Method and apparatus for phase-domain semi-coherent demodulation

BACKGROUND OF THE INVENTION

Technical Field of the Invention

0001The present invention relates generally to the field of wireless technology and, more particularly, to a method of and system for digital radio transceivers.

Description of Related Art

0002Wireless technologies such as, for example, terrestrial and satellite mobile communications and short-range wireless systems such as BLUETOOTH, often use M-ary differential encoded phase shift keying (MDPSK) for transmitting data. MDPSK is typically employed because of its advantageous characteristics, such as nonnecessity of carrier recovery circuits, fast acquisition performance, phase ambiguity resolution, and good performance over multipath fading channels.

0003A current solution for improving MDPSK detection performance utilizes a conventional differential detection circuit equipped with an infinite impulse response (IIR) filter combined with decision feedback. The carrier frequency offset typically generated in mobile communications is compensated for by a carrier frequency tracking loop. The semi-coherent demodulator approximates the performance of a coherent MDPSK demodulator without requiring carrier phase acquisition and tracking.

0004Referring now to <figref idref="f0001">FIGURE 1</figref>, a known semi-coherent demodulator 100 is illustrated. In the FIGURES, the bold arrows indicate a complex signal and the thin arrow indicate a real signal. An input signal <i>x_i</i> is received in complex form by the semi-coherent demodulator 100. The semi-coherent demodulator 100 manipulates the input signal <i>x_i</i> into amplitude <i>A_i</i>¹⁰⁰ and phase θ<i>_i</i>¹⁰⁰ components of a real signal via a magnitude calculator 104 and a phase calculator 106, respectively, according to the following equation: <maths id="math0001" num="(1)"><math display="block"><msub><mi>x</mi><mi>i</mi></msub><mo>=</mo><msup><mtable><mtr><mtd><msub><mi>A</mi><mi>i</mi></msub></mtd></mtr></mtable><mn>100</mn></msup><mo>⁢</mo><msup><mi>e</mi><mrow><mi>j</mi><mo>⁢</mo><msup><msub><mi>θ</mi><mi>i</mi></msub><mn>100</mn></msup></mrow></msup><mspace width="1em" /><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>…</mo></math><img file="EP1516469B1_D0001.tif" /></maths> To create a reference signal <i>u_i</i>¹⁰⁰, an impact of modulation on the input signal <i>x_i</i> is removed from Equation 1. The impact of the modulation may be removed by rotating the input signal <i>x_i</i> by a delayed decision ϕ_<i>i</i>-1¹⁰⁰ of a decision unit 110. The decision ϕ<i>_i</i>¹⁰⁰ is based on a reference phase ψ<i>_i</i>¹⁰⁰ and the phase component θ<i>_i</i>¹⁰⁰ described in more detail below. The rotation of the input signal <i>x_i</i> is achieved by subtracting the output decision (ϕ<i>_i</i>¹⁰⁰ of the decision unit 110 from the phase component θ<i>_i</i>¹⁰⁰ of the input signal <i>x_i</i>.

0005A phase sum adder 112 performs the subtraction of the decision ϕ<i>_i</i>¹⁰⁰ from the phase component θ<i>_i</i>¹⁰⁰ in order to yield a rotated input phase ξ<i>_i</i>¹⁰⁰. The rotated input phase ξ<i>_i</i>¹⁰⁰ is input along with the amplitude <i>A_i</i>¹⁰⁰ to a magnitude-and-phase-to-complex converter 114. The magnitude-and-phase-to-complex converter 114 outputs the reference signal <i>u_i</i>¹⁰⁰ The following equation holds true for the reference signal <i>u_i</i>¹⁰⁰: <maths id="math0002" num="(2)"><math display="block"><msup><msub><mi>u</mi><mi>i</mi></msub><mn>100</mn></msup><mo>=</mo><msup><msub><mi>A</mi><mi>i</mi></msub><mn>100</mn></msup><mo>⁢</mo><msup><mi>e</mi><mrow><mi>j</mi><mo>⁢</mo><mfenced><msup><msub><mi>θ</mi><mi>i</mi></msub><mn>100</mn></msup><mo>-</mo><msup><msub><mi>ϕ</mi><mi>i</mi></msub><mn>100</mn></msup></mfenced></mrow></msup><mmultiscripts><mi>i</mi><mprescripts /><mspace width="2em" /><none /></mmultiscripts><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>…</mo></math><img file="EP1516469B1_D0002.tif" /></maths>

