Power control with space time transmit diversity

Power control with space time transmit diversity
RE44858

A circuit is designed with a measurement circuit (432). The measurement circuit is coupled to receive a first input signal (903) from a first antenna (128) of a transmitter and coupled to receive a second input signal (913) from a second antenna (130) of the transmitter. Each of the first and second signals is transmitted at a first time. The measurement circuit produces an output signal corresponding to a magnitude of the first and second signals. A control circuit (430) is coupled to receive the output signal and a reference signal. The control circuit is arranged to produce a control signal at a second time in response to a comparison of the output signal and the reference signal.

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Patent RE44858
Priority Dec 31 1998
Filed Jul 20 2011
Issued Apr 22 2014
Expiry Dec 31 2018
Inventors Dabak, Ana…
Assg.orig Texas Inst…
Assg.curr Intel Corp…
Entity Large
Referenced by 1
References 27
Maint.: all paid

0. 45. A method of processing signals for a transceiver, comprising the steps of:

receiving a first input signal transmitted from a first antenna of a transmitter remote from the transceiver at a first time;

receiving a second input signal transmitted from a second antenna of the transmitter at the first time;

measuring each of the first and second input signals and producing at least one output signal;

comparing the at least one output signal to a reference signal; and

producing a first power control signal and a second power control signal to control transmit power from the first and second transmit antennas in response to the step of comparing.

0. 36. A transceiver circuit, comprising:

a measurement circuit coupled to receive a first input signal from a first antenna of a transmitter remote from the transceiver and coupled to receive a second input signal from a second antenna of the transmitter, each of the first and second input signals being transmitted at a first time, the measurement circuit producing an output signal in response to the first and second input signals; and

a control circuit coupled to receive the output signal and a reference signal, the control circuit arranged to produce a first power control signal and a second power control signal to control transmit power from the first and second transmit antennas.

0. 1. A circuit, comprising:

a measurement circuit coupled to receive a first wideband code division multiple access signal, comprising at least one pilot, from a first antenna of a remote transmitter and coupled to receive a second wideband code division multiple access signal, comprising at least one pilot, from a second antenna of the remote transmitter, each of the first and second wideband code division multiple access signals being transmitted at a first time, the measurement circuit producing a first output signal corresponding to a magnitude of the first wideband code division multiple access signal and a second output signal corresponding to a magnitude of the second wideband code division multiple access signal; and

a control circuit coupled to receive the output signal and a reference signal, the control circuit arranged to produce a first transmit power control signal and a second transmit power control signal at a second time in response to a comparison of the output signal and the reference signal, each of the first and second transmit power control signals set to control transmit power of respective said first and second antennas.

0. 2. A circuit as in claim 1, further comprising an estimate circuit coupled to receive at least a first predetermined signal and a second predetermined signal from the remote transmitter, each of the first and second predetermined signals having respective predetermined values, the estimate circuit producing at least one of the first estimate signal and the second estimate signal in response to the first and second predetermined signals.

0. 3. A circuit as in claim 2, wherein each of the first and second predetermined signals are pilot symbols.

0. 4. A circuit as in claim 3, wherein the measurement circuit, the control circuit and the estimate circuit are formed on a single integrated circuit.

0. 5. A circuit as in claim 3, wherein each of the first and second estimate signals is a Rayleigh fading parameter estimate.

0. 6. A circuit as in claim 3, wherein a total path diversity of each of the first and second symbol estimates is at least twice a number of transmitting antennas.

0. 7. A circuit as in claim 1, wherein the measurement circuit is further coupled to receive a third input signal from a third antenna of the remote transmitter and coupled to receive a fourth input signal from a fourth antenna of the remote transmitter, each of the third and fourth input signals being transmitted at the first time, and wherein the output signal further corresponds to at least one of the third and fourth input signals.

0. 8. A circuit as in claim 7, wherein each of the input signals comprise at least one pilot symbol.

0. 9. A circuit as in claim 7, wherein each of the input signals is a wideband code division multiple access signal.

0. 10. A circuit as in claim 7, wherein the output signal corresponds to a sum of magnitudes of the input signals.

0. 11. A circuit as in claim 7, wherein the control signal comprises at least one transmit power control signal.

