Patent Application
20110090991
1. Field of the Invention
The present invention relates generally to digital communication systems, and more particularly to a methods and apparatus for phase reference tracking of digital phase modulated signals in the receiver.
2. Background
Digital phase modulation is one of the popular digital modulations due to its simplicity and robustness. Source information is transmitted by selecting phases of the signal according to the information bits. Continuous phase modulation (CPM), Phase-shift keying (PSK) and differential phase-shift keying (DPSK) are examples of digital phase modulation.
In the receiver, it is necessary to detect an accurate phase reference for decoding the transmitted information bits. Otherwise, phase reference errors may cause significant performance degradation. For differentially encoded digital phase modulations such as DPSK, DQPSK and D8PSK, a phase reference can be derived from the previous symbol to facilitate the demodulation. For simple receivers, DPSK signals may be differentially decoded. That means, previous phase is used as a reference for the current symbol. However, since this reference is noisy, the performance can degrade up to 3 dB, compared to the performance with perfect phase reference. Phase reference tracking is also useful for DPSK signals.
To facilitate such a phase reference estimate, a training sequence is often transmitted at the beginning of a data packet. The phase reference may be easily estimated with the training sequence known at the receiver, but the throughput may be slightly decreased as the training sequence does not contain source information. Moreover, the phase reference may be time-varying due to the imperfect oscillators at the transmitter (TX) or the receiver (RX). In this case, phase reference tracking will be necessary for the receiver to maintain best performance while receiving information bits. Phase references may be heavily time-varying due to the mismatching between TX and RX oscillators. This mismatching is so-called frequency offset (FO). Moreover frequency drift may cause difficulty in tracking accurate phase reference. By estimating and/or tracking this FO, phase reference may be kept accurate.
For this phase reference tracking, multiple symbol detection [1] based on maximum likelihood sequence detection (MLSD) was proposed, but its complexity exponentially increases with the number of observation symbols. Furthermore, U.S. Pat. No. 7,245,672 issued to Smit et al., entitled “Method and apparatus for phase-domain semi-coherent demodulation” disclosed that a first-order IIR filter in phase-domain, of which complexity further decreases due to the phase operations instead of the complex signal operations as shown in
According to above problems, the related field needs a simple and robust phase tracking method, where the phase reference is tracked in phase-domain with a high order digital phase-locked loop, for general phase-modulated signals. Also, related field suggests a better way to track phase for differentially encoded digital phase modulations, such as DBPSK, (π/4) DQPSK and DBPSK modulated signals.
It is an objective of the present invention to provide an effective and robust method for phase reference tracking of digital phase modulated signals in the receiver. It tracks the phase errors and generates reliable phase reference to estimate.
To achieve the above objective, the present invention provides a method used for phase reference tracking of digital phase modulated signals in the receiver, comprising the steps of: converting a received complex signal to the received phase rn, feeding the received phase rn to a phase reference tracking unit, producing an estimated transmit phase {tilde over (s)}n from the phase reference tracking unit, feeding the estimated transmit phase {tilde over (s)}n to a coherent decoder, and producing a decoded symbol ân from the coherent decoder.
According to one aspect of the present invention, the received complex signal can be encoded by BPSK, MPSK, PSK and DPSK modulation systems.
According to one aspect of the present invention, the received phase rn can be converted to different forms according the received complex signal.
Another objective of the present invention is to provide an effective and robust apparatus for phase reference tracking of digital phase modulated signals in the receiver. The phase reference tracking unit takes the received phase and the decoded symbols as its input, generates reliable phase reference to estimate by tracking phase errors due to frequency offset and the variation of frequency offset. A gradient algorithm in phase-domain based on the measured phase error is utilized in the phase reference tracking unit.
To achieve the above objective, the present invention provides an apparatus used for phase reference tracking of digital phase modulated signals in the receiver, comprising: a complex-to-phase converter, used for converting the in-phase (In) and the quadrature (Qn) components of a received complex signal to a received phase rn, the phase reference tracking unit, which is electrically connected to the complex-to-phase converter, used for producing an estimated transmit phase {tilde over (s)}n, and the coherent decoder, which is electrically connected to the phase reference tracking unit, used for producing a decoded symbol ân and sending a re-modulation phase signal ŝn to the phase reference tracking unit.