0006The reference signal <i>u_i</i>¹⁰⁰ may remain disturbed by impairments such as noise and intersymbol interference (ISI). The impairments may be averaged out by integration at an integrator 108. The integrator 108 operates in the complex domain in order to ensure that the amplitude A<i>_i</i>¹⁰⁰ of the semi-coherent demodulator 100 is considered. A coherency parameter α is input with the reference signal <i>u_i</i>¹⁰⁰ to form the output of the integrator 108, a reference vector <i>r_i</i>¹⁰⁰. Many approaches may be employed to integrate the reference signal µ<i>_i</i>¹⁰⁰. In an embodiment of the invention, an exponential integration window yields the following equation: <maths id="math0003" num="(3)"><math display="block"><msup><msub><mi>r</mi><mi>i</mi></msub><mn>100</mn></msup><mo>=</mo><mi>α</mi><mo>*</mo><msup><msub><mi>r</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mn>100</mn></msup><mo>+</mo><mfenced><mn>1</mn><mo>-</mo><mi>α</mi></mfenced><mo>*</mo><msup><msub><mi>u</mi><mi>i</mi></msub><mn>100</mn></msup><mspace width="1em" /><mmultiscripts><mi>i</mi><mprescripts /><mspace width="2em" /><none /></mmultiscripts><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>…</mo></math><img file="EP1516469B1_D0003.tif" /></maths> The reference vector <i>r_i</i>¹⁰⁰ is input to a complex-to-phase converter 116. A reference phase ψ<i>_i</i>¹⁰⁰ is output from the complex-to-phase converter 116 to a unit delay 118.

0007As noted above, in order to remove the impact of the modulation, a tentative decision is made at the decision unit 110 about a transmitted symbol of the input signal <i>x_i</i>. The tentative decision is input to the phase sum adder 112. The decision ϕ<i>_i</i>¹⁰⁰, which is made at the decision unit 110, is based upon a phase difference between the actual input phase component θ<i>_i</i>¹⁰⁰ and a previous reference phase ψ_<i>i</i>-1¹⁰⁰. The previous reference phase ψ_<i>i</i>-1¹⁰⁰ is output from the unit delay 118. The unit delay 118 receives as an input the reference phase ψ<i>_i</i>¹⁰⁰ from the complex-to-phase converter 116. The phase difference between the actual input phase component θ<i>_i</i>¹⁰⁰ and the previous reference phase ψ_<i>i</i>-1¹⁰⁰ is calculated by a second phase sum adder 120 and input to the decision unit 110.

0008The function of the decision unit 110 is dependent on the number of modulation levels M. For example, for M=2, the following equation is true: <maths id="math0004" num="(4)"><math display="block"><msup><msub><mi>ϕ</mi><mi>i</mi></msub><mn>100</mn></msup><mo>=</mo><mfenced open="{" close="}"><mtable><mtr><mtd><mi>π</mi></mtd><mtd><mi mathvariant="italic">if</mi><mo>⁢</mo><mfenced open="|" close="|"><msup><msub><mi>θ</mi><mi>i</mi></msub><mn>100</mn></msup><mo>-</mo><msup><msub><mi>ψ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mn>100</mn></msup></mfenced><mo>≥</mo><mfrac><mi>π</mi><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi mathvariant="italic">elsewhere</mi></mtd></mtr></mtable></mfenced></math><img file="EP1516469B1_D0004.tif" /></maths> The decision ϕ<i>_i</i>¹⁰⁰ is input to a second unit delay 122. A delayed decision ϕ_<i>i</i>-1¹⁰⁰ output by the second unit delay 122 is then input to a phase sum adder 124 and a phase sum adder 126. The first additional phase sum adder 124 subtracts the delayed decision ϕ_<i>i</i>-1¹⁰⁰ from the output of the phase sum adder 120. The output of the phase sum adder 124 is an output <i>y_i</i>¹⁰⁰ of the semi-coherent demodulator 100.

0009A previous phase difference θ_<i>i</i>-1¹⁰⁰ is replaced with a corrected previous phase difference γ_<i>i</i>-1¹⁰⁰. The corrected previous phase difference γ_<i>i</i>-1¹⁰⁰ includes less noise than the previous phase difference θ_<i>i</i>-1¹⁰⁰. The corrected previous phase difference γ_<i>i</i>-1¹⁰⁰ is denoted by: <maths id="math0005" num="(5)"><math display="block"><msup><msub><mi>γ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mn>100</mn></msup><mo>=</mo><msup><msub><mi>ψ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mn>100</mn></msup><mo>+</mo><msup><msub><mi>ϕ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mn>100</mn></msup><mspace width="1em" /><mi>i</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>…</mo></math><img file="EP1516469B1_D0005.tif" /></maths> The output <i>y_i</i>¹⁰⁰ of the semi-coherent demodulator 100, and thus also the output of phase sum adder 124, is given by the following equation: <maths id="math0006" num="(6)"><math display="block"><msup><msub><mi>y</mi><mi>i</mi></msub><mn>100</mn></msup><mo>=</mo><msup><msub><mi>θ</mi><mi>i</mi></msub><mn>100</mn></msup><mo>-</mo><msup><msub><mi>γ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mn>100</mn></msup><mspace width="1em" /><mmultiscripts><mi>i</mi><mprescripts /><mspace width="2em" /><none /></mmultiscripts><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>…</mo></math><img file="EP1516469B1_D0006.tif" /></maths>

0010The phase sum adder 126 subtracts the delayed decision ψ_<i>i</i>-1¹⁰⁰ from the decision ϕ<i>_i</i>¹⁰⁰ to produce a decision of the output <i>D</i>(<i>y_i</i>¹⁰⁰). The decision <i>D</i>(<i>y_i</i>¹⁰⁰) is input to a look-up table (LUT) 128 to output detected bits.

0011Calculations in both the phase and complex domains increase computational complexity. Phase-to-complex converters, complex-to-phase converters, integrators, etc. are needed to perform the necessary additional calculations. The additional computations result in excessive power consumption and silicon area in order to achieve the increased performance of the MDPSK semi-coherent demodulator 100.

0012<patcit id="pcit0001" dnum="US20010031022A"><text>US 2001/0031022</text></patcit> shows a phase-domain demodulator in which a reference signal is generated from a received modulated signal, and wherein a phase detector unit detects the phase difference between a complex valued signal and the previous reference signal.

SUMMARY OF THE INVENTION

0013These and other drawbacks are overcome by embodiments of the present invention, which provide a phase domain semi-coherent demodulator. Embodiments of the invention may not require a perfect carrier frequency synchronization between a transmitter and receiver in a communications system. Embodiments of the present invention also reduce complexity by performing calculations in the phase domain rather than the complex domain. The phase domain semi-coherent demodulator includes a receiver for receiving at least a phase component of an input signal. The phase domain semi-coherent demodulator may include a decision unit for forming a decision based on a delayed reference signal and the phase component of the input signal. In addition the phase domain semi-coherent demodulator may include a phase sum adder, which may operate in modulo 2π addition, for subtracting the decision from the phase component of the input signal to form a rotated input phase, a second phase sum adder for subtracting the delayed reference signal from the rotated input phase to form a resulting signal, and a scaler for scaling the resulting signal to form an update signal. A third phase sum adder adds the update signal to the delayed reference signal to form a reference signal.

0014In another aspect of the present invention, a method calculates information in the phase domain for a semi-coherent demodulator. The method includes receiving at least a phase component of an input signal and forming, by a decision unit, of a decision value based on a delayed reference signal and the phase component of the input signal. The method may include subtracting the decision value from the phase component of the input signal to form a rotated input phase and subtracting the delayed reference signal from the rotated input phase to form a resulting signal. The resulting signal may be scaled to form an update signal. The update signal may be added to the delayed reference signal to form a reference signal.

0015In another aspect, the present invention relates to an article of manufacture for phase-domain semi-coherent demodulation of an input signal. The article of manufacture includes at least one computer readable medium and processor instruction contained on the at least one computer readable medium. The processor instructions are configured to be readable from the at least one computer readable medium by at least one processor and thereby cause the at least one processor to operate as to receive at least a phase component of an input signal and form, by a decision unit, a decision value based on a delayed reference signal and the phase component of the input signal. The decision may be subtracted from the phase component of the input signal to form a rotated input phase. The delayed reference signal is subtracted from the rotated input phase to form a resulting signal. The resulting signal is scaled to form an update signal. The update signal is added to the delayed reference signal to form a reference signal.

