CN117981283A - Robust equalization method under the condition of known intersymbol interference - Google Patents

Abstract

The invention relates to a method for robust equalization of a received signal in the presence of a known ii, wherein EL-VA is applied. The object is to provide a method for improving the robustness with respect to time and DC offset estimation errors when applying VA for MLSE, assuming a constant and known impulse response h, which is solved by the following steps: step 1: sampling, by the synchronization unit, the received signal r at an estimated time offset p ₀ provided at p=0 corresponding to the discrete-time sequence r ₀＝{r₀ (k) }, where k represents a discrete-time step, k=0, 1,..while the received signal r is additionally sampled at an early time offset-T _s assuming p= -1 relative to p ₀ corresponding to the discrete-time sequence r _‑Ts＝{r_‑Ts (k) }, and the received signal r is additionally sampled at a later time offset +t _s assuming p= +1 relative to an estimated time offset p ₀ corresponding to the discrete-time sequence r _+Ts＝{r_+Ts (k) }; step 2: for each hypothesis p= -1,0, +1, calculating a branch metric μ _k (b, p) based on the respective sampled received signal r _pTs (k) for the hypothesis p= -1,0, +1; step 3: for each hypothesis p= -1,0, +1, based on the respective branch metrics μ _k (b, k), recursively computing path metrics m _k (S, p) and survival path q _k (S, p) for the respective VA for all S e {0,1,..s-1 }; step 4: calculating a value for a path metric m _k (s, p); step 5: based on the survivor path (III), a decision is made on the most likely received information symbol (II), where D is the survivor depth.

Description

Robust equalization method under the condition of known intersymbol interference

The invention discloses a method for carrying out stable equalization on a received signal under the condition of known intersymbol interference, wherein an early-late Viterbi (Veterbi) algorithm is adopted.

Intersymbol interference (ISI) is a well-known drawback encountered in communication systems; see J.G.Proakis.digital communications.McGraw-Hill,1995.

Let x= { X (k) } be the information symbol sequence transmitted at discrete time steps k=0, 1..where X (k) is an element of a certain symbol alphabet X.

In the presence of ISI and additive noise, the received sequence r= { r (k) } is typically modeled as:

Where h= { h (0),..h (L) } is a discrete time causal impulse response of length l+1, where L is some integer value, and n= { n (k) } is a discrete time zero mean (gaussian) noise sequence, v is the index of the sum.

In most cases, the symbol x (k) cannot be obtained directly from the sample r (k) at time step k. In order to mitigate the effects of ISI, many equalization or detection concepts are known, such as linear equalization, decision feedback equalization, maximum Likelihood Sequence Estimation (MLSE) (see for example Jr：Jr.G.D.Forney.Maximum-Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference.IEEE Transcations on Information Theory,pages 363-378,May 1972or J.G.Proakis.Digital Communications.McGraw-Hill,1995), or maximum a posteriori estimation (MAP)), which is a mathematical algorithm that extracts useful data from a noisy data stream.

As is well known, the MLSE based on the Viterbi algorithm is an optimal sequence estimator under certain conditions, see for example J.G. Proakis.digital communications.McGraw-Hill,1995.

Regarding equation (1), it is assumed that pulse h is known. Some communication systems allow estimating h based on a specific training or trial sequence. This is useful, for example, if ISI is caused by multipath propagation. Multipath propagation is understood to be a phenomenon that causes a radio signal to arrive at a receiving device through multiple paths with different propagation delays.

On the other hand, for some communication systems, multipath propagation is not relevant, but ISI still exists, due to the constant known pulse h. A typical example is Pulse Amplitude Modulation (PAM), in which ISI is deliberately introduced. PAM is a form of signal modulation in which message information is encoded in the amplitude of a series of signal pulses. It is a linear modulation scheme in which a discrete time symbol sequence { a (k) } of a (k) ∈a in a complex constellation letter a is shaped by a transmission pulse g (t). The continuous-time baseband signal x (t) is composed ofObtained, where k is a discrete time index, T is a continuous time variable, and T is a symbol period. However, ISI may also be present for nonlinear modulation schemes such as Gaussian Frequency Shift Keying (GFSK) as specified in the bluetooth standard (see ：Bluetooth SIG.Bluetooth Core Specification.Bluetooth Core Specification Version 5.2,December 2019). here, a gaussian filter with a defined bandwidth-time product bt=0.5 is employed for improved spectral shaping.