0. 12. A circuit, comprising:

a measurement circuit coupled to receive a first input signal from a first antenna of a transmitter at a first time and coupled to receive a second input signal from a second antenna of the transmitter at a third time, the measurement circuit producing a first output signal corresponding to a magnitude of the first input signal and producing a second output signal corresponding to a magnitude of the second input signal; and

a control circuit coupled to receive the first and second output signals and a reference signal, the control circuit arranged to produce a first control signal at a second time after the first time in response to a comparison of the first output signal and the reference signal, the control circuit arranged to produce a second control signal at a fourth time after the third time in response to a comparison of the second output signal and the reference signal.

0. 13. A circuit as in claim 12, wherein each of the first and second input signals comprise at least one pilot symbol.

0. 14. A circuit as in claim 12, wherein each of the first and second control signals comprise at least one transmit power control signal.

0. 15. A circuit as in claim 12, wherein each of the first and second input signals is a wideband code division multiple access signal.

0. 16. A circuit as in claim 12, further comprising an estimate circuit coupled to receive at least a first predetermined signal and a second predetermined signal from the transmitter source, each of the first and second predetermined signals having respective predetermined values, the estimate circuit producing the first estimate signal and the second estimate signal in response to the first and second predetermined signals.

0. 17. A method of processing signals for a communication system, comprising the steps of:

receiving at least one control signal, comprising at least one transmit power control signal, transmitted from an external source at a first time;

producing a transmit power level corresponding to at least one of a plurality of antennas in response to the control signal; and

transmitting a plurality of signals to the external source at a respective said transmit power level at a second time from a respective said plurality of antennas, wherein the at least one transmit power control signal includes a plurality of transmit power control signals, and wherein the respective said transmit power level for each of said plurality of antennas is set by a respective transmit power control signal of the plurality of transmit power control signal.

0. 18. A method of processing signals as in claim 17, wherein the respective said transmit power level has a same transmit power adjustment for each of said plurality of antennas in response to one transmit power control signal.

0. 19. A method of processing signals, comprising the steps of:

selecting a diversity pattern having plural elements corresponding to plural signal sources and plural times;

selecting a symbol pattern having a plurality of symbols corresponding to plural signal sources and plural times;

producing an overlay of each element of the diversity pattern with the symbol pattern.

0. 20. A method as in claim 19, wherein each element of the diversity pattern is one of a true and a complement of another element in the diversity pattern.

0. 21. A method as in claim 19, wherein each symbol of the symbol pattern is at least one of a true, a complement and a conjugate of another symbol in the symbol pattern.

0. 22. A method as in claim 19, further comprising the steps of:

transmitting a first symbol of the symbol pattern corresponding to a first element of the diversity pattern from a first antenna at a first time;

transmitting a second symbol of the symbol pattern corresponding to the first element of the diversity pattern from a second antenna at the first time;

transmitting a fifth symbol of the symbol pattern corresponding to a second element of the diversity pattern from a third antenna at the first time; and

transmitting a sixth symbol of the symbol pattern corresponding to the second element of the diversity pattern from a fourth antenna at the first time.

0. 23. A method as in claim 22, further comprising the steps of:

transmitting a third symbol of the symbol pattern corresponding to the first element of the diversity pattern from the first antenna at a second time;

transmitting a fourth symbol of the symbol pattern corresponding to the first element of the diversity pattern from the second antenna at the second time;

transmitting a seventh symbol of the symbol pattern corresponding to the second element of the diversity pattern from the third antenna at the second time; and

transmitting an eighth symbol of the symbol pattern corresponding to the second element of the diversity pattern from the fourth antenna at the second time.

0. 24. A method as in claim 19, further comprising the steps of:

transmitting a first symbol of the symbol pattern corresponding to a first element of the diversity pattern from a first antenna at a first time;

transmitting a second symbol of the symbol pattern corresponding to the first element of the diversity pattern from a second antenna at the first time;

transmitting a fifth symbol of the symbol pattern corresponding to a second element of the diversity pattern from a third antenna at a third time; and

transmitting a sixth symbol of the symbol pattern corresponding to the second element of the diversity pattern from a fourth antenna at the third time.

0. 25. A method as in claim 24, further comprising the steps of:

transmitting a third symbol of the symbol pattern corresponding to the first element of the diversity pattern from the first antenna at a second time;

transmitting a fourth symbol of the symbol pattern corresponding to the first element of the diversity pattern from the second antenna at the second time;

transmitting a seventh symbol of the symbol pattern corresponding to the second element of the diversity pattern from the third antenna at a fourth time; and

transmitting an eighth symbol of the symbol pattern corresponding to the second element of the diversity pattern from the fourth antenna at the fourth time.