BRIEF DESCRIPTION OF THE DRAWINGS

0016Further advantages and specific details of the present invention will become apparent hereinafter from the detailed description given below in conjunction with the following drawings. <ul id="ul0001" list-style="none" compact="compact"><li><figref idref="f0001">FIGURE 1</figref>, previously described in part, is a block diagram that schematically illustrates a known MDPSK semi-coherent demodulator;</li><li><figref idref="f0002">FIGURE 2</figref> is a block diagram of a phase domain semi-coherent demodulator in accordance with principles of the present invention; and</li><li><figref idref="f0002">FIGURE 3</figref> is a flow diagram of a method of calculating the reference phase in the phase domain.</li></ul>

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS OF THE INVENTION

0017Semi-coherent demodulators generally use the amplitude information of the input signal <i>x_i</i> to perform calculations. It should be understood that various symbols used in the Detailed Description may relate to a signal itself or to a signal used to transmit an angle or other value.

0018A semi-coherent demodulator may be implemented in hardware, such as an Application-Specific Integrated Circuit (ASIC), or in software. The software may run on a Digital Signal Processor (DSP) or other processor. The implementation of the semi-coherent demodulator may depend on design choices and/or constraints of a manufacturer or communication product. The semi-coherent demodulator, as shown in <figref idref="f0001">FIGURE 1</figref>, requires various phase-to-complex and complex-to-phase conversions to be performed, thereby increasing complexity. The semi-coherent demodulator 100 may be implemented in a receiver portion 10 of a wireless communication device 20.

0019Referring now to <figref idref="f0002">FIGURE 2</figref>, a phase-domain semi-coherent demodulator 200 is illustrated. A decision ϕ<i>_i</i>²⁰⁰ from a decision unit 210 is subtracted from a phase component θ<i>_i</i>²⁰⁰ of an input signal <i>x_i</i> at a phase sum adder 212. In the phase-domain semi-coherent demodulator 200, an output of the phase sum adder 212, a rotated input phase ξ<i>_i</i>²⁰⁰, is not converted into a complex signal. Instead, the rotated input phase ξ<i>_i</i>²⁰⁰ is input to a phase sum adder 230. The phase sum adder 230 subtracts a delayed reference phase ψ_<i>i</i>-1²⁰⁰ from the rotated input phase ξ<i>_i</i>²⁰⁰ in order to obtain a resulting signal ζ<i>_i</i>²⁰⁰. Rewriting Equation 3 in the phase domain yields the following equation: <maths id="math0007" num="(7)"><math display="block"><mtable columnalign="left"><mtr><mtd><msup><mtable><mtr><mtd><msub><mi>ψ</mi><mi>i</mi></msub></mtd></mtr></mtable><mn>200</mn></msup><mo>=</mo><mi mathvariant="italic">phase</mi><mfenced><msub><mi>r</mi><mi>i</mi></msub></mfenced></mtd></mtr><mtr><mtd><msup><mtable><mtr><mtd><msub><mi>ψ</mi><mi>i</mi></msub></mtd></mtr></mtable><mn>200</mn></msup><mo>=</mo><mi mathvariant="italic">phase</mi><mo>⁢</mo><mfenced><mi>α</mi><mo>*</mo><msup><mi>e</mi><mrow><mi>j</mi><mo>⁢</mo><msub><mi>ψ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub></mrow></msup><mo>+</mo><mfenced><mn>1</mn><mo>-</mo><mi>α</mi></mfenced><mo>*</mo><msup><mi>e</mi><mrow><mi>j</mi><mo>⁢</mo><msub><mi>ξ</mi><mi>i</mi></msub></mrow></msup></mfenced></mtd></mtr><mtr><mtd><msup><mtable><mtr><mtd><msub><mi>ψ</mi><mi>i</mi></msub></mtd></mtr></mtable><mn>200</mn></msup><mo>=</mo><mi mathvariant="italic">phase</mi><mo>⁢</mo><mfenced><msup><mi>e</mi><mrow><mi>j</mi><mo>⁢</mo><msub><mi>ψ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub></mrow></msup><mo>⁢</mo><mfenced><mi>α</mi><mo>+</mo><mfenced><mn>1</mn><mo>-</mo><mi>α</mi></mfenced><mo>*</mo><msup><mi>e</mi><mrow><mi>j</mi><mo>⁢</mo><mfenced><msub><mi>ξ</mi><mi>i</mi></msub><mo>-</mo><msub><mi>ψ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub></mfenced></mrow></msup></mfenced></mfenced></mtd></mtr><mtr><mtd><msup><mtable><mtr><mtd><msub><mi>ψ</mi><mi>i</mi></msub></mtd></mtr></mtable><mn>200</mn></msup><mo>=</mo><msup><mtable><mtr><mtd><msub><mi>ψ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub></mtd></mtr></mtable><mn>200</mn></msup><mo>+</mo><mi>arctan</mi><mfenced><mfrac><mrow><mfenced><mn>1</mn><mo>-</mo><mi>α</mi></mfenced><mo>*</mo><mi>sin</mi><mfenced><msub><mi>ζ</mi><mi>i</mi></msub></mfenced></mrow><mrow><mi>α</mi><mo>+</mo><mfenced><mn>1</mn><mo>-</mo><mi>α</mi></mfenced><mo>*</mo><mi>cos</mi><mfenced><msub><mi>ζ</mi><mi>i</mi></msub></mfenced></mrow></mfrac></mfenced></mtd></mtr><mtr><mtd><msup><mtable><mtr><mtd><msub><mi>ψ</mi><mi>i</mi></msub></mtd></mtr></mtable><mn>200</mn></msup><mo>=</mo><msup><mtable><mtr><mtd><msub><mi>ψ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub></mtd></mtr></mtable><mn>200</mn></msup><mo>+</mo><msup><mtable><mtr><mtd><msub><mi mathvariant="italic">ϑ</mi><mi>i</mi></msub></mtd></mtr></mtable><mn>200</mn></msup></mtd></mtr></mtable></math><img file="EP1516469B1_D0007.tif" /></maths> Simplification of Equation 7 shows that the reference phase ψ<i>_i</i>²⁰⁰ at instant i may be obtained by adding an update value ϑ<i>_i</i>²⁰⁰ to the delayed reference phase ψ_<i>i</i>-1²⁰⁰ without the need for calculations in the complex domain. Thus, complex calculations that would require additional processing and larger silicon area as well as consume additional power are avoided.

