CN101179291B - Condition maximum likelihood estimation based ultra-wideband communication system synchronization method - Google Patents
Condition maximum likelihood estimation based ultra-wideband communication system synchronization method Download PDFInfo
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Abstract
The invention belongs to the field of wireless communications technology and specifically relates to a synchronous method of an ultra wideband (UWB) communications system based on a maximal likelihood estimation of condition. Circulation stability existing in a UWB symbol structure is used for restraining frame level noise for received waveform and constructing a noise template required synchronously; then the invented noise template is used for estimating and obtaining a parameter of A<SUB>Xi</SUB> which represents the energy in a frame, and the parameter is user for estimating and represents a timing deviation of n<SUB>f</SUB> of the frame level; lastly, provided sliding correlative search is used for obtaining the timing deviation inside the frame of Xi. The preceding two items provided by the invention can effectively restrain the effect on noise component during parameter estimating, improve the synchronous deviation performance in mean square under the condition of a low signal-to-noise ratio and decrease the lower limit of the synchronous deviation performance in the mean square under the condition of a high signal-to-noise ratio.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a synchronization method applied to a pulse system ultra wide band (IR-UWB) communication system.
Background
Ultra-wideband (UWB) technology has become one of the wireless communication technologies of great interest in recent years in the academic and industrial fields. In the IR-uwb (impulse Radio uwb) scheme, a subnanosecond or picosecond pulse sequence is used to directly perform baseband transmission, so that performance degradation caused by Carrier Frequency Offset (CFO) is avoided, and system complexity is greatly reduced because carrier processing is not required. In addition, good multipath discernability attenuates energy loss caused by indoor multipath fading, making it possible for UWB signals to propagate at low transmit power and share the spectrum with other communication means. More particularly, through calculation of a shannon formula, the ultra-narrow pulse serving as a normal ultra-wideband signal promises extremely high channel capacity, and a new way is provided for short-distance high-speed wireless communication. However, the design of UWB communication systems is very challenging, due to the use of extremely narrow pulses for transmission. Among them, the design of the timing synchronization link is particularly important. Studies have shown that even very small timing errors can cause large bit error rate performance degradation. Conventional UWB synchronization locally generates a template from parameters obtained from channel estimation and obtains symbol synchronization by sliding correlation of a signal with the template. The evaluation of the algorithm from the aspect of hardware realization can find that the DSP finishes accurate channel estimation, and the system introduces an ADC with a sampling rate of up to several GHz, so that the ADC samples pulses with a pulse width of less than 1 nanosecond at a high speed; meanwhile, a large amount of sliding correlation is a little test for the computing power of the DSP. Researchers [1] proposed a Data-aided (DA) algorithm based on Conditional maximum likelihood estimation (CML). The significant advantage of this algorithm is that the sliding correlation is only done at the symbol level to obtain timing synchronization at the frame level. NT (Noise Template, NT) is formed by means of the received signal, and estimation of CML is performed based on a criterion of a General Likelihood Ratio Test (GLRT), thereby obtaining a timing offset amount at a frame level. However, the original algorithm has two problems. Firstly, under the condition of low signal-to-noise ratio, the mean square estimation performance is not ideal because the noise suppression is not very effective; secondly, under the condition of high signal-to-noise ratio, because the algorithm does not introduce a fine synchronization link, the mean square error cannot be further reduced along with the improvement of the signal-to-noise ratio, and a lower limit (low bound) exists theoretically.
The original CML estimation synchronization method has the following defects:
1. the period of waveform averaging operation of the original CML estimation algorithm is a symbol period, and a limited training sequence is not fully utilized, so that the formation of NT is influenced, and the influence of noise is large.
2. An estimate of the energy of a frame is derived from the correlation of NT with the received signal, and the received signal is then not noise suppressed, thereby affecting the estimate of the amount of frame-level timing offset.
3. The original CML estimation algorithm only comprises a coarse synchronization link and does not consider a fine synchronization problem.
Disclosure of Invention
The invention aims to provide a novel CML estimation-based ultra-wideband system synchronization method, so as to more effectively inhibit noise influence, provide a first-level fine synchronization link and further reduce timing errors.
The invention provides an ultra-wideband system synchronization method based on CML estimation, belonging to a Data-aided mode (Data-aided). Therefore, first, a set of training sequences is constructed, which consists of a Preamble sequence and a postamble sequence (as shown in fig. 3 (b)), wherein the Preamble sequence (Preamble) M1+M2(M1＝M2) For the generation of Noise Template (Noise Template, NT), Post-synchronization sequence (Post-amble) M3For estimating the amount of frame-level timing deviation nf。
The synchronization process comprises the following steps:
(1) using preamble M in preamble sequence1Noise template NT constructed by symbol sequence1The influence of noise generation is suppressed by a waveform averaging operation at the frame level. Noise template NT1The structure formula is as follows:
wherein <math><mrow>
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</mrow></math> NfNumber of frames in a single symbol, TfFor the interval of the frame, the number of frames,r (t) is the received waveform loaded with the timing offset, t is the time variable.
Then will be
By TfExtended to length T for cycle continuationsNT of (2)1. New structured NT1The following formula:
wherein T iss＝Nf×TfAnd represents a single symbol interval.