0. 26. A method as in claim 24, further comprising the steps of:

not transmitting from the third and the fourth antennas during a part of the first time; and

not transmitting from the first and the second antennas during a part of the third time.

0. 27. A method of processing signals, comprising the steps of:

receiving an overlay pattern of transmitted symbols from plural signal sources at plural times;

decoding the overlay pattern according to a diversity pattern having plural elements corresponding to plural signal sources and plural times; and

decoding the overlay pattern according to a symbol pattern having a plurality of symbols corresponding to plural signal sources and plural times, the symbol pattern corresponding to each of plural elements of the diversity pattern.

0. 28. A method as in claim 27, wherein each element of the diversity pattern is one of a true and a complement of another element in the diversity pattern.

0. 29. A method as in claim 27, wherein each symbol of the symbol pattern is at least one of a true, a complement and a conjugate of another symbol in the symbol pattern.

0. 30. A method as in claim 27, further comprising the steps of:

receiving a first symbol of the symbol pattern corresponding to a first element of the diversity pattern from a first antenna at a first time;

receiving a second symbol of the symbol pattern corresponding to the first element of the diversity pattern from a second antenna at the first time;

receiving a fifth symbol of the symbol pattern corresponding to a second element of the diversity pattern from a third antenna at the first time; and

receiving a sixth symbol of the symbol pattern corresponding to the second element of the diversity pattern from a fourth antenna at the first time.

0. 31. A method as in claim 30, further comprising the step of decoding the first, second, fifth and sixth symbols.

0. 32. A method as in claim 30, further comprising the steps of:

receiving a third symbol of the symbol pattern corresponding to the first element of the diversity pattern from the first antenna at a second time;

receiving a fourth symbol of the symbol pattern corresponding to the first element of the diversity pattern from the second antenna at the second time;

receiving a seventh symbol of the symbol pattern corresponding to the second element of the diversity pattern from the third antenna at the second time; and

receiving an eighth symbol of the symbol pattern corresponding to the second element of the diversity pattern from the fourth antenna at the second time.

0. 33. A method as in claim 27, further comprising the steps of:

receiving a first symbol of the symbol pattern corresponding to a first element of the diversity pattern from a first antenna at a first time;

receiving a second symbol of the symbol pattern corresponding to the first element of the diversity pattern from a second antenna at the first time;

receiving a fifth symbol of the symbol pattern corresponding to a second element of the diversity pattern from a third antenna at a third time; and

receiving a sixth symbol of the symbol pattern corresponding to the second element of the diversity pattern from a fourth antenna at the third time.

0. 34. A method as in claim 33, further comprising the steps of:

not decoding a symbol from the third and the fourth antennas during the first time; and

not decoding from the first and the second antennas during the third time.

0. 35. A method as in claim 33, further comprising the steps of:

receiving a third symbol of the symbol pattern corresponding to the first element of the diversity pattern from the first antenna at a second time;

receiving a fourth symbol of the symbol pattern corresponding to the first element of the diversity pattern from the second antenna at the second time;

receiving a seventh symbol of the symbol pattern corresponding to the second element of the diversity pattern from the third antenna at a fourth time; and

receiving an eighth symbol of the symbol pattern corresponding to the second element of the diversity pattern from the fourth antenna at the fourth time.

0. 37. A circuit as in claim 36, wherein each of the first and second input signals comprises at least one pilot symbol.

0. 38. A circuit as in claim 36, wherein each of the first and second input signals is a wideband code division multiple access signal.

0. 39. A circuit as in claim 36, wherein the output signal comprises a sum of the magnitude of each of the first and second input signals.

0. 40. A circuit as in claim 36, wherein the output signal comprises a first output signal and a second output signal, the first output signal corresponding to a magnitude of the first input signal and the second output signal corresponding to a magnitude of the second input signal.

0. 41. A circuit as in claim 36, wherein the first and second power control signals have a same value.

0. 42. A circuit as in claim 36, wherein the first and second power control signals have different values.

0. 43. A circuit as in claim 36, wherein the measurement circuit and the control circuit are formed on a single integrated circuit.

0. 44. A circuit as in claim 36, wherein the measurement circuit is further coupled to receive a third input signal from a third antenna of the transmitter and coupled to receive a fourth input signal from a fourth antenna of the transmitter, each of the third and fourth input signals being transmitted at the first time, and wherein the output signal further corresponds to at least one of the third and fourth input signals.