0020The update value ϑ<i>_i</i>²⁰⁰ is a zero-mean stochastic variable, that is bounded to the ranges [-π/2,π/2],[-π/4,π/4], and [-π/8,π/8] for M=2, 4, and 8, respectively. The update value ϑ<i>_i</i>²⁰⁰ may be relatively small, thereby allowing a simplification in the calculation of the update value ϑ<i>_i</i>²⁰⁰. The simplification is based on the following equation: <maths id="math0008" num="(8)"><math display="block"><mi>with</mi><mspace width="1em" /><mtable columnalign="left"><mtr><mtd><msup><msub><mi mathvariant="italic">ϑ</mi><mi mathvariant="italic">i</mi></msub><mn mathvariant="italic">200</mn></msup><mo mathvariant="italic">=</mo><msub><mi mathvariant="italic">c</mi><mn mathvariant="italic">1</mn></msub><mo mathvariant="italic">*</mo><msup><msub><mi mathvariant="italic">ζ</mi><mi mathvariant="italic">i</mi></msub><mn mathvariant="italic">200</mn></msup><mo mathvariant="italic">+</mo><msub><mi mathvariant="italic">c</mi><mn mathvariant="italic">2</mn></msub><mo mathvariant="italic">*</mo><msup><mfenced><msup><msub><mi mathvariant="italic">ζ</mi><mi mathvariant="italic">i</mi></msub><mn mathvariant="italic">200</mn></msup></mfenced><mn mathvariant="italic">2</mn></msup><mo mathvariant="italic">+</mo><msub><mi mathvariant="italic">c</mi><mn mathvariant="italic">3</mn></msub><mo mathvariant="italic">*</mo><msup><mfenced><msup><msub><mi mathvariant="italic">ζ</mi><mi mathvariant="italic">i</mi></msub><mn mathvariant="italic">200</mn></msup></mfenced><mn mathvariant="italic">3</mn></msup></mtd></mtr><mtr><mtd><msub><mi mathvariant="italic">c</mi><mn mathvariant="italic">1</mn></msub><mo mathvariant="italic">=</mo><mn mathvariant="italic">1</mn><mo mathvariant="italic">-</mo><mi mathvariant="italic">α</mi></mtd></mtr><mtr><mtd><msub><mi mathvariant="italic">c</mi><mn mathvariant="italic">2</mn></msub><mo mathvariant="italic">=</mo><mfrac><mn mathvariant="italic">1</mn><mn mathvariant="italic">6</mn></mfrac><mo>⁢</mo><mi mathvariant="italic">α</mi><mo mathvariant="italic">-</mo><mfrac><mn mathvariant="italic">1</mn><mn mathvariant="italic">2</mn></mfrac><mo>⁢</mo><msup><mi mathvariant="italic">α</mi><mn mathvariant="italic">2</mn></msup><mo mathvariant="italic">+</mo><mfrac><mn mathvariant="italic">1</mn><mn mathvariant="italic">3</mn></mfrac><mo>⁢</mo><msup><mi mathvariant="italic">α</mi><mn mathvariant="italic">3</mn></msup></mtd></mtr><mtr><mtd><msub><mi mathvariant="italic">c</mi><mn mathvariant="italic">3</mn></msub><mo mathvariant="italic">=</mo><mo mathvariant="italic">-</mo><mfrac><mn mathvariant="italic">1</mn><mn mathvariant="italic">120</mn></mfrac><mo>⁢</mo><mi mathvariant="italic">α</mi><mo mathvariant="italic">+</mo><mfrac><mn mathvariant="italic">1</mn><mn mathvariant="italic">8</mn></mfrac><mo>⁢</mo><msup><mi mathvariant="italic">α</mi><mn mathvariant="italic">2</mn></msup><mo mathvariant="italic">-</mo><mfrac><mn mathvariant="italic">5</mn><mn mathvariant="italic">12</mn></mfrac><mo>⁢</mo><msup><mi mathvariant="italic">α</mi><mn mathvariant="italic">3</mn></msup><mo mathvariant="italic">+</mo><mfrac><mn mathvariant="italic">1</mn><mn mathvariant="italic">2</mn></mfrac><mo>⁢</mo><msup><mi mathvariant="italic">α</mi><mn mathvariant="italic">4</mn></msup><mo mathvariant="italic">-</mo><mfrac><mn mathvariant="italic">1</mn><mn mathvariant="italic">5</mn></mfrac><mo>⁢</mo><msup><mi mathvariant="italic">α</mi><mn mathvariant="italic">5</mn></msup></mtd></mtr></mtable></math><img file="EP1516469B1_D0008.tif" /></maths>

