Abstract:
Embodiments of apparatuses, articles, methods, and systems for efficient generation of a time domain signal in multi-carrier communications are generally described herein. Other embodiments may be described and claimed.

Description:
FIELD 
     Embodiments of the present invention relate generally to the field of wireless transmission, and more particularly, to efficient generation of a time domain signal in multi-carrier communications. 
     BACKGROUND 
     Multi-carrier communications may include one or more channels as control channels. For example, the 3GPP Long Term Evolution (“LTE”) Release 8 (September 2009) standard provides that user equipment (“UE”) generate a physical random access channel (“PRACH”). 
     A PRACH may include a preamble with an expected or target length. One way of generating a PRACH is to provide an inverse fast Fourier transform (“IFFT”) engine capable of handling an input having an expected or target length of 24,576 samples. For reference, the maximum IFFT input size for other signals may only be 2,048 samples. Implementation of this method in silicon may not be trivial. 
     Another way of generating a PRACH is to use a hybrid frequency/time generation scheme. According to this scheme, a length of the PRACH signal at the input of the IFFT engine may be the same as for other signals. Complementary signal processing may then be applied in the time domain on the IFFT output to achieve the expected preamble length. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments are illustrated by way of example and not by way of limitation in the figures of the accompanying drawings, in which like references indicate similar elements. 
         FIG. 1  illustrates a system having a transceiver for transmitting a signal in accordance with some embodiments. 
         FIGS. 2-7  illustrate various sequences of filters of a filter bank that may be used for upsampling a series of samples to various frequencies in accordance with some embodiments. 
         FIG. 8  illustrates a method of implementing a PRACH in accordance with various embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Various aspects of the illustrative embodiments will be described using terms commonly employed by those skilled in the art to convey the substance of their work to others skilled in the art. However, it will be apparent to those skilled in the art that alternate embodiments may be practiced with only some of the described aspects. For purposes of explanation, specific devices and configurations are set forth in order to provide a thorough understanding of the illustrative embodiments. However, it will be apparent to one skilled in the art that alternate embodiments may be practiced without the specific details. In other instances, well-known features are omitted or simplified in order not to obscure the illustrative embodiments. 
     Further, various operations will be described as multiple discrete operations, in turn, in a manner that is most helpful in understanding the present invention; however, the order of description should not be construed as to imply that these operations are necessarily order dependent. In particular, these operations need not be performed in the order of presentation. 
     The phrase “in one embodiment” is used repeatedly. The phrase generally does not refer to the same embodiment; however, it may. The terms “comprising,” “having,” and “including” are synonymous, unless the context dictates otherwise. 
     In providing some clarifying context to language that may be used in connection with various embodiments, the phrases “NB” and “A and/or B” mean (A), (B), or (A and B); and the phrase “A, B, and/or C” means (A), (B), (C), (A and B), (A and C), (B and C) or (A, B and C). 
     As used herein, reference to an “element” may refer to a hardware, a software, and/or a firmware element employed to obtain a desired outcome. Although only a given number of discrete elements may be illustrated and/or described, such elements may nonetheless be represented by additional elements or fewer elements without departing from the spirit and scope of embodiments of this disclosure. 
     Referring now to  FIG. 1 , a system  10  for generation of a plurality of channels including a PRACH is shown in accordance with an embodiment. System  10  may be a UE as provided by the LTE standard, such as a cellular telephone or a smart telephone. In some embodiments system  10  has a transceiver  12  that includes a frequency-to-time domain transformer, here in the form of an IFFT engine  14 . In some embodiments the IFFT engine  14  may be shared with other channels, and it may support a signal length of up to, e.g., 2048 samples. Transceiver  12  may also include a symbol buffer  16  that may be shared among multiple channels and may be used for buffering and other functions. 
     An upsampling element  18  is provided to upsample a series of samples output from IFFT engine  14 . Upsampling element  18  may support variable upsampling ratios as provided by the LTE standard. Upsampling element  18  may implement a cascade and/or series of filters where all filters are used for a 20 MHz bandwidth signal and subsets are used for other bandwidths. Filtering efficiency provided by the cascaded or series of filters may be increased through the use of half/third band type filters and by implementing polyphase decomposition. 
     In some embodiments, upsampling element  18  may reduce, either in full (i.e., eliminate) or in part, unwanted edge effects that may be present at a beginning and end of a signal by cyclically interpolating a series of samples. Cyclic interpolation may be implemented by, for instance, linear interpolation of a series of samples, combined with a control block that inserts samples into the series in a cyclic way. In some embodiments, the transceiver  12  may include an address generator  20  coupled with the symbol buffer  16 . The address generator  20  may generate addresses in such way that a signal is output from the symbol buffer  16  in a cyclic manner. This may be done to support insertion of cyclic prefixes. Unwanted samples may be removed from transition gaps. 
     Also included in transceiver  12  is a numerically-controlled oscillator (“NCO”)  22  to convert series of samples into a signal. NCO  22  may be responsible for shifting a frequency of the signal. For instance, all channels may be shifted by ½ carrier spacing (carrier spacing=15 KHz in LTE), and a PRACH may be shifted by ½ carrier spacing plus delta. Delta may be determined from the LTE standard. NCO  22  may output to an antenna  24  for transmission. 