0. 46. A method as in claim 45, wherein each of the first and second input signals comprises at least one pilot symbol.

0. 47. A method as in claim 45, wherein each of the first and second input signals is a wideband code division multiple access signal.

0. 48. A method as in claim 45, wherein the output signal comprises a sum of the magnitude of each of the first and second input signals.

0. 49. A method as in claim 45, wherein the output signal comprises a first output signal and a second output signal, the first output signal corresponding to a magnitude of the first input signal and the second output signal corresponding to a magnitude of the second input signal.

0. 50. A circuit as in claim 45, wherein the first and second power control signals have a same value.

0. 51. A circuit as in claim 45, wherein the first and second power control signals have different values.

R_j²=a_j¹S₁−a_j²S₂* tm [6]
R_j³=a_j¹−a_j^{2 tm [}7]
R_j⁴=a_j¹S₁+a_j²S₁* tm [8]
a_j¹=(R_j¹+R_j³)/2 [9]
a_j²=(R_j¹−R_j³)/2 [10]
Referring now to FIG. 3, there is a schematic diagram of a phase correction circuit of the present invention that may be used with a remote mobile receiver. This phase correction circuit receives input signals R_j²and R_j⁴on leads 324 and 326 at symbol times 2T and 4T, respectively. Each input signal has a value determined by the transmitted pilot symbols as shown in equations [6] and [8], respectively. The phase correction circuit receives a complex conjugate of a channel estimate of a Rayleigh fading parameter a_j^1*corresponding to the first antenna on lead 302 and a channel estimate of another Rayleigh fading parameter a_j²corresponding to the second antenna on lead 306. Complex conjugates of the input signals are produced by circuits 308 and 330 at leads 310 and 322, respectively. These input signals and their complex conjugates are multiplied by Rayleigh fading parameter estimate signals and summed as indicated to produce path-specific first and second symbol estimates at respective output leads 318 and 322 as in equations [11] and [12].
R_j²a_j^1*+R_j^4*a_j²=(51 a_j¹|²+|a_j²|²)S₁ [11]
−R_j^2*a_j²+R_j⁴a_j^1*=(|a_j¹|²+|a_j²|²)S_s [12]
These path-specific symbol estimates are then applied to a rake combiner circuit 404 (FIG. 4) to sum individual path-specific symbol estimates, thereby providing net soft symbols or pilot symbol signals as in equations [13] and [14].

$\begin{matrix} {\tilde{S}}_{1} = \sum_{j = 1}^{L} R_{j}^{2} α_{j}^{1 *} + R_{j}^{4 *} α_{j}^{2} & [13] \\ {\tilde{S}}_{2} = \sum_{j = 1}^{L} - R_{j}^{2 *} α_{j}^{2} + R_{j}^{4} α_{j}^{1 *} & [14] \end{matrix}$
These soft symbols or estimates provide a path diversity L and a transmit diversity 2. Thus, the total diversity of the STTD system is 2L. This increased diversity is highly advantageous in providing a reduced bit error rate.

Referring now to FIG. 4, there is a simplified diagram of a mobile communication system that may use the phase correction circuit (FIG. 3) with closed-loop power control of the present invention. The mobile communication system includes an antenna 400 for transmitting and receiving external signals. The diplexer 402 controls the transmit and receive function of the antenna. Multiple fingers of rake combiner circuit 404 combine received signals from multiple paths. Symbols from the rake combiner circuit 404, including pilot symbol signals of equations [13] and [14], are applied to a bit error rate (BER) circuit 410 and to a Viterbi decoder 406. Decoded symbols from the Viterbi decoder are applied to a frame error rate (FER) circuit 408. Averaging circuit 412 produces one of a FER and BER. This selected error rate is compared to a corresponding target error rate from reference circuit 414 by comparator circuit 416. The compared result is applied to bias circuit 420 via circuit 418 for generating a signal-to-interference ratio (SIR) reference signal on lead 424.