0021ϑ<i>_i</i>²⁰⁰ may be approximated by the first three terms of the series expansion shown in Eqn. (8). A coherency parameter α, as shown in Equation 8, is determined for a particular system associated with the phase domain semi-coherent demodulator 200.

0022To further simplify the phase-domain semi-coherent demodulator 200, the third order equation with coefficients <i>c</i>₁, <i>c</i>₂, and <i>c</i>₃ may be reduced to a first-order equation without significant loss of performance. The first-order approximation allows a scaler 232 to be utilized to scale the instantaneous error signal ζ<i>_i</i>²⁰⁰ by the coefficient <i>c</i>₁. The output of the scaler 232 is the update value ϑ<i>_i</i>²⁰⁰ as described by Equation 8. A phase sum adder 234 adds the update value ϑ<i>_i</i>²⁰⁰ to the delayed reference phase ψ_<i>i</i>-1 in order to output the reference phase ψ<i>_i</i>²⁰⁰. If the implementation of scaling is simple compared to phase addition, another addition may be removed at the cost of an additional scaling operation. This may be seen by the following equation: <maths id="math0009" num="(9)"><math display="block"><msub><mi>c</mi><mn>1</mn></msub><mo>*</mo><mfenced><msup><msub><mi>ξ</mi><mi>i</mi></msub><mn>200</mn></msup><mo>-</mo><msup><msub><mi>ψ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mn>200</mn></msup></mfenced><mo>+</mo><msup><msub><mi>ψ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mn>200</mn></msup><mo>=</mo><msub><mi>c</mi><mn>1</mn></msub><mo>*</mo><msup><msub><mi>ξ</mi><mi>i</mi></msub><mn>200</mn></msup><mo>+</mo><mfenced><mn>1</mn><mo>-</mo><msub><mi>c</mi><mn>1</mn></msub></mfenced><mo>*</mo><msup><msub><mi>ψ</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mn>200</mn></msup></math><img file="EP1516469B1_D0009.tif" /></maths>

