System and method for communicating with shaped cyclic time-domain waveforms

Embodiments of a system and method for generating a shaped cyclic time-domain waveform are generally described herein. In some embodiments, a first transform may be performed on an input symbol vector to generate a transformed input vector in a transform domain. The transformed input symbol vector may be expanded to generate an expanded symbol vector. At least some elements of the expanded symbol vector may be weighted with a weighting vector selected for pulse shaping to generate a weighted symbol vector. A second transform may be performed on the weighted symbol vector to generate an output symbol vector for subsequent processing and transmission. The second transform may be an inverse of the first transform and may comprise a greater number of points than the first transform.

TECHNICAL FIELD

Embodiments pertain to wireless communications. Some embodiments relate to communicating with cyclic waveforms. Some embodiments relate to the application of Nyquist cyclic modulation (NCM) to millimeter-wave wireless communications.

BACKGROUND

For wireless communications, it is desirable that the modulation structure be amenable to robust operation and implementation efficiency. The selection of a modulation technique is critical for high rate wireless to support spectrally efficiency, detection efficiency, simplified acquisition, low peak-to-average power ratios (PAPRs), minimal channel dispersion, and reduced implementation complexity.

Thus, there are general needs for improved modulators and demodulators that provide spectral efficiency, detection efficiency, simplified acquisition, low PAPR, minimal channel dispersion, and reduced implementation complexity.

DETAILED DESCRIPTION

FIG. 1is a functional diagram of a cyclic modulator in accordance with some embodiments. Cyclic modulator100may be configured to communicate shaped cyclic time-domain waveforms. A demodulator, such as demodulator200(FIG. 2), may be used to demodulate signals transmitted by the cyclic modulator100. As described in more detail below, a process for extending a cyclic block at the modulator100and contracting the cyclic block at the demodulator200is provided. This process may support shaping of the cyclic blocks for the spectral containment and may support adjustment of signal peak-to-average power ratio, among other things. In some embodiments, the expansion and contraction process may allow mid-frequency domain signal shaping.

In these embodiments, the cyclic modulator100may have one or more processing elements arranged to perform a first transform on an input symbol vector103to generate a transformed input vector105in a transform domain (e.g., the frequency domain). The one or more processing elements may also be arranged to extend the transformed input symbol vector105to generate an expanded symbol vector107and weight at least some elements of the expanded symbol vector107with a weighting vector127selected for pulse shaping to generate a weighted symbol vector109. The one or more processing elements may also be arranged to perform a second transform on the weighted symbol vector109to generate an output symbol vector111for subsequent processing and transmission. The output symbol vector111may comprise a time-domain symbol vector. The second transform may be the inverse of the first transform and the second transform may comprise a greater number of points than the first transform.

After subsequent processing of the output symbol vector111, cyclic modulator100may transmit a shaped cyclic time-domain waveform119with one or more antennas. The shaped cyclic time-domain waveform119may be a pulse-shaped waveform. These embodiments are described in more detail below.

As illustrated inFIG. 1, the first transform may be performed by transform element104, the expansion of the transformed input symbol vector105may be performed by expansion element106, the weighting of the elements of the expanded symbol vector107may be performed by alteration element108, and the second transform may be performed by transform element110.

In some embodiments that implement Nyquist filtered cyclic modulation (NCM), cyclic modulator100may transmit an NCM waveform that provides low PAPR, inherent rejection of channel dispersion and reduced acquisition complexity. In some embodiments, a parallel implementation of the cyclic modulator100may support multi-gigabit-per-second modems. These embodiments are described in more detail below.

In some embodiments, the first transform (performed by transform element104) may be an N-point (or N-length) fast-Fourier transform (FFT) to transform the input symbol vector103to the frequency domain and the second transform (performed by transform element110) may be an M-point (or M-length) inverse FFT (IFFT) to transform the expanded symbol vector107to the time-domain. In these embodiments M and N are whole numbers and M is greater than N.

In some example embodiments, N may be 64 and M may be 128, although the scope of the embodiments is not limited in this respect as M may be any number greater than N and less than 512, for example. In some embodiments, N may be 64 and M may be around 100. In some embodiments, N may correspond to the number of elements of the input symbol vector103and M may correspond to the number of elements of the expanded symbol vector107as well as the number of elements of the weighted symbol vector109. In some embodiments, the symbol vectors may be ordered lists of elements (e.g., tuples).

In some embodiments, transforms other than an FFT for the first transform and an IFFT for the second transform may be used. For example, the first transform may be a discrete Fourier transform (DFT) and the second transform may be an inverse discrete Fourier transform (IDFT).

In accordance with embodiments, to generate the expanded symbol vector107, the expansion element106may be arranged to add at least M-N elements to the transformed input vector105. In some embodiments, this added expansion may support a larger frequency domain. In some embodiments, each element (instead of just some of the elements) of the expanded symbol vector107may be weighted with a weighting vector127.

In some embodiments, the input symbol vector103may comprise quadrature-amplitude modulation (QAM) symbols or modulation pulses. To generate the expanded symbol vector107, the expansion element106may be arranged to cyclically extend the transformed input vector105by adding symbol content outside a central symbol vector to generate a resultant cyclic symbol vector q(t) (i.e., the expanded symbol vector107). Examples of this are illustrated in FIG.5described below. The resultant cyclic symbol vector q(t) may correspond to a circular convolution of the QAM symbols with a Nyquist filter response.

In some embodiments, to weight at least some elements of the expanded symbol vector107, the alteration element108may be arranged to perform a root-Nyquist filtering process by complex vector multiplication in the frequency domain. In these embodiments, the weights of weighting vector127may be selected to perform Nyquist shaping in accordance with the Nyquist filter response (i.e., for NCM). Other shaping, such as Butterworth shaping, may alternatively be performed.

In some embodiments, some weights of the weighting vector127may have a zero value and some weights having non-zero values. In these embodiments, the non-zero valued weights may be applied to elements that are to be operated on by the second transform.

In accordance with some embodiments, a filter with finite time-domain support may be used as part of the filtering process performed by alteration element108. In this way, after filtering, the inverse transform of the weighted frequency domain signal (i.e., the second transform performed by transform element110) may result in a filtered time-domain signal where the transients (of infinite extent) will appear to have wrapped into the symbol vector in a cyclic manner. In these embodiments, the extent of the frequency domain filter representation may be limited to approximate a filter with greater frequency support (e.g., those frequencies where the values of the filter are non-zero). In these embodiments, the original filter may be non-zero over a larger range but is approximated with a filter that is shorter (e.g., zero over an extended frequency range).

In some embodiments, the expansion of the transformed input vector105(i.e., by expansion element106) to generate the expanded symbol vector107may comprise extending an aperture in the frequency domain. In these embodiments, an aperture may refer to a segment of samples that may be considered significant. For example, when there are 64 points in the first transform output, the frequency domain aperture may have a length of 64 (i.e., 64 samples). When there are 128 points in the second transform, the second transform may have an aperture of length 128 (i.e., 128 samples). The expansion added by expansion element106may establish a map between these two apertures that behaves in a manner that is desirable for a particular application (e.g., to perform well controlled filtering).

In some embodiments, the modulation symbols that comprise output symbol vector111as presented by the second transform may be twice oversampled.

In some embodiments, the one or more processing elements of the cyclic modulator100may further be arranged to apply a mapping to the output symbol vector111to generate a parallel set of output time samples113. In these embodiments, the mapping applied to the output symbol vector111may be applied by time-domain (TD) mapping element112.

In some embodiments, the output symbol vector111may comprise an in-phase signal (I) and quadrature signal (Q) (i.e., complex modulation symbols). The mapping that is applied may be arranged to cyclically extend the output symbol vector111(which is a time-domain symbol vector) and cyclically shift the quadrature signal by one-half symbol from the in-phase signal to produce an offset modulated signal block corresponding to the output time samples113.

The output time samples113may be converted from parallel to serial form by parallel-to-serial (P/S) converter114to generate time samples115(e.g., baseband signals) which may be converted to analog form by digital-to-analog converter (DAC)116for subsequent up-conversion to RF signals by RF circuitry118and for transmission by one or more antennas.

As further illustrated inFIG. 1, prior to performance of the first transform by transform element104, a data stream101may be converted to parallel form and may undergo a bit-to-symbol mapping process to generate the input symbol vector103. Modulation formats may include standard modulation formats (e.g., PSK and QAM formats) as well as offset modulation formats.

FIG. 2is a block diagram of a demodulator in accordance with some embodiments. Demodulator200may be suitable for the demodulation of a shaped cyclic time-domain waveform that may have been transmitted by a cyclic modulator, such as cyclic modulator100(FIG. 1), although the scope of the embodiments is not limited in this respect. In some embodiments, cyclic modulator100and demodulator200may comprise a modem or may be part of a wireless communication system.

In accordance with embodiments, the demodulator200may comprise one or more processing elements arranged to perform a third transform on a time-domain symbol vector209generated from a received signal201. The third transform may convert the time-domain symbol vector209to a frequency-domain representation211. The processing elements of the demodulator200may also be arranged to perform a frequency-domain weighting at least some elements of the frequency-domain representation211(e.g., by application of a weighting vector227) to generate a weighted symbol vector213, and perform a compression process on the weighted symbol vector213to produce a corrected symbol vector215having a reduce number of elements (i.e., symbols). The processing elements of the demodulator200may also be arranged to perform a fourth transform on only some elements of the corrected symbol vector215to generate an output signal vector217that is an estimate of transmitted modulation symbols. The third transform may be an inverse of the fourth transform and the third transform may comprise a greater number of points than the fourth transform.

In these embodiments, frequency-domain weighting may be performed by alteration element212and may be responsible for matched recovery and equalization of general time-domain symbol pulse shapes. In some embodiments, the third transform may be performed by transform element210, the compression process may be performed by compression process element214, and the fourth transform may be performed by fourth transform element216. In these embodiments, the compression process may compress the number of values being processed.

In some embodiments, the third transform (i.e., performed by transform element210) may be an inverse of the second transform (i.e., performed by transform element110of the cyclic modulator100(FIG. 1)) and has the same number of points as the second transform. The fourth transform (i.e., performed by transform element216) may be an inverse of the first transform (i.e., performed by transform element104of the cyclic modulator100) and may have the same number of points as the first transform although the scope of the embodiments is not limited in this respect.

In some alternate embodiments, the fourth transform (i.e., performed by transform element216) may have a different number of points as the first transform (i.e., performed by transform element104). In these alternate embodiments, the fourth transform may be an M-point size transform (e.g., rather than an N-point size transform) to detect and equalize the offset symbols.

In some embodiments, the processing elements of the demodulator200may also be arranged to discard the elements225of the corrected symbol vector215that are not to be operated on by the fourth transform. The elements that are retained may correspond to the elements that were added by the expansion element106of the cyclic modulator100.

In some embodiments, the compression process element214may support a reduction of samples for more efficient recovery processing. As illustrated inFIG. 2, compression process element214may operate on the weighted symbol vector213, which may have M elements, however this is not a requirement as the compression process element214may operate on a subset of these elements (e.g., N elements of vector213).

In some embodiments, the third transform may be an M-point FFT, and the fourth transform is an N-point IFFT. M and N may be whole numbers and M may be greater than N.

In some embodiments, the frequency-domain weighting (i.e., performed by the alternation element212) may apply a mapping that cyclically filters the signal (i.e., the frequency-domain representation211). In some embodiments, the mapping may act as an adaptive frequency-domain filter or equalizer.

In some embodiments, the demodulator200may also include time-domain mapping element208to apply a mapping to a received time-domain signal207to produce the time-domain symbol vector209for performance of the third transform thereon. In these embodiments, the mapping applied to the received time-domain signal207may be a time-domain format process performed by the time-domain mapping element208. In some embodiments, the mapping applied to received time-domain signal207may be an inverse of the mapping applied by time-domain mapping element112(FIG. 1) of the cyclic modulator100(FIG. 1). In some embodiments, the mapping may identify and remove a cyclic extension from the received time-domain signal207and may cyclically shift the quadrature component of the baseband waveform by one-half symbol (e.g., relative to the in-phase component) to map an offset modulation to a non-offset format to produce symbol vector209.

As illustrated inFIG. 2, demodulator200may also include RF recovery circuitry202to process the received RF signal201and analog-to-digital converter (ADC)204to perform filtering and convert the received signal to digital baseband samples205. Serial-to-parallel (S/P) converter206may generate the received time-domain signal207from the baseband samples205. Demodulator200may also include P/S converter and data decision circuitry218to generate decision values from the output signal vector217for mapping to the output data219. Although not specifically discussed, demodulator200may be configured to compensate for frequency offset induced by the RF, as well as address cyclic vector alignment in accordance with conventional techniques.

FIG. 3illustrates Nyquist filtering of complex symbols in accordance with some embodiments. As shown inFIG. 3, pulses scaled with a QAM constellation302(e.g., 4-QAM (i.e., QPSK) or 32 QAM) may be Nyquist filtered by Nyquist filter304to produce a complex pulse train306. In practice, the Nyquist filter304may be divided into root-Nyquist filters that may serve to band limit and pulse shape at the transmitter (e.g., cyclic modulator100(FIG. 1)) and act as the matched filter at the receiver (e.g., demodulator200(FIG. 2)). In these embodiments, the Nyquist filters exhibit a property that the modulation bandwidth is well constrained and there is little or no inter-symbol interference (ISI) at the symbol sampling instance. The pulses may be sampled at two-samples per symbol to help avoid interpolation in recovery and the D/A reconstruction filters may be specifically configured depending on the Nyquist shape factor. Nyquist pulses have a well contained spectrum and zero ISI at the sample instance. As illustrated inFIG. 3, pulses cross zero at the adjacent symbol peaks.

FIG. 4illustrates the forming of a symbol vector by summing a collection of delayed Nyquist pulses in accordance with some embodiments. As illustrated inFIG. 4, an ensemble of k complex Nyquist pulses402may be combined to generate a signal P(t)410. The real part of the pulses pk(t) is represented in the figure. As illustrated, delayed versions of the pulses are added to define a symbol vector.FIG. 4shows that that the Nyquist pulses create controlled ISI within a symbol vector and filter transients at the edges of the symbol vectors create interference between adjacent symbol vectors. Note that the signal P(t)410is notional as the sketch does not show ISI. An output symbol vector for transmission by cyclic modulator100(FIG. 1) may be formed by summing a collection of k delayed Nyquist pulses.

FIG. 5illustrates the construction of a cyclic symbol vector in accordance with some embodiments. A cyclic symbol vector may be identified by adding in the symbol transients502outside of the central symbol vector504. This can be envisioned as wrapping the symbol vector around a cylinder506of circumference equal to and then adding the portions that overlap onto the base symbol. The resultant cyclic symbol vector q(t)508may equivalently be formed by circular convolution of the QAM modulation pulses with a Nyquist filter.

Cyclic symbol vector q(t)508may be constructed by summing the filter transients s1(t) and s3(t)502into the base symbol interval s2(t)504. Cyclic symbol vector q(t)508may also be generated by cyclically convolving the filter response with the complex modulation pulses. The cyclic symbol vectors may be cyclically extended (by the TD mapping element112(FIG. 1)) prior to transmission by sending a segment, {tilde over (q)}k(t), from the end of the symbol prior to the base symbol, qk(t).

FIG. 6illustrates a train of train of cyclically extended symbol vectors in accordance with some embodiments. The train of cyclically extended symbol vectors602may be transmitted by the cyclic modulator100(FIG. 1). This demonstrative waveform construction may be useful to illustrate the structural properties of the NCM waveform, which may be transmitted by cyclic modulator100.

Referring toFIG. 1, in accordance with some embodiments, the cyclic modulator100may accept a set of data streams that are serialized then presented to an encoder, such as a forward-error correcting (FEC) encoder. A pseudo-random sequence generator may be used to sustain channel operation, scramble user data, and for testing. A preamble (e.g., a symbol vector pilot) may be periodically inserted in the stream. The resulting bit stream (i.e., data stream101) may be converted to QAM symbols by symbol mapper102then presented to an N-length Fast Fourier Transform (FFT) in transform element104. Information in the transform domain may be cyclically expanded by expansion element106and then root-Nyquist filtered in the frequency domain by alteration element108. In these embodiments, the root-Nyquist filtering may be a complex vector multiplication as opposed to a time-domain convolution and so it is more efficient. The frequency domain vector may be transformed into a cyclic symbol vector via an M-length inverse FFT by transform element110(i.e., M may be greater than N). A guard interval is added (i.e., time domain cyclic extension) by time-domain mapping element112and the result may be serialized (by P/S converter114). In some embodiments, dual D/A converters may be used produce a baseband signal representation that is transmitted via RF circuitry118. In these embodiments, cyclic modulator100may generate a cyclic waveform as described above in which the first transform element104, the expansion element106, the alteration element108, and the second transform element110are configured to efficiently operate on parallel streams. In an example embodiment in which M is 128 and N is 64, the symbol vector103may contains 64 modulation symbols represented at 2 samples per symbol. For a symbol rate of 5 GHz, the cyclic modulator100may produce symbol vectors at a 5 GHz÷N which is a 78 MHz rate.

In accordance with embodiments, the demodulator200(FIG. 2) may accept quadrature samples and the acquisition process establishes basic timing alignment and frequency error from the cyclic extension in accordance with conventional techniques. The frequency may be tracked continuously and sample timing adjusted by varying integral sample delay and fractional sample tracking as a linear phase shift yielding a uniform, adjustable group delay in an adaptive frequency domain equalizer. Given alignment to within the extended cyclic symbol vector, a subset of samples may be converted to parallel format (e.g., by S/P converter206) and processed through an M-length FFT (e.g. by transform element210). Matched root-Nyquist filtering may be performed by the alteration element108along with compensation for other known circuit dispersion (e.g., D/A and A/D converter droop and analog baseband filter effects). This adaptive equalization process performed by the alteration element108may help mitigate cyclic ISI. The equalized vector output may be reduced to the N-length IFFT (by transform element216) and eventually streamed to a symbol-to-bit mapper to generate demodulated symbols which may be FEC decoded then formatted for a user interface.

In some embodiments, the modulator and demodulator architecture illustrated inFIGS. 1 and 2may be replicated and the channels interconnected to support subband processing with spatial multiplexing techniques. In some embodiments, the acquisition process applies pilot symbol vectors to sound the channel and estimates the channel matrix at the discrete frequencies. Channel variations for different modem deployments may vary. Channel dynamics in airborne collection applications may be estimated for compensation updates at a 10 Hz rate. Therefore, channel estimation and correction matrix computations may be addressable in a signal processor.

FIG. 7illustrates an estimate of NCM analog power spectral density in accordance with some embodiments. As discussed above, the cyclic structure may be applied in the modulator to control ISI and mitigate the impact of the RF dispersion. Residual dispersion may be addressed by the cyclic extension and adaptive equalization. Consider a signal that carries 25 Gbps using 32 QAM and operates at a 5 GHz symbol rate and a 10 GHz sample rate. An estimate of the NCM analog power spectral density704is shown inFIG. 7. The spectrum passband of 5 GHz702occurs at about the −5 dB point of the spectrum. The Sin(x)x shaped curve706is included in the plot for comparison and represents a spectrum with no filtering applied.

In some embodiments, a modem for a MODEM for millimeter-wave communications is provided. In these embodiments, the modem may comprise one or more processing elements arranged to perform a first N-point FFT on an input symbol vector of QAM symbols to generate a transformed input vector in a transform domain, cyclically extend the transformed input symbol vector by adding symbol content outside a central symbol vector to generate an expanded symbol vector, weight at least some elements of the expanded symbol vector with a weighting vector selected for pulse shaping to generate a weighted symbol vector, perform an M-point IFFT on the weighted symbol vector to generate an output symbol vector for subsequent processing and transmission, and apply a mapping to the output symbol vector to generate a parallel set of output time samples.

In these embodiments, M may be greater than N. To weight at least some elements of the expanded symbol vector, the one or more processing elements may be arranged to perform a root-Nyquist filtering process by complex vector multiplication in the frequency domain.