Pilot symbols from the rake combiner 404 are applied to the SIR measurement circuit 432. The SIR measurement circuit produces a received signal strength indicator (RSSI) estimate from an average of received pilot symbols. The SIR measurement circuit also produces an interference signal strength indicator (ISSI) estimate from an average of interference signals from base stations and other mobile systems over many time slots. The SIR measurement circuit produces an SIR estimate from a ratio of the RSSI signal to the ISSI signal. This SIR estimate is compared with a target SIR by circuit 426. This comparison result is applied to TPC command circuit 430 via circuit 428. The TPC command circuit 430 sets a TPC symbol control signal that is transmitted to a remote base station. This TPC symbol instructs the base station to either increase or decrease transmit power by preferably 1 dB for subsequent transmission.

Referring now to FIG. 9A, there is a signal flow diagram of an embodiment of closed-loop power control for a STTD system of the present invention. The STTD system transmits forward link time slots 900-902 from antenna A1 in parallel with forward link time slots 910-912 from antenna A2. Pilot symbols 903 of time slot 900 from antenna A1 and pilot symbols 913 of time slot 910 from antenna A2 are transmitted at time t_m. Circuit 918, included in SIR measurement circuit 432 (FIG. 4), sums these pilot symbols. The sum is compared to a target SIR on lead 424. A result of the comparison is applied to TPC command circuit 430 via circuit 428. The TPC command circuit produces TPC symbol 920 (FIG. 9A) for transmission to the remote base station in the reverse link. The remote base station adjusts transmit power of antenna A1 for time slot 901 and transmit power of antenna A2 for time slot 911 at time t_sin response this TPC symbol. This method of closed-loop transmit power control is highly advantageous in regulating transmit power with minimum variance. Channel estimates and corresponding pilot symbol signal estimates are greatly improved by STTD. Accuracy of subsequent measurement of these received pilot symbol signal magnitudes is greatly improved. Transmit power variance is minimized for both antennas A1 and A2 by transmit power adjustment in a time slot immediately following the measured pilot symbol signal time slot.

Turning now to FIG. 9B, there is a signal flow diagram of another embodiment of closed-loop power control for a STTD system of the present invention. The STTD system transmits forward link time slots 930-932 from antenna A1 in parallel with forward link time slots 940-942 from antenna A2. Pilot symbols 933 of time slot 930 from antenna A1 are transmitted at time t_m1. The SIR measurement circuit 432 (FIG. 4) measures these pilot symbols and compares them with a target SIR on lead 424. The TPC command circuit 430 produces TPC symbol 947 (FIG. 9B) for transmission to the remote base station in the reverse link. The remote base station adjusts transmit power of antenna A1 for time slot 931 at time t_s1in response this TPC symbol. Pilot symbols 944 of time slot 941 from antenna A2 are transmitted at time t_m2. The SIR measurement circuit 432 (FIG. 4) measures these pilot symbols and produces TPC symbol 950 (FIG. 9B) for transmission to the remote base station in the reverse link. The remote base station adjusts transmit power of antenna A2 for time slot 942 at time t_s2in response this TPC symbol. This embodiment of the present invention, therefore, provides a further advantage of independent power control of each transmit antenna. Transmit power variance is minimized by adjusting transmit power for each antenna in a time slot immediately following the measured pilot symbol signal time slot.

The signal flow diagram of FIG. 9C illustrates yet another embodiment of closed-loop power control for a STTD system of the present invention. The STTD system transmits forward link time slots 960-962 from antenna A1 in parallel with forward link time slots 970-972 from antenna A2. Pilot symbols 963 of time slot 960 from antenna A1 and pilot symbols 973 of time slot 970 from antenna A2 are transmitted at time t_m. The SIR measurement circuit 432 (FIG. 4) measures each of these pilot symbols and compares them to a target SIR on lead 424. A result of the comparison is applied to TPC command circuit 430 via circuit 428. The TPC command circuit produces TPC symbols 984 and 985 (FIG. 9C) corresponding to antennas A1 and A2, respectively. Both TPC symbol signals are transmitted to the remote base station in the same time slot of the reverse link. The remote base station independently adjusts transmit power of antennas A1 and A2 at time t_sin response to TPC symbols 984 and 985, respectively. This method of closed-loop transmit power control is highly advantageous in regulating transmit power with minimum variance. Transmit power of each antenna A1 and A2 is independently controlled. Transmit power variance is minimized for both antennas2 by transmit power adjustment in a time slot immediately following the measured pilot symbol signal time slot.