0023The reference phase ψ<i>_i</i>²⁰⁰ is delayed by a unit delay 218 to form a delayed reference phase ψ_<i>i</i>-1²⁰⁰. The delayed reference phase ψ_<i>i</i>-1²⁰⁰ is utilized in further calculations. A phase sum adder 220 subtracts the delayed reference phase ψ_<i>i</i>-1²⁰⁰ from the phase component θ<i>_i</i>²⁰⁰. The output of the phase sum adder 220 is received by the decision unit 210 and a phase sum adder 224.

0024The decision unit 210 forms the decision ϕ<i>_i</i>²⁰⁰, which is delayed by a unit delay 222 to form the delayed decision ϕ_<i>i</i>-1²⁰⁰. The phase sum adder 224 subtracts the delayed decision ϕ_<i>i</i>-1²⁰⁰ from the output of the phase sum adder 220. The output of the phase sum adder 224 is an output <i>y_i</i>²⁰⁰ of the phase-domain semi-coherent demodulator 200. The delayed decision ϕ_<i>i</i>-1²⁰⁰ is subtracted from the decision ϕ<i>_i</i>²⁰⁰ at a phase sum adder 226 to produce a decision of the output <i>D</i>(<i>y_¡</i>²⁰⁰). The decision <i>D(y</i>_i²⁰⁰) is input to a look-up table (LUT) 228 to output detected bits.

0025<figref idref="f0002">FIGURE 3</figref> is a flow diagram illustrating a method 300 of calculating the reference phase ψ<i>_i</i>²⁰⁰ in the phase domain. The flow 300 begins at step 302. At step 302, the delayed reference signal ψ_<i>i</i>-1²⁰⁰ is subtracted from the rotated input phase ξ<i>_i</i>²⁰⁰ to obtain the instantaneous error signal ξ<i>_i</i>²⁰⁰. The instantaneous error signal ξ<i>_i</i>²⁰⁰ is scaled by the coefficient <i>c</i>₁ to form the update value ϑ<i>_i</i>²⁰⁰ at step 304. At step 306, the update value ϑ<i>_i</i>²⁰⁰ is added to the delayed reference signal ψ_<i>i</i>-1²⁰⁰ to form the reference phase ψ<i>_i</i>²⁰⁰. The reference signal ψ<i>_i</i>²⁰⁰ may be utilized in various calculations and decisions in order to attain the output y<i>_i</i>²⁰⁰ of the phase domain semi-coherent demodulator 200 and to produce the decision of the output <i>D</i>(<i>y_i</i>²⁰⁰) as noted above.

0026Although in the description above one scaler 232 to scale the instantaneous error signal ζ<i>_i</i>²⁰⁰ has been shown, various additional scalers may be employed in this invention to form higher-order approximations to yield better results. However, to obtain more accurate results, there is by necessity a trade off in increased complexity.

0027Embodiments of the present invention may be implemented in, for example, integrated circuits or chip sets, wireless systems, and receiver system products. For example, a computer is operative to execute software adapted to perform the demodulation techniques of the present invention. Demodulation software is adapted to reside on a computer readable medium, such as a magnetic disk within a disk drive unit. The computer readable medium may also include a flash memory card, EEROM based memory, bubble memory storage, ROM storage, etc. The software adapted to perform the demodulation method may also reside, in whole or in part, in the static or dynamic main memories or in firmware within a processor (i.e. within microcontroller, microprocessor or microcomputer internal memory). The demodulation method may also be applicable to implementations in integrated circuits, field programmable gate arrays (FPGAs), chip sets or application specific integrated circuits (ASICs), wireless systems, and other communication system products.

0028While exemplary embodiment(s) of the present invention have been described, it should be recognized that the invention can be varied in many ways without departing therefrom. Because the invention can be varied in numerous ways, it should be understood that the invention should be limited only insofar as is required by the scope of the following claims.