     System  10  may be used to process a plurality of series of samples  26  for a plurality of channels. However, while multiple series of samples pass through IFFT engine  14 , symbol buffer  16  and NCO  22 , the upsampling element  18  may be dedicated to only processing a first series of samples  28 . First series of samples  28  may contain control information for all channels. For example, first series of samples may be a PRACH generated by a UE. 
     In some embodiments, the upsampling element  18  may support various interpolation factors to enable the system  10  to support all configurations defined by the LTE standard and yet still share an IFFT engine among both the PRACH and other channels. These interpolation factors may include, but are not limited to, 0.75, 1.5, 3, 6 and 12. 
     For example, assume a transmission signal bandwidth of 20 MHz. If a PRACH preamble format of 0 (as defined in the LTE standard) is in use, then the expected sequence length of the PRACH may be 27,744 samples (3,168 samples for a cyclic prefix plus 24,576 samples for the nominal IFFT size). However, the input of an IFFT engine shared between the PRACH and other channels may be shorter—e.g., 264 samples (3,168/12) for the cyclic prefix and 2,048 samples (24,576/12) for the nominal IFFT size—to accommodate the 20 MHz bandwidth. To alter the PRACH signal of length of 2,312 samples (264+2,048) to achieve the expected length of 27,744 samples, the PRACH may be interpolated by a factor of 12 (2,312 samples×12=27,744 samples). Accordingly, upsampling element  18  may be configured to upsample a series of samples from a lower sampling rate (e.g., 2.56 MHz) to a higher sampling rate (e.g., 30.72 MHz) in order to achieve the expected PRACH sequence length. 
     One manner of upsampling a series of samples in accordance with some embodiments is to pass the series through one or more of a plurality of available interpolation filters in various sequences in order to upsample an input series of samples to an appropriate sampling rate. The appropriate sampling rate and the various sequences of filters may be based on a particular frequency bandwidth available for transmitting information. 
     Various sequences of a filter bank  110  are shown in  FIGS. 2-7  in accordance with some embodiments.  FIGS. 2-6  assume frequency division duplexing (“FDD”).  FIG. 7  assumes time division duplexing (“TDD”). A series of samples may be passed through various sequences of one or more of these filters in order to upsample the series of samples for transmission within various bandwidths. In these examples, the sampling rate at the input of the filter bank  110  is 2.56 MHz for FDD and 15.36 MHz for TDD, but it should be understood that other input sampling rates may be used without departing from the scope of the present disclosure. It should also be understood that this particular filter bank  110  is not limiting, and other combinations and/or sequences of filters may be used without departing from the scope of the present disclosure. 
     A first sequence of filters is shown in  FIG. 2  and may be used where a bandwidth of a signal to be output from an NCO (e.g., NCO  22  of  FIG. 1 ) is 20 MHz or 15 MHz. This sequence includes a first interpolation filter  112  with an interpolation factor of 2, a second interpolation filter  114  with an interpolation factor of 0.75, a third interpolation filter  116  with an interpolation factor of 2, a fourth interpolation filter  118  with an interpolation factor of 2, and a fifth interpolation filter  120  with an interpolation factor of 2, yielding a total interpolation factor of 12 (2×0.75×2×2×2=12). 
     When a series of samples sampled at a sampling rate of 2.56 MHz passes through first interpolation filter  112 , the series of samples emerges at a sampling rate of 5.12 MHz (2.56 MHz×interpolation factor of 2=5.12 MHz). When the series of samples at 5.12 MHz passes through second interpolation filter  114  having an interpolation factor of 0.75, the series of samples emerges at a sampling rate of 3.84 MHz. When the series of samples at 3.84 MHz passes through third interpolation filter  116  having an interpolation factor of 2, the series of samples emerges at a sampling rate of 7.68 MHz. When the series of samples at 7.68 MHz passes through fourth interpolation filter  118  having an interpolation factor of 2, the series of samples emerges at a sampling rate of 15.36 MHz. Finally, when the series of samples at 15.36 MHz passes through fifth interpolation filter  120  having an interpolation factor of 2, the series of samples emerges at a sampling rate of 30.72 MHz. 
     A second sequence of filters from filter bank  110  is shown in  FIG. 3  and may be used where a bandwidth of a signal to be output from an NCO (e.g., NCO  22  of  FIG. 1 ) is 10 MHz. This sequence includes first interpolation filter  112 , second interpolation filter  114 , third interpolation filter  116 , and fourth interpolation filter  118 , yielding a total interpolation factor of 6 (2×0.75×2×2=6). 
     When a series of samples sampled at a sampling rate of 2.56 MHz passes through the sequence of filters of  FIG. 2 , the sampling rate changes are the same as in the sequence of  FIG. 1 , except that the series of samples is not passed through fifth interpolation filter  120 . Thus, when the series of samples emerges from fourth interpolation filter  118 , the series has a sampling rate of 15.36 MHz. 
