatus  10  may also include a processor  20  configured to provide signals to and receive signals from the transmitter and receiver, respectively, and to control the functioning of the apparatus. Processor  20  may be configured to control the functioning of the transmitter and receiver by effecting control signaling via electrical leads to the transmitter and receiver. Likewise, processor  20  may be configured to control other elements of apparatus  10  by effecting control signaling via electrical leads connecting processor  20  to the other elements, such as a display or a memory. The processor  20  may, for example, be embodied in a variety of ways including circuitry, at least one processing core, one or more microprocessors with accompanying digital signal processor(s), one or more processor(s) without an accompanying digital signal processor, one or more coprocessors, one or more multi-core processors, one or more controllers, processing circuitry, one or more computers, various other processing elements including integrated circuits (for example, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), and/or the like), or some combination thereof. Accordingly, although illustrated in  FIG. 9  as a single processor, in some example embodiments the processor  20  may comprise a plurality of processors or processing cores. 
         [0057]    Signals sent and received by the processor  20  may include signaling information in accordance with an air interface standard of an applicable cellular system, and/or any number of different wireline or wireless networking techniques, comprising but not limited to Wi-Fi, wireless local access network (WLAN) techniques, such as Institute of Electrical and Electronics Engineers (IEEE) 802.11, 802.16, and/or the like. In addition, these signals may include speech data, user generated data, user requested data, and/or the like. 
         [0058]    The apparatus  10  may be capable of operating with one or more air interface standards, communication protocols, modulation types, access types, and/or the like. For example, the apparatus  10  and/or a cellular modem therein may be capable of operating in accordance with various first generation (1G) communication protocols, second generation (2G or 2.5G) communication protocols, third-generation (3G) communication protocols, fourth-generation (4G) communication protocols, Internet Protocol Multimedia Subsystem (IMS) communication protocols (for example, session initiation protocol (SIP) and/or the like. For example, the apparatus  10  may be capable of operating in accordance with 2G wireless communication protocols IS-136, Time Division Multiple Access TDMA, Global System for Mobile communications, GSM, IS-95, Code Division Multiple Access, CDMA, and/or the like. In addition, for example, the apparatus  10  may be capable of operating in accordance with 2.5G wireless communication protocols General Packet Radio Service (GPRS), Enhanced Data GSM Environment (EDGE), and/or the like. Further, for example, the apparatus  10  may be capable of operating in accordance with 3G wireless communication protocols, such as Universal Mobile Telecommunications System (UMTS), Code Division Multiple Access 2000 (CDMA2000), Wideband Code Division Multiple Access (WCDMA), Time Division-Synchronous Code Division Multiple Access (TD-SCDMA), and/or the like. The apparatus  10  may be additionally capable of operating in accordance with 3.9G wireless communication protocols, such as Long Term Evolution (LTE), Evolved Universal Terrestrial Radio Access Network (E-UTRAN), and/or the like. Additionally, for example, the apparatus  10  may be capable of operating in accordance with 4G wireless communication protocols, such as LTE Advanced and/or the like as well as similar wireless communication protocols that may be subsequently developed. 
         [0059]    It is understood that the processor  20  may include circuitry for implementing audio/video and logic functions of apparatus  10 . For example, the processor  20  may comprise a digital signal processor device, a microprocessor device, an analog-to-digital converter, a digital-to-analog converter, and/or the like. Control and signal processing functions of the apparatus  10  may be allocated between these devices according to their respective capabilities. The processor  20  may additionally comprise an internal voice coder (VC)  20   a , an internal data modem (DM)  20   b , and/or the like. Further, the processor  20  may include functionality to operate one or more software programs, which may be stored in memory. In general, processor  20  and stored software instructions may be configured to cause apparatus  10  to perform actions. For example, processor  20  may be capable of operating a connectivity program, such as a web browser. The connectivity program may allow the apparatus  10  to transmit and receive web content, such as location-based content, according to a protocol, such as wireless application protocol, WAP, hypertext transfer protocol, HTTP, and/or the like. 
         [0060]    Apparatus  10  may also comprise a user interface including, for example, an earphone or speaker  24 , a ringer  22 , a microphone  26 , a display  28 , a user input interface, and/or the like, which may be operationally coupled to the processor  20 . The display  28  may, as noted above, include a touch sensitive display, where a user may touch and/or gesture to make selections, enter values, and/or the like. The processor  20  may also include user interface circuitry configured to control at least some functions of one or more elements of the user interface, such as the speaker  24 , the ringer  22 , the microphone  26 , the display  28 , and/or the like. The processor  20  and/or user interface circuitry comprising the processor  20  may be configured to control one or more functions of one or more elements of the user interface through computer program instructions, for example, software and/or firmware, stored on a memory accessible to the processor  20 , for example, volatile memory  40 , non-volatile memory  42 , and/or the like. The apparatus  10  may include a battery for powering various circuits related to the mobile terminal, for example, a circuit to provide mechanical vibration as a detectable output. The user input interface may comprise devices allowing the apparatus  20  to receive data, such as a keypad  30  (which can be a virtual keyboard presented on display  28  or an externally coupled keyboard) and/or other input devices. 