Referring now to FIG. 10A, advantages of the present invention will be explained in detail with reference to the simulation of weighted multi-slot average (WMSA) channel estimation for STTD and TSTD for 5 Hz Doppler. The simulation curves show a coded bit error rate (BER) for a range of ratios of energy per bit (Eb) over noise (N0). The 5 Hz Doppler corresponds to mobile station movement with respect to a base station at walking speed. For a coded BER of preferably 10⁻³, STTD shows approximately 0.75 dB improvement with respect to TSTD. Both show significant improvement over OTD. The simulation curves of FIG. 10B compare power control for STTD and TSTD for 5 Hz Doppler. For example, STTD shows approximately 0.9 dB improvement over TSTD for a coded BER of preferably 10⁻³.

Simulation curves of FIG. 11A show a coded bit error rate (BER) for a range of Eb/N0 for WMSA channel estimation at 200 Hz Doppler, corresponding to mobile station movement with respect to a base station at a vehicular speed of 120 kmph (80 mph). The STTD system shows approximately 0.25 dB improvement with respect to OTD at a coded BER of preferably 10⁻³. A similar advantage over TSTD is likely in view of the similarity of TSTD and OTD curves. Likewise, for a preferable coded BER of 10⁻³, the curves of FIG. 11B show a 0.75 dB improvement in power control for STTD over TSTD for 200 Hz Doppler. The STTD system, therefore, provides significantly improved BER over OTD and TSTD systems of the prior art.

Although the invention has been described in detail with reference to its preferred embodiment, it is to be understood that this description is by way of example only and is not to be construed in a limiting sense. For example, advantages of the present invention may be achieved by a digital signal processing circuit as will be appreciated by those of ordinary skill in the art having access to the instant specification. Furthermore, the advantages of STTD accuracy and independent transmit antenna power control as described in FIG. 9C may be achieved with a single TPC symbol signal. A QPSK TPC symbol signal includes four states, including two states for each of the real and imaginary components. The real components, for example, may correspond to antenna A1 and the imaginary components may correspond to antenna A2. Thus, a state of the real or imaginary component of a single TPC symbol may be used to independently adjust transmit power of antenna A1 or antenna A2, respectively.

Moreover, advantages of the present invention may be extended to four transmit antennas by including the previously described STTD symbol pattern (FIG. 2) as an overlay of the OTD (FIG. 5) or TSTD (FIG. 8) symbol patterns. The STTD overlay pattern for OTD with four antennas is given by equation [15].

$\begin{matrix} \langle \begin{matrix} {Ant}_{1} \\ {Ant}_{2} \\ {Ant}_{3} \\ {Ant}_{4} \end{matrix} \rangle = \langle \begin{matrix} a & b & a & b \\ - b^{*} & a^{*} & - b^{*} & a^{*} \\ c & d & - c & - d \\ - d^{*} & c^{*} & d^{*} & - c^{*} \end{matrix} \rangle & [15] \end{matrix}$
This STTD overlay pattern for OTD substitutes the STTD symbol pattern of FIG. 2 for each OTD symbol of FIG. 5. For example, the four upper-left matrix elements └a b −b* a*┘ of equation [15] correspond to STTD symbols └S₁S₂−S₂* S₁*┘ of FIG. 2. These four elements of equation [15] and the four top-right duplicate matrix elements correspond to elements [S₁S₁] on lead 504 (FIG. 5). Likewise, the four bottom-left matrix elements and the four bottom-right matrix elements of equation [15] correspond to elements [S₂−S₂] on lead 506 (FIG. 5). An STTD overlay pattern for TSTD is given by equation [16] whereφ corresponds to null elements when alternate antennas are transmitting.

$\begin{matrix} \langle \begin{matrix} {Ant}_{1} \\ {Ant}_{2} \\ {Ant}_{3} \\ {Ant}_{4} \end{matrix} \rangle = \langle \begin{matrix} a & b & ϕ & ϕ \\ - b^{*} & a^{*} & ϕ & ϕ \\ ϕ & ϕ & c & d \\ ϕ & ϕ & - d^{*} & c^{*} \end{matrix} \rangle & [16] \end{matrix}$

It is understood that the inventive concept of the present invention may be embodied in a mobile communication system as well as circuits within the mobile communication system. It is to be further understood that numerous changes in the details of the embodiments of the invention will be apparent to persons of ordinary skill in the art having reference to this description. It is contemplated that such changes and additional embodiments are within the spirit and true scope of the invention as claimed below.

INVENTORS:

Dabak, Anand G., Hosur, Srinath

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