     A third sequence of filters is shown in  FIG. 4  and may be used where a bandwidth of a signal to be output from an NCO (e.g., NCO  22  of  FIG. 1 ) is 5 MHz. This sequence includes first interpolation filter  112 , second interpolation filter  114  and third interpolation filter  116 , yielding a total interpolation factor of 3 (2×0.75×2=3). When a series of samples sampled at a sampling rate of 2.56 MHz passes through the sequence of filters of  FIG. 4 , the sampling rate changes are the same as in  FIGS. 2 and 3 , except that the series of samples is not passed through fourth or fifth interpolation filters  118  and  120 . Thus, when the series of samples emerges from third interpolation filter  116 , the series has a sampling rate of 7.68 MHz. 
     A fourth sequence of filters is shown in  FIG. 5  and may used where a bandwidth of a signal to be output from an NCO (e.g., NCO  22  of  FIG. 1 ) is 3 MHz. This sequence includes first interpolation filter  112  and second interpolation filter  114 , yielding a total interpolation factor of 1.5 (2×0.75=1.5). When a series of samples sampled at a sampling rate of 2.56 MHz passes through the sequence of filters of  FIG. 5 , the sampling rate changes are the same as in previously described sequences, except that the series of samples is not passed through third, fourth or fifth interpolation filters  116 ,  118  and  120 . Thus, when the series of samples emerges from second interpolation filter  114 , the series has a sampling rate of 3.84 MHz. 
     For a bandwidth of a signal to be output from an NCO (e.g., NCO  22  of  FIG. 1 ) of 1.4 MHz, a fifth sequence of filters is shown in  FIG. 6  and only includes second interpolation filter  114  with an interpolation factor of 0.75. Thus, a series of samples sampled at a sampling rate of 2.56 MHz emerges from second interpolation filter  114  with a sampling rate of 1.92 MHz. 
     Another sequence of filters is shown in  FIG. 7 , and assumes the transmitting device uses TDD, rather than FDD as have the aforementioned sequences. The bandwidth of the signal transmitted by the TDD device is 20 MHz or 15 MHz. A series of samples input to such a device at 15.36 MHz may be passed through a filter having an interpolation factor of 2, such as fifth interpolating filter  120 , to increase its sampling rate to 30.72 MHz. 
     The above-described sequences of filters are efficient because a higher sampling frequency at an input of the filter allows for the reduction of filter taps. Thus, filters located closer to the beginning of the cascade of filters may be implemented with less filter taps. For example, the number of taps in the fifth interpolating filter  120  in the sequence of filters of  FIG. 2  (20 MHz or 15 MHz) is minimal, at only two taps. 
     The interpolation filters described above may be implemented in various ways to achieve various levels of efficiency. For example, first interpolation filter  112 , third interpolation filter  116 , fourth interpolation filter  118  and fifth interpolation filter  120  may be implemented using half-band type filters. Every second coefficient in this type of filter is equal to zero, thus reducing the overall complexity of the filters. Similarly, second interpolation filter  114  may be implemented by choosing a third-band type filter. Every third coefficient in this type of filter is equal to zero, thus reducing the overall complexity of the filters. 
     Additionally, one or more filters may be implemented using polyphase decomposition. Polyphase decomposition allows reduction of a large finite impulse response filter with M taps into set of smaller sub-filters having a number of taps=M/interpolation factor. For instance, two sub-filters may be used in the case of factor 2 interpolation, and three sub-filters may be used in case of factor 3 interpolation. This allows for the reduction of storage requirements by a factor of two for half-band type filters, because every second coefficient is equal to zero and thus the second sub-filter is degenerated—and by a factor of one third for third-band type filters. 
       FIG. 8  depicts a method  200  of implementing a PRACH according to some embodiments. At  202 , a first series of samples for a first channel and a second series of samples for a PRACH are transformed from a frequency domain to a time domain. At  204 , a cyclic prefix is added to the first and second series of samples, in order to reduce, in full or in part, inter-symbol interference. At  206 , the second series of samples (i.e., PRACH) is cyclically interpolated to reduce edge effects. At  208 , the second series of samples is passed through one or more interpolation filters to upsample the second series of samples, as described above. At  210 , the first series of samples is converted into a first channel of a signal and the second series of samples is converted into a second channel of the signal. The second channel of the signal may be the PRACH. 
     While the examples described above involve generation of a PRACH, this is not meant to be limiting, and other types of signals may be generated in accordance with the present disclosure. For example, disclosed methods may be used to generate a ranging signal for the IEEE 802.16 standard, IEEE Std. 802.16-2009, published May 29, 2009. 
     Although the present invention has been described in terms of the above-illustrated embodiments, it will be appreciated by those of ordinary skill in the art that a wide variety of alternate and/or equivalent implementations calculated to achieve the same purposes may be substituted for the specific embodiments shown and described without departing from the scope of the present invention. Those with skill in the art will readily appreciate that the present invention may be implemented in a very wide variety of embodiments. This description is intended to be regarded as illustrative instead of restrictive on embodiments of the present invention.