However, even for a constant impulse response h, it can be assumed that the value of r (k) has been accurately obtained at the optimal sampling time of the symbol time. For most receivers, the samples r (k) are compared with the corresponding continuous time received signalCorrelation, wherein/>Where T is the symbol time and T ₀ is the unknown timing offset. In a communication system, a received signal/>Usually, an over-sampling is first performed to obtain a sequence/>Where T _s = T/l, m = 0, 1. An initial synchronization unit as part of the receiver calculates an estimate of the best time offset T ₀ at the resolution of T _s by T ₀＝p₀T_s.

The estimation of the p ₀ value is typically based on a known preamble and synchronization sequence. Furthermore, it is also possible to base the extraction sequenceSymbol interval equalization is performed.

If there is an estimation error in the estimation value p ₀, the MLSE will lose optimality. In this case, the relationship in equation (1) is no longer fully established, and thus the MLSE-based equalization may be greatly reduced.

Another potential performance penalty occurs in the case of an additional DC offset such that

In contrast to the noise sequence n= { n (k) }, the sequence c= { c (k) } may not have zero mean distribution, resulting in a deviation of the MLSE. For GFSK, for example, the DC offset may be caused by a residual frequency offset that is in turn related to insufficient frequency offset correction of the synchronization unit or insufficient frequency offset tracking caused by frequency drift.

Thus, the Viterbi-based algorithm can mitigate ISI effects of the known pulse h by the MLSE. However, if the received signal does not achieve optimal synchronization in terms of time and dc offset, performance may be degraded.

It is therefore an object of the present invention to provide a method that improves the robustness of time and dc offset estimation errors when applying the Viterbi algorithm for MLSE assuming a constant and known impulse response h.

This object is solved by a method according to independent claim 1. A method of robust equalization of a received signal r in the presence of known intersymbol interference, wherein an early-late Viterbi algorithm is applied, the method comprising the steps of:

-step 1: sampling, by the synchronization unit, the received signal r at an estimated time offset p ₀ provided at an assumption p=0 corresponding to the discrete-time sequence r ₀＝{r₀ (k) }, where k represents a discrete-time step, k=0, 1,..while the received signal r is additionally sampled at an early time offset-T _s at an estimated time offset p ₀ corresponding to the discrete-time sequence r _-Ts＝{r_-Ts (k) } at an assumption p= -1, where T _s =t/l is the time resolution of the time offset synchronization unit, l is an oversampling factor relative to the symbol time T, and the received signal r is additionally sampled at a later time offset +t _s at an estimated time offset p ₀ corresponding to the discrete-time sequence r _+Ts＝{r_+Ts (k) };

-step 2: for each step k=0, 1,..each time offset at · assumes p= -1,0, +1, based on the respective sampled received signal r _pTs (k) assuming p= -1,0, +1, a branch metric μ _k (b, p) for each branch b is calculated;

-step 3: for each step k=0, 1,..each time offset at · is assumed to be p= -1,0, +1, based on the respective branch metric μ _k (b, p), recursively calculating path metrics m _k (S, p) and survival paths q _k (S, p) of the corresponding Veterbi algorithm for all state numbers S e {0,1,.. S-1 };

-step 4: calculate at each step k=0, 1 -A value for a path metric m _k (s, p);

-step 5: based on survival path For most likely received information symbolsA decision is made where D is the depth of survival.

Maximum Likelihood Sequence Estimation (MLSE) using the Veterbi Algorithm (VA) is known to be based on a mesh model. A grid is a graph whose nodes are ordered in vertical slices (time), each node at each time being connected to at least one node at an earlier time and at least one node at a later time. There is only one node at the earliest and latest times in the trellis diagram. Trellis diagrams are used in both communication theory and in encrypted encoders and decoders.

Typically, in the Veterbi Algorithm (VA) in the prior art, for each state number S e {0,1,..s-1 } of the trellis diagram of s= |x| ^L states, a path metric m _k (S) and a survival path q _k (S) are recursively calculated in a time step k=0, 1. The state s _k-1 at step k is an L-tuple where s _k-1 = (x (k-L),... An L-tuple is a finite ordered list (sequence) of elements. An L tuple is a sequence (or ordered list) of L elements, where L is a non-negative integer.

Thus, the path metric m _k (s, p) can be understood as a path metric assuming p. The survival path q _k (s, p) can be understood as a survival path assuming p, and in most practical cases the length of the survival path, i.e. the survival depth D, can be limited to a certain finite depth d≡5l, with a small performance penalty.

For the Viterbi algorithm, the state transitions s _k-1→s_k at step k of the received samples r { k }, the branch metric μ _k (b) for branch b= (s _k-1, x (k)) is represented by Given. For k=0, this means that the value of x (-1) must be known. For k= -1, s _-1 means the time index before the origin k=0. Since the syncword preceding the information part is known, it is usually fully padded.

The initial state is used to initialize the path metric m _-1(s) with respect to the update m _k-1→m_k at the first step k=0.

Fig. 1 shows state transitions of the binary symbol alphabet (|x|=2).

It is also well known that at step k.gtoreq.D, the maximum path metric (i.e.Corresponding to state/>Survival path q _k(s) of (a) to obtain information symbolWhere D is the depth of survival. For the Viterbi algorithm, each update extends the survival path for each state. For most practical cases, D.apprxeq.5L is sufficient (see J.G.Proakis.digital communications.McGraw-Hill, 1995).

In a variant of the method of the invention, the branch metric μ _k (b, p) consists of Calculation of/>, where P.epsilon.P specifies a hypothesis from the set P.

According to the method of the invention, the branch metrics are considered in a slightly generalized computational version, with the Viterbi algorithm being additionally considered at early (p= -1) and late (p= +1) time offsets with respect to the estimated time offset p0 (p=0). This means that in addition to sampling at the center (p=0), sampling is performed at an early time offset-T _s and a late time offset +t _s with respect to the estimated time offset p ₀ delivered by the synchronization unit. Thus, for each hypothesis P ε P= { -1,0, +1}, a special Viterbi algorithm VA (P) is applied and the path metric m _k (s, P) and the survival path q _k (s, P) are recursively updated accordingly. For termination information sequences with integrated checksums, it is assumed that an increase in the number can reduce the packet error rate. However, the application of independent checksums is not always applicable.

In another variant of the method of the invention, the path metric m _-1(s) (m _k in the case of k= -1) is initialized by using the initial state s _-1 of the known values x (-1),..x (-L) in the case of the first step size k=0 (s _k in the case of k= -1).

For recursively calculating the time step k=0, 1,..the path metric m _k (S) and the survival path q _k (S), for each state S e {0,1,..s-1 } of the trellis diagram with s= |x| ^L states, the value of X (-1) and X (-L), i.e., the initial state S _k-1, must be known for k=0. Typically, this is fully filled, since the sync word preceding the information part is known.

Thus, in another variant of the method of the invention, the initial state of the bluetooth system is obtained from the known access codes. In bluetooth systems, each baseband packet starts with an access code, which is one of three types: CAC (channel access code), DAC (device access code) and IAC (inquiry access code). In different modes of operation, the bluetooth device will use the corresponding access code type. CAC (channel access code) identifies the piconet. The DAC (device access code) is used for special signaling procedures and the IAC (inquiry access code) is used to discover other bluetooth units within range.

In another variant of the method of the invention, at each step k, the path metrics m _k (S, P) for all S e S and all P e P pass through a common termNormalization is performed, where α is a constant. Since each Viterbi algorithm computes a separate path metric m _k (s, p), at step k+.D, the path-to-live can be basedTo determine information symbol/>Wherein,

In a practical fixed point implementation, typically only a limited dynamic range is available for storing the value M _k (s, p) within the interval (-2 ^M+1,...,2^M -1) of a certain bit width m+1. Thus, it is common practice to avoid overflow to subtract the maximum value of the path metric from all path metrics, normalize the path metric at each step k and saturate values below-2 ^M +1. Thus, with equation 3, for all S ε S and all P ε P, a common term must be passedThe path metric m _k (s, p) is normalized, where α is a constant.

In an advantageous variant of the inventive method, DC estimation and DC compensation in the branch metrics are also applied.

Thus, in a variant of the inventive method taking into account DC estimation and DC compensation, the method is extended to:

-at a step k >0, the received value of the received signal r is to be determined Passing to a delay buffer of length D;

-at step k≡d, based on the output of the delay buffer and the information symbols Calculating a distance signal d (k), and d (k) is calculated by:

-further filtering the distance signal d (k) to reduce noise, resulting in a signal d _f (k);

-applying the filtered signal d _f (t) to the improved branch metric calculation according to:

assume reliable estimates at step k.gtoreq.D Is available. This means that for k=d, the value of x (-L) must be known.

According to equation (2), the distance value of the expected path metric m _k (s, p) can be calculated as:

In the absence of noise terms, D (k) =c (k-D) for k+.d. In the absence of noise and c (k) =0, The visual estimate is equal to the real sequence. Thus, the expression/> Equal to the received samples r (k). Thus, if c (k) varies only slowly over time, d (k) provides an estimate of the DC component. This is especially useful if the DC part needs to be tracked due to drift.

Since d (k) is subject to gaussian noise, it should be further filtered according to another variant of the method of the invention, wherein the filtered signal d _f (k) is filtered by d _f (k) =β·d (k) + (1- β) ·d (k-1), where β is the filter coefficient, where 0< β < 1. This is advantageous since for a certain positive integer value m, β is of the form 2 ^-m, only a simple drift operation is required.

In a further variant of the process according to the invention, the process consists ofThe defined reference value V _r is implemented based on a look-up table with entries of |x| ^L+1, where |x| is the number of elements of the symbol alphabet X, and the reference value V _r is used to calculate the distance signal d _k and the branch metric μ _k (b, p). The reference value V _r is used to simplify the convolution calculation. For bluetooth with |x|=2 and l=2, the number of entries of the lookup table is equal to 8.

Thus, advantageously, the method of the present invention can be applied to demodulation of binary Gaussian Frequency Shift Keying (GFSK) signals according to Bluetooth Core Specification, rev 5.2 (month 12 2019).

How the proposed inventive method improves the robustness of signal reception in terms of time and DC offset estimation error will be explained in more detail with exemplary embodiments.

The drawings show

FIG. 1 is an example trellis diagram of binary symbols;

FIG. 2 is a calculation scheme of the early-late Veterbi algorithm of the present invention;

Fig. 3 is a DC estimation and compensation implementation in a user equipment.