(2) Reusing last M in a preamble sequence2(usually M)1＝M2) Noise template NT constructed by symbol sequence2The influence of noise generation is suppressed by a waveform averaging operation at the frame level. Template NT2The structure formula is as follows:
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Then p is addedrf2(T) by TfExtended to length T for cycle continuationsNT of (2)2. Novel NT structure2The following formula:
(3) for the generated NT1And NT2Averaging is performed to obtain the noise module NT, as shown in the following formula:
(4) for the generated NT1And NT2Performing noise template cross-correlation estimation to obtain a parameter A representing the energy of a frameξAs shown in the following formula:
(5) according to the CML algorithm, using the estimated AξThe constructed NT, Post-amble M3 and other known parameters calculate the frame-level timing offset nfAs shown in the following formula:
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(6) At the time of obtaining frame-level timing deviation
On the basis of the above-mentioned method, a region sliding correlation search (a Regional sliding correlation search) is addedSearch, RSCS) estimates ξ by capturing the τ value for the correlation peak, i.e.:
wherein τ is inFront and rear span of 2TfStep search in the region, step size Δ τ (Δ τ e (0, T)f]) Adjusting according to the requirement of precision; for the noise template NT, a step cyclic shift is adopted to match the sliding of the correlation window in r (t) to realize a sliding correlation operation.
(7) Finally, the total delay estimation is obtained <math><mrow>
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In the present invention, the preamble sequence may consist of a set of all "+ 1" sequences: "+ 1, +1, …", the postamble sequence is made up of a set of "+ 1 and-1" alternating sequences: "+ 1, -1, +1, -1 …".
Advantageous effects
The novel ultra-wideband system synchronization method based on CML estimation adopted by the synchronization method provided by the invention fully utilizes the limited training sequence to estimate the energy, and adopts a frame-level noise suppression means to improve the parameter estimation precision under the condition of low signal-to-noise ratio to a great extent, thereby effectively improving the mean square error performance; in addition, the lower limit of the mean square error performance is greatly reduced by adding primary fine synchronization.
Drawings
FIG. 1: signal to noise ratio Eb/N0Time domain signal waveform comparison of 6 dB. (a) Averaging the waveform with 800 symbols; (b) averaging the waveform with 100 symbols; (c) noiselessAnd (4) sound suppression.
FIG. 2: signal to noise ratio Eb/N0Time domain signal waveform comparison of 6dB, M1＝50，N f20. (a) Passing through the signal waveform without noise; (b) a signal waveform after frame-level averaging; (c) signal waveforms after symbol-level averaging; (d) and no noise suppression is performed.
FIG. 3: and comparing the training sequence configuration schemes. (a) Configuring an original training sequence scheme; (b) and (3) a training sequence configuration scheme of noise template cross-correlation estimation.
FIG. 4: the performance comparison of the normalized mean square error accumulated for three different techniques and the original algorithm is given under the CM1 channel of IEEE802.15.3a.
Detailed Description
In the PAM-TH IR-UWB system, each information bit is transmitted by a symbol (symbol), each symbol comprising NfFrames (frames) in which each frame contains one pulse and the frame interval is TfPulse width Tp＜＜Tf. The symbol interval is therefore Ts：＝NfTf. When a Time-hopping code (TH code) is introduced, each frame is further divided into NcChip by chip interval Tc. TH code is denoted cj∈[0，Nc-1]，
j∈[1，Nf]So that the single symbol waveform is
Wherein p (T) is a pulse width TpThe extremely narrow pulse shape of (a).
The invention is mainly directed to binary PAM modulation, with symbols denoted as s [ n ]]Belongs to +/-1, and occurs in an independent equal probability with energy of epsilons. The UWB transmit waveform is therefore:
the signal u (t) passes through the multi-path fading channel of L paths, and the attenuation and delay of each path are respectively shownShown as { alphalAnd { tau } andlin which τ is0＜τ1＜…＜τL-1. The most interesting parameter for timing synchronization is the arrival time tau of the first path0. Thus the expression for a channel can be written as:
wherein tau isl，0：＝τl-τ0Defined as the relative delay of each multipath.
Thus, the waveform of the signal u (t) after passing through the channel is:
thus, the complete receiving end signal waveform is:
wherein w (t) is subject to a mean of 0 and a variance of σ2Additive White Gaussian Noise (AWGN).
Without loss of generality assumeτ0∈[0，Ts) Thus, τ can be defined0：＝nfTf+ xi, where nf：＝
τ0/Tf 
And the margin xi is epsilon [0, Tf)。
Then, the waveform of the receiving end loaded with the delay information is:
the CML algorithm [1] essentially finds the start position of a frame by collecting the energy of a Training Sequence (TS) from which a timing error is calculated. Energy harvesting will directly affect the accuracy of the estimation. By correlating the received signal with a template to obtain the energy of the symbol, i.e.
From the definition of energy, the ideal template is a waveform that exactly matches r (t). The traditional synchronization generates a correlation template through channel estimation, but the channel estimation cost is extremely high under the condition of dense multipath, so NT is proposed to replace the channel estimation to complete the construction of the template. Specifically, a set of full "+ 1" sequences is sent in the first part of the training sequence, since there is no symbol modulation problem with full "+ 1" sequences <math><mrow>
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</mrow></math> Thereby to pair of continuous M1Each length is TsThe training sequence of (a) is averaged to obtain an approximate ideal template, as shown in the following formula
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is called Noise Template (Noise Template) because
Each branch, delay tau, containing multipath0And a noise component.
After averaging, the variance of the noise component is reduced to σ2/M1Following M1Increase in NT, the NT approaches the ideal template.
However, observing the waveform when the signal-to-noise ratio is relatively low (as in FIG. 1(a)) reveals that even M is present1100, noise cannot be effectively suppressed; an attempt to average over 800 symbols (see fig. 1(b)) partially suppresses the noise. In actual communication, the cost of completing synchronization once by 800 symbols is quite large, and the baud rate is limited to a great extent. Considering that the averaging operation is based on the periodicity of the received signal, shortening the period of the averaging operation will greatly increