Techniques for communicating over single-or multiple-antenna channels having both temporal and spectral fluctuations
View Patent ↗This inventions provides techniques for estimating both temporal and spectral channel fluctuations with the duration of a data symbol. Certain pulse shaping functions are Discrete Prolate Spheroidal Sequences (DPSSs) and are used primarily because of their relatively limited Inter-Symbol Interference (ISI) properties. During reception, these properties allow one or more parameters of a joint time-frequency channel model to be more easily determined. Once the one or more parameters are determined, they can be applied to received symbols to correct the temporal fluctuations, spectral fluctuations, or both of the channel over which a communication took place. The techniques may be adapted for the Multiple-In, Multiple-Out communication situation.
1. A method, comprising:
determining one or more parameters of a channel model that permits non-stationarity within each individual data symbol; and
applying the one or more parameters to one or more received symbols to determine one or more decoded symbols.
2. The method of claim 1 , wherein the channel model is modeled as a transfer function relating transmitted symbols to received symbols, the transfer function comprising the one or more parameters.
3. The method of claim 1 , wherein the parameters of the channel model comprise a time slope coefficient, a frequency slope coefficient, and a complex amplitude.
4. The method of claim 3 , wherein there are a plurality of antennas receiving signals and wherein the time slope coefficient, frequency slope coefficient, and complex amplitude are matrices with a number of entries corresponding to a square of the number of antennas, wherein the method further comprises the step of demodulating, for each of the receivers, a respective one of the signals to create the received symbols, and wherein the step of determining further comprises the step of determining the parameters by using pilot symbols in received symbols from each of the receivers.
5. The method of claim 1 , further comprising the step of demodulating a received signal by using one or more Discrete Prolate Spheroidal Sequences (DPSSs) to create the received symbols.
6. The method of claim 5 , further comprising the step of demodulating the received signal by using a plurality of DPSSs, the step of demodulating producing a received symbol for each of the plurality of DPSSs.
7. The method of claim 6 , wherein a first predetermined number of the received symbols correspond to known pilot symbols, and wherein the step of determining the one or more parameters further comprises solving a system of equations using the known pilot symbols to determine the parameters.
8. The method of claim 7 , wherein the system of equations is represented through an equation having a plurality of matrices, the equation comprising a reception matrix having received symbols corresponding to the known pilot symbols, a pilot matrix having the known pilot symbols, and a channel model matrix having the parameters, wherein the equation is the reception matrix minus a product of the channel model matrix and the pilot matrix.
9. The method of claim 8 , wherein the step of determining one or more parameters further comprises the step of minimizing a magnitude of the equation.
10. The method of claim 8 , wherein a second predetermined number of the received symbols correspond to data symbols, and wherein the step of applying further comprises the step of applying a second system of equations to the data symbols, the second system of equations comprising the parameters.
11. The method of claim 10 , wherein:
the parameters of the channel model comprise a time slope coefficient, a frequency slope coefficient, and a complex amplitude;
the data symbols are represented by a data vector; and
the second system of equations comprises:
a first multiplication of a unity matrix, the data vector, and the complex amplitude;
a second multiplication of a time operator matrix, the data vector, and the time slope coefficient;
a third multiplication of a frequency operator matrix, the data vector, and the frequency slope coefficient; and
an addition of results of the first, second, and third multiplications, whereby the decoded symbols result from the addition.
12. An apparatus, comprising:
a parameter determination module adapted to determine one or more parameters of a channel model that permits non-stationarity within each individual data symbol; and
a symbol decoding module coupled to the parameter determination module and adapted to apply the one or more parameters to one or more received symbols to determine one or more decoded symbols.
13. The apparatus of claim 12 , wherein the channel model is modeled as a transfer function relating transmitted symbols to received symbols, the transfer function comprising the one or more parameters.
14. The apparatus of claim 12 , wherein the parameters of the channel model comprise a time slope coefficient, a frequency slope coefficient, and a complex amplitude.
15. The apparatus of claim 12 , further comprising a demodulator module coupled to both the parameter determination module and the symbol decoding module, the demodulator module demodulating a received signal by using one or more Discrete Prolate Spheroidal Sequences (DPSSs) to create the received symbols.
16. The apparatus of claim 15 , wherein:
the demodulator is further adapted to demodulate the received signal by using a plurality of DPSSs, the demodulating producing a received symbol for each of the plurality of DPSSs;
a first predetermined number of the received symbols correspond to known pilot symbols and the apparatus is adapted to couple the pilot symbols to the parameter determination module;
a second predetermined number of the received symbols correspond to data symbols and the apparatus is adapted to couple the data symbols to the symbol decoding module; and
the parameter determination module is further adapted to solve a system of equations using the known pilot symbols to determine the parameters.