         [0061]    As shown in  FIG. 9 , apparatus  10  may also include one or more mechanisms for sharing and/or obtaining data. For example, the apparatus  10  may include a short-range radio frequency (RF) transceiver and/or interrogator  64 , so data may be shared with and/or obtained from electronic devices in accordance with RF techniques. The apparatus  10  may include other short-range transceivers, such as an infrared (IR) transceiver  66 , a Bluetooth (BT) transceiver  68  operating using Bluetooth wireless technology, a wireless universal serial bus (USB) transceiver  70 , a Bluetooth Low Energy link, ZigBee link, a cellular device-to-device link, a wireless local area link, a Wi-Fi link, and/or any other short-range radio technology. In this regard, the apparatus  10  and, in particular, the short-range transceiver may be capable of transmitting data to and/or receiving data from electronic devices within the proximity of the apparatus, such as within 10 meters, for example. The apparatus  10  including the WiFi or wireless local area networking modem may also be capable of transmitting and/or receiving data from electronic devices according to various wireless networking techniques, including 6LoWpan, Wi-Fi, Wi-Fi low power, WLAN techniques such as IEEE 802.11 techniques, IEEE 802.15 techniques, IEEE 802.16 techniques, and/or the like. 
         [0062]    The apparatus  10  may comprise memory, such as a subscriber identity module (SIM)  38 , a removable user identity module (R-UIM), an eUICC, an UICC, and/or the like, which may store information elements related to a mobile subscriber. In addition to the SIM, the apparatus  10  may include other removable and/or fixed memory. The apparatus  10  may include volatile memory  40  and/or non-volatile memory  42 . For example, volatile memory  40  may include Random Access Memory (RAM) including dynamic and/or static RAM, on-chip or off-chip cache memory, and/or the like. Non-volatile memory  42 , which may be embedded and/or removable, may include, for example, read-only memory, flash memory, magnetic storage devices, for example, hard disks, floppy disk drives, magnetic tape, optical disc drives and/or media, non-volatile random access memory (NVRAM), and/or the like. Like volatile memory  40 , non-volatile memory  42  may include a cache area for temporary storage of data. At least part of the volatile and/or non-volatile memory may be embedded in processor  20 . The memories may store one or more software programs, instructions, pieces of information, data, and/or the like which may be used by the apparatus for performing functions of the user equipment/mobile terminal. The memories may comprise an identifier, such as an international mobile equipment identification (IMEI) code, capable of uniquely identifying apparatus  10 . The functions may include one or more of the operations disclosed herein with respect to the user equipment including polar noise shaper  150 , such as the functions disclosed at process  800  and the like. The memories may comprise an identifier, such as an international mobile equipment identification (IMEI) code, capable of uniquely identifying apparatus  10 . In the example embodiment, the processor  20  may be configured using computer code stored at memory  40  and/or  42  to operations disclosed herein with respect to the polar noise shaper  150 , such as the functions disclosed at process  800  and the like. 
         [0063]      FIG. 10  depicts an example implementation of a network node  100 , such as for example base station, an access point, and the like. The network node  1000  may include one or more antennas  1020  configured to transmit via a downlink and configured to receive uplinks via the antenna(s)  1020 . The network node  1000  may further include a plurality of radio interfaces  1040  coupled to the antenna  1020 . The radio interfaces may correspond one or more of the following: Long Term Evolution (LTE, or E-UTRAN), Third Generation (3G, UTRAN, or high speed packet access (HSPA)), Global System for Mobile communications (GSM), wireless local area network (WLAN) technology, such as for example 802.11 WiFi and/or the like, Bluetooth, Bluetooth low energy (BT-LE), near field communications (NFC), and any other radio technologies. The radio interfaces  1040  may further include other components, such as for example filters, converters (for example, digital-to-analog converters and the like), mappers, a Fast Fourier Transform (FFT) module, and the like, to generate symbols for a transmission via one or more downlinks and to receive symbols (for example, via an uplink). In some example embodiments, the radio interfaces  1040  may further include polar noise shaper  150 . 
         [0064]    The network node  1000  may further include one or more processors, such as for example processor  1030 , for controlling the network node  1000  and for accessing and executing program code stored in memory  1035 . In some example embodiments, memory  1035  includes code, which when executed by at least one processor causes one or more of the operations described herein with respect to network node including the polar shaper disclosed herein. For example, network node  1000  including polar shaper may perform operations disclosed herein with respect to the polar noise shaper  150 , such as the functions disclosed at process  800  and the like. 
         [0065]    Some of the embodiments disclosed herein may be implemented in software, hardware, application logic, or a combination of software, hardware, and application logic. The software, application logic, and/or hardware may reside on memory  40 , the control apparatus  20 , or electronic components, for example. In some example embodiment, the application logic, software or an instruction set is maintained on any one of various conventional computer-readable media. In the context of this document, a “computer-readable medium” may be any non-transitory media that can contain, store, communicate, propagate or transport the instructions for use by or in connection with an instruction execution system, apparatus, or device, such as a computer or data processor circuitry, with examples depicted at  FIGS. 9 and 10  computer-readable medium may comprise a non-transitory computer-readable storage medium that may be any media that can contain or store the instructions for use by or in connection with an instruction execution system, apparatus, or device, such as a computer. 
         [0066]    Without in any way limiting the scope, interpretation, or application of the claims appearing below, a technical effect of one or more of the example embodiments disclosed herein is enabling RF power DACs to be used in user equipment and other radios, systems, and the like in which OOB noise may be kept relatively low. 
         [0067]    If desired, the different functions discussed herein may be performed in a different order and/or concurrently with each other. Furthermore, if desired, one or more of the above-described functions may be optional or may be combined. Although various aspects of the invention are set out in the independent claims, other aspects of the invention comprise other combinations of features from the described embodiments and/or the dependent claims with the features of the independent claims, and not solely the combinations explicitly set out in the claims. It is also noted herein that while the above describes example embodiments, these descriptions should not be viewed in a limiting sense. Rather, there are several variations and modifications that may be made without departing from the scope of the present invention as defined in the appended claims. Other embodiments may be within the scope of the following claims. The term “based on” includes “based on at least.” The use of the phase “such as” means “such as for example” unless otherwise indicated.