According to one aspect of the present invention, the apparatus used for phase reference tracking of digital phase modulated signals in the receiver can be applied in BPSK, MPSK, PSK and DPSK modulation systems.
According to one aspect of the present invention, the types of the coherent decoder can be selected according to BPSK, MPSK and DPSK modulation systems.
All the objects, advantages, and novel features of the invention will become more apparent from the following detailed descriptions when taken in conjunction with the accompanying drawings.
Although the invention has been explained in relation to several preferred embodiments, the accompanying drawings and the following detailed descriptions are the preferred embodiment of the present invention. It is to be understood that the following disclosed descriptions will be examples of present invention, and will not limit the present invention into the drawings and the special embodiment.
Phase reference tracking is not necessary for some phase-modulated signals such as Gaussian frequency shift-keying (GFSK) and DPSK. However, it is well-known that coherent detection may help to improve performances up to 3 dB. Here, a simple, robust and generalized method for phase reference tracking in phase-domain is provided.
To understand the spirit of the present invention, referring to
The apparatus used for phase reference tracking of digital phase modulated signals in the receiver can be applied in BPSK, MPSK, PSK and DPSK modulation systems. The received complex signal 101 can be encoded by BPSK, MPSK, PSK and DPSK modulation systems. The received phase rn 111 can be converted to different forms according to the received complex signal 101. The types of the coherent decoder 130 can be selected according to BPSK, MPSK and DPSK modulation systems.
Now, referring to
Moreover, to compensate the delay (d) caused in the coherent decoder and to generate the estimated transmit phase {tilde over (s)}n 149 with correct timing, a coherent decoder 140, which is electrically connected to the first subtracter 121, is provided. Therefore, the estimated transmit phase {tilde over (s)}n 149 and the decoded symbol ân 212 turn into a estimated transmit phase with a delay (d) {tilde over (s)}n-d 144 and decoded symbol with a delay (d) ân-d 132 which are also denoted as decoded symbols 133.
The construction of the block diagram of the apparatus according the present invention may be modified and/or simplified with combining the phase reference tracking units and the coherent decoder units by removing redundant units and/or re-organizing the block diagrams.
Besides, the procedure of the present invention can further described as the following steps:
The received complex signal can be encoded by BPSK, MPSK, PSK and DPSK modulation systems. The received phase rn 111 can be converted to different forms according to the received complex signal.
Moreover, the procedure of producing an estimated transmit phase {tilde over (s)}n 141 further comprising the steps of:
The procedure of producing an estimated transmit phase {tilde over (s)}n further comprising the steps of:
The delay (d) is used for generating the estimated transmit phase {tilde over (s)}n 141 with correct timing.
The procedure of producing a decoded symbol ân 212 further comprising the steps of:
The re-modulation phase signal ŝn 141 is feed to a phase reference tracking unit and used for the calculation of a tracking error εn 145. The method used for phase reference tracking of digital phase modulated signals in the receiver as described above, the method is generalized with n-th order tracking.
A complex-to-phase converter 110 converts the incoming received complex signal 101, consisting of the in-phase (In) and the quadrature (Qn) components, to a received phase rn 111 using the following equation:
where n represents the symbol time index. Note that the operations on phase are based on modular 2π. The received phase rn 111 can be converted to different forms according the received complex signal and also can be converted to different forms according the received complex signal 101.
This received phase rn 111 is fed to a phase reference tracking unit 120, which produces an estimated transmit phase {tilde over (s)}n 141. This estimated transmit phase {tilde over (s)}n 141 is an estimated transmit phase and is fed to a coherent decoder 130. Since the allowed transmit phase is quantized for a digital phase modulation, the coherent decoder 130 decodes the estimated transmit phase {tilde over (s)}n 141 based on a de-mapping table to produce the decoded symbol with a delay (d) ân-d 132. For example, the coherent decoder 130 decodes for BPSK can be found in TABLE 1 below. If required, the coherent decoder 130 may utilize the received complex signal 101. The coherent decoder 130 also uses a “mapping” table to reconstruct the phase (also known as re-modulation) for the decoded symbol ân 132, denoted ŝn-d 131, and sends it to the phase reference tracking unit 120. An example for the mapping table for BPSK modulated signal is shown in Table 2 below.
Inside the phase reference tracking unit 120, the estimated transmit phase {tilde over (s)}n 141 at the receiver is calculated by subtracting the previous phase reference estimate {tilde over (θ)}n-1 142 from rn 111. A tracking error εn 145 is calculated by subtracting ŝn-d 131 from {tilde over (s)}n-d 144, where d is a delay introduced by the coherent decoder 130. Then, a phase correction factor due to frequency error, {tilde over (θ)}′n 147, and a phase reference estimate, {tilde over (θ)}n 148, are updated with the well-known gradient method:
{tilde over (θ)}′n={tilde over (θ)}′n-1+βεn, Eq. (2a)
{tilde over (θ)}n={tilde over (θ)}n-1+αεn+{tilde over (θ)}′n, Eq. (2b)
where 0≦α≦1 and 0≦β≦1. Note that {tilde over (θ)}′n 147 is a phase-error correction factor based on an estimated frequency-offset between the TX and the RX. Such a phase tracking loop is traditionally known as a second order phase-locked-loop (PLL). This tracking scheme can be easily generalized to a third order PLL as follows:
{tilde over (θ)}″n={tilde over (θ)}″n-1+γεn, Eq. (3a)
{tilde over (θ)}′n={tilde over (θ)}′n-1+βεn+{tilde over (θ)}′n, Eq. (3b)
{tilde over (θ)}n={tilde over (θ)}n-1+αεn+{tilde over (θ)}′n, Eq. (3c)
where 0≦α≦1, 0≦β≦1 and 0≦γ≦1. In the same manner, this tracking can be further generalized to an n-th order PLL. Note that this 3-rd order PLL can track not only static frequency errors but also time-varying frequency errors.
Note that the above n-th order phase reference tracking algorithm may be applied to any phase-modulated signals. In general, the inputs of the phase reference tracking unit 120 are the received phase rn 111 and the re-modulation phase signal ŝn-d 131. The output of the phase reference tracking unit 120 is the estimated transmit phase {tilde over (s)}n 141, after proper phase/frequency error correction, at the receiver. If required, the overall block diagram may be re-organized to save computational power and/or hardware size.
For clearer explanations, consider an M-ary PSK signal. In the transmitter (TX), k (=log2 M) information bits are mapped to one of the M phases. Let an and sn be the n-th symbol with k information bits and its corresponding mapped phase, respectively. This, the transmit phase, sn may be represented as
sn=(an), n=0, 1, . . . , M−1, Eq. (4)
where (•) denotes the phase-mapping function. Note the phase mapping for M=2 is shown in TABLE 2. In the proposed MPSK receiver (RX) shown in
r
n
=s
n+θn, Eq. (5)
where θn is the phase mismatching caused by the phase mismatching between the TX and the RX. The proposed second order PLL for decoding sn and tracking θn for a received MPSK signal is as follows:
Decoding/Phase-Tracking algorithm for MPSK signals (
For n=0 to N-1
{tilde over (s)}
n
=r
n−{tilde over (θ)}n-1 Eq. (6a)
â
n=−1({tilde over (s)}n) Eq. (6b)
ŝ
n=(ân) Eq. (6c)
εn={tilde over (s)}n−ŝn Eq. (6d)
{tilde over (θ)}′n={circumflex over (θ)}′n-1+βεn Eq. (6e)
{tilde over (θ)}n={tilde over (θ)}n-1+αεn+{tilde over (θ)}′n Eq. (6f)
An PSK coherent decoder 210 comprises a de-mapping unit and a mapping unit. The function (•) is the de-mapping unit 213, i.e., the inverse function of
(•). This de-mapping unit is for decoding an MPSK signal to produce a decoded symbol ân 212. This decoded symbol ân 212 is mapped again to generate a re-modulation phase signal ŝn 149 with the mapping unit 211. Note an example de-mapping table is given in TABLE 1 and the corresponding mapping table is given in TABLE 2 for a BPSK modulated signal.
Inside the phase reference tracking unit 220, the n-th estimated transmit phase {tilde over (s)}n 141, is calculated by subtracting the previous phase reference estimate {tilde over (θ)}n-1 142 from rn 111. Initial phase reference {tilde over (θ)}−1 is assumed to be estimated with the help of a training sequence which is known to both TX and RX. Even if this initial phase reference {tilde over (θ)}−1 is well-estimated, this reference may be further tracked for better Rx performance. Moreover, this invention may help to track phase reference with the phase variations during receiving due to imperfection in the Tx or the Rx path.
Then, an error εn 145 is calculated by subtracting ŝn 149 from {tilde over (s)}n 141. Note that εn 145 tends to be smaller with a more accurate {tilde over (θ)}n-1 142. A phase correction factor due to FO between the TX and the RX, {tilde over (θ)}′n 147, is obtained with εn 145 and β 146 from the previous estimate {tilde over (θ)}′n-1. Note: Units 125 and 129 represent “sample delays” and the circuitry shown in 220 implements Eq. (6e). The initial estimate {tilde over (θ)}′1 may be set to zero or previous estimate based on a training sequence. Finally, a phase reference estimate {tilde over (θ)}n 148 is updated with εn 145, α 143 and {tilde over (θ)}′n 147 from {tilde over (θ)}n-1 142 using Eq. (6f). This process shall be repeated until every symbol is decoded.
This invention can be also applied to DPSK signals. DPSK signals are popular for many communication systems due to the simple non-coherent detections even though coherent detections outperform non-coherent detections by up to 3 dB. Those non-coherent detection losses may be reduced by reliable phase reference tracking.
U.S. Pat. No. 7,245,672 disclosed the so-called ‘semi-coherent demodulation for DPSK signals' (
Smit's decoding algorithm for DPSK signals (
For n=0 to N-1
{tilde over (s)}
n
=r
n−{tilde over (θ)}n-1 Eq. (7a)
ŝ
n
=
D({tilde over (s)}n) Eq. (7b)
εn={tilde over (s)}n−ŝn Eq. (7c)
{tilde over (θ)}n={tilde over (θ)}n-1+αεn Eq. (7d)
â
n=(ŝn−ŝn-1) Eq. (7e)
where D(a) is a function that gives out the phase of the closest constellation to a. For π/4 DQPSK, the number of the possible ŝn 149 values is eight, not four due to the π/4 shifting. In this case, a less reliable phase error estimate, εn 145, is generated per Eq. (7c). A PSK decoder unit 310 decodes a PSK signal with the first-order PLL in phase-domain, generating the re-modulation phase signal ŝn 149. Then, a differential decoder unit 320 differentially the re-modulation phase signal ŝn 149, generating ân 212. Due to the differential decoding in Eq. (7e), single error in ŝn 149 causes double errors in ân 212 for a DPSK signal.
Here, we propose a method for a DPSK signal to overcome the disadvantages of the prior invention such as the first-order PLL tracking limitation, unreliable phase error estimate for π/4 DQPSK, and the double errors. Let's consider an M-ary DPSK signal similar to a MPSK signal. In the TX, k (=log2 M)information bits are mapped to one of the M phases. Let an and xn be the n-th symbol with k information bits and its corresponding mapped phase, respectively. This phase, xn may be represented as
x
n=(an), n=0, 1, . . . , N−1. Eq. (8)
Those mapped phases are accumulated before transmitting. In the RX, the phase of the received phase rn 111 may be represented as
where θn is the phase mismatching between the TX and the RX as previous explained. The proposed algorithm of θn estimation for DPSK is as follows:
A Phase Tracking and Decoding algorithm for DPSK Signals (
For n=1 to N-1
{tilde over (s)}n=rn−{tilde over (θ)}n-1 Eq. (10a)
{tilde over (x)}
n
={tilde over (s)}
n
−ŝ
n-1 Eq. (10b)
â
n
=M
−1({tilde over (x)}n) Eq. (10c)
{circumflex over (x)}
n=(ân) Eq. (10d)
ŝ
n
=ŝ
n-1
+{circumflex over (x)}
n (10e)
εn={tilde over (s)}n−ŝn Eq. (10f)
{tilde over (θ)}′n={tilde over (θ)}′n-1+βεn Eq. (10g)
{tilde over (θ)}n={tilde over (θ)}n-1+αεn+{tilde over (θ)}′n Eq. (10h)
This algorithm is similar to that for MPSK signals except the coherent decoder 410. Because the mapped phase xn is accumulated in the TX, ŝn-1 is subtracted from {tilde over (s)}n 141 before de-mapping, as is shown in Eq. (10b) and illustrated in coherent decoder 410. The initial phase reference {tilde over (θ)}0 may be set to r0 or a previous estimate. The other initial estimate {tilde over (θ)}′0 may be set to zero or a previous estimate.
This algorithm can be re-written without {tilde over (s)}n 141 and ŝn 149 as follows:
An Alternative implementation of phase-tracking and decoding algorithm for DPSK Signals
For n=1 to N-1
The algorithm for DPSK signals is further simplified by introducing {tilde over (φ)}n. Let
{tilde over (x)}
n
=r
n−{tilde over (φ)}n-1, Eq. (13)
Since {tilde over (θ)}n={tilde over (θ)}n-1+αεn+{tilde over (f)}n, φn can be derived as follows:
Therefore, the algorithm for DPSK signals may be written as follows:
An Alternative Algorithm for Phase-Tracking and Decoding of DPSK Signals (
For n=1 to N-1
{tilde over (x)}
n
=r
n−{tilde over (φ)}n-1 Eq. (15a)
â
n=({tilde over (x)}n) Eq. (15b)
{circumflex over (x)}
n=(ân) Eq. (15c)
εn={circumflex over (x)}n−{circumflex over (x)}n Eq. (15d)
{tilde over (θ)}′n={tilde over (θ)}′n-1+βεn Eq. (15e)
{tilde over (φ)}n=rn−(1−α)·εn+{tilde over (θ)}′n Eq. (15f)
This DPSK phase-tracking and decoding algorithm is simpler than the Smit's algorithm if a higher-order PLL for phase-tracking is disabled. Moreover, this is more robust for π/4 DPSK signals than the Smit's because the hard-decisional error probability is smaller with a greater distance among a four-phase constellation set than an eight-phase constellation set. In Smit's algorithm, ŝn 149 is set to the closest constellation from {tilde over (s)}n 141 (Eq. (7b)). Since the number of constellations is eight, the minimum phase distance among constellations is only π/4. For the current invention, the minimum phase distance to decide {circumflex over (x)}n 414 is π/2. Note that this algorithm is also good for heavy phase variations caused by frequency errors thanks to the higher order tracking. The double errors are also avoidable with this invention. Current error in ân 212 may cause phase tracking degraded but not necessarily cause the next symbol error. In Smit's, an error in ŝn 149 causes double errors for sure with a DPSK signal which is not shifted. Note that single error is still possible with Smit's for a π/4 shifted DQPSK signal.
Even though the proposed algorithm shown in the above are all 1st or 2nd order PLL's, one can easily generalize it to a 3rd order PLL as follows:
For n=1 to N-1
{tilde over (x)}
n
=r
n−{tilde over (φ)}n-1 Eq. (16a)
â
n=({tilde over (x)}n) Eq. (16b)
{circumflex over (x)}
n=(ân) Eq. (16c)
εn={tilde over (x)}n−{circumflex over (x)}n Eq. (16d)
{tilde over (θ)}″n={tilde over (θ)}″n-1+γεn (where 0≦γ≦1) Eq. (16e)
{tilde over (θ)}′n={tilde over (θ)}′n-1+βεn+{tilde over (θ)}′n Eq. (16f)
{tilde over (φ)}n=rn−(1−α)·εn+{tilde over (θ)}′n Eq. (16g)
When compared to a 2nd order PLL as shown in Eq. (15), the only difference in the above is the addition of {tilde over (θ)}″n, which can be used to track the FO variations. For Bluetooth applications, one found the 3rd order PLL, proposed in the above, offers the best performance against dirty packets, for which a FO and a sine-wave based frequency variation are both added to the transmitted BT EDR packets.