Fig. 2 shows a calculation scheme of the early-late Veterbi algorithm (EL-VA) of the present invention. In an embodiment of the present invention, the proposed early-late Viterbi algorithm (EL-VA) is applied to demodulate binary GFSK signals according to the Bluetooth standard (Bluetooth sig. Bluetooth core specification. Bluetooth Core Specification, rev 5.2, 12 months 2019). Here, the effect of inter-symbol interference (ISI) can be well approximated by a pulse of length 3, i.e. l=2, which results in s=2 ^L =4 states per Viterbi Algorithm (VA), see fig. 1. The method of the invention adopts 1.1-1.3 VA. One 1.1 is used to process the received signal r, which is sampled at an estimated time offset p ₀ provided by the synchronization unit at an assumption p=0 corresponding to the discrete time sequence r ₀＝{r₀ (k) }2.1, where k represents the discrete time step, k=0, 1. The second VA 1.2 is used to process the received signal r, at an early time offset-T _s, where T _s = T/l is the time resolution of the time offset synchronization unit, where l is the oversampling factor with respect to the symbol time T, assuming p= -1, with respect to the estimated time offset p ₀ corresponding to the discrete time sequence r _-Ts＝{r_-Ts (k) } 2.2. And the third VA 1.3 is used to process the received signal r which is additionally sampled at the late time offset +t _s with respect to the estimated time offset p ₀ corresponding to the discrete-time sequence r _+Ts＝{r_+Ts (k) }2.3 at p= +1. The total state number of EL-VA is 3×4=12, which is relatively low in complexity. The oversampling factor of the synchronization unit is l=6. The improvement in sensitivity measurement measured according to the specification of a noisy (dirty) transmitter is about 1dB compared to VA in the prior art, see (Bluetooth sig. Radio Frequency PHYSICAL LAYER (RF PHY)/Test kit. RF-PHY. Ts. P15, month 1 2020). Transmitters in modems for wireless data transmission according to the Bluetooth (BT) or Bluetooth low energy (Bluetooth Low Energy, BLE) standards (see "Bluetooth Core Specification, rev 5.2,Bluetooth Special Interest Group,2019-12-31") may appear "noisy", meaning that their carrier frequency may oscillate for the duration of the transmitted data packets. The above-mentioned standard defines a time-varying offset limitation of the nominal carrier frequency, and a worst-case transmitter model of sinusoidal frequency modulation with certain amplitude and period. The performance of the transmitter implementation may be as poor as defined or better. This provides space for low complexity/low cost transmitter implementations, thereby reducing throughput performance. Advanced transmitter implementations, however, may in this respect behave completely "clean", which means that their carrier frequency may be considered stable for the duration of the data packet, limited only by local oscillator phase noise, which may not impair transmission. The bluetooth test specification defines receiver performance tests using defined worst case "noisy" transmitters, see "Radio Frequency Bluetooth Test Suite,Rev.RF.TS.p30edition 2,Bluetooth Special Interest Group,2020-01-27".

Fig. 3 illustrates implementing DC estimation and compensation in a User Equipment (UE). In an embodiment of the invention, the proposed method, in particular DC compensation, is applied to demodulation of binary GFSK signals according to the Bluetooth standard (Bluetooth sig. Bluetooth Core Specification, rev 5.2, month 12 2019). At step k not less than 0, input sample2 Is passed to a delay buffer 13 of depth D, which is indexed/>And (5) selecting. The delay buffer 13 has a length D, where D is the depth of survival. Based on the output of delay buffer 13 and the information symbols at step k.gtoreq.DThe distance d (k) 16 is calculated, and d (k) 16 is calculated from:

The distance signal d (k) 16 is further filtered by a filter 15 to reduce noise, resulting in a signal d _f (k) 17. The filtered signal d _f (t) 17 is applied to the improved branch metric calculation 4 to the EL-VA calculation unit 1 according to:

The impulse response h is constant and known, and is input to the EL-VA calculation unit 1 and the distance calculation unit 14. The improvement in sensitivity measurement is about 0.5dB compared to EL-VA without DC compensation, depending on the specification of the noisy emitter, see (Bluetooth sig. Radio Frequency PHYSICAL LAYER (RF PHY)/Test wait. RF-PHY. Ts. P15, month 1 2020).

From the following componentsThe defined reference value v _r is implemented based on a look-up table. For demodulating binary (|x|=2 and l=2) GFSK signals according to the bluetooth standard, the look-up table has 2 ^L+1 =8 entries, which are used to calculate the distance signal d _k and the branch metric μ _k (b, p). An advantage of using a look-up table for the reference value v _r is that the calculation of the convolution used in equation 4 is simplified.

The main idea of the invention is to improve the robustness with respect to time and DC offset estimation errors when applying the Viterbi algorithm for MLSE, assuming a constant and known impulse response h. The Viterbi algorithm itself is not intended to make synchronization good enough, but rather to address the problem of reducing residual synchronization errors. This is advantageous if the synchronization cannot be improved or the improvement of the synchronization is much more complicated.

List of reference numerals

1.1 First Viterbi algorithm

1.2 Second or early Viterbi algorithm

1.3 Third or late Viterbi algorithm

2.1 Received signal sampled at assumed p=0 (center)

2.2 Received signal sampled at early time offset

2.3 Received signal sampled at late time offset

3. Impulse response

4.1 Branch metrics at the center hypothesis p=0

4.2 Branch metrics at early time offsets

4.3 Branch metrics at late time offsets

5. Corresponding survival path of all states

6. Corresponding path metrics for all states

Calculation of 7 arg-max m _k (s, p)

8. Multiplexer for multiplexing

9. Detected information symbols

10. Optimal Viterbi hypothesis

11. Best state

12. Optimal (maximum) path metric

13. Delay buffer

14. Distance calculation unit

15. Filter device

16. Distance signal

17. Filtering distance signals

Claims (10)

1. A method of robust equalization of a received signal with known intersymbol interference, wherein an early-late Viterbi algorithm (1.1-1.3) is applied, the method comprising the steps of:

-step 1: sampling (2.1) the received signal r by the synchronization unit at an estimated time offset p ₀ provided at an assumption p=0 corresponding to the discrete-time sequence r ₀＝{r₀ (k) }, where k represents a discrete-time step, k=0, 1, while the received signal r is additionally sampled at an early time offset-T _s at an estimated time offset p ₀ corresponding to the discrete-time sequence r _-Ts＝{r_-Ts (k) } at an assumption p= -1, where T _s =t/l is the time resolution of the time offset synchronization unit, l is the oversampling factor relative to the symbol time T, and the received signal r is additionally sampled at a later time offset +t _s at an estimated time offset p ₀ corresponding to the discrete-time sequence r _+Ts＝{r_+Ts (k) };

-step 2: for each step k=0, 1,..each time offset at · assumes p= -1,0, +1, and based on the respective sampled received signal r _pTs (k) assuming p= -1,0, +1, a branch metric μ _k (b, p) for each branch b is calculated (4.1-4.3);

-step 3: for each step k=0, 1,..each time offset at · is assumed to be p= -1,0, +1, based on the respective branch metric μ _k (b, p), recursively calculating path metrics m _k (S, p) and survival paths q _k (S, p) of the corresponding Veterbi algorithm for all state numbers S e {0,1,.. S-1 };

-step 4: calculate at each step k=0, 1 -A value (7) for a path metric m _k (s, p) (6);

-step 5: based on survival path (5) For most likely received information symbolsA decision is made where D is the depth of survival.

2. The method of claim 1, wherein the branch metric μ _k (b, p) (4.1-4.3) is defined byTo calculate, among others

3. The method according to one of the preceding claims, wherein the path metric m _-1(s) is initialized by using the initial state s _-1 with a known value x (-1) at a first step size k = 0.

4. A method as claimed in claim 3, wherein the initial state of the bluetooth system is obtained from a known access code.

5. The method of claim 1, wherein at each step k, path metrics m _k (S, P) (6) for all S e S and all P e P pass through a common termNormalization, where α is a constant.

6. The method of claim 1, wherein DC estimation and DC compensation are applied in the branch metrics.

7. The method of claim 1 or 6, wherein

-At a step k >0, the received value of the received signal r is to be determinedTo a delay buffer (13) of length D;

-at step k≡d, based on the output of the delay buffer and the information symbols (9) Calculating a distance signal d (k) (16), and d (k) (16) is calculated from:

-further filtering and noise reducing the distance signal d (k) (16) to obtain a signal d _f (k) (17);

-applying the filtered signal d _f (t) (17) to the improved branch metric calculation according to:

8. The method of claim 7, wherein the filtered signal df (k) (17) is filtered by d _f (k) = β -d (k) + (1- β) ·d (k-1), where β is a filter coefficient, 0< β 1.

9. The method according to one of the preceding claims, wherein the method is carried out by The defined reference value V _r is implemented based on a look-up table with entries of |x| ^(L+1), where |x| is the number of elements of the symbol alphabet X, and the reference value V _r is used to calculate the distance signal d _k and the branch metric μ _k (b, p).

10. The method according to one of the preceding claims, applied for demodulation of binary gaussian frequency shift keying signals according to Bluetooth Core SPEC I F I CATI on, rev 5.2 at month 12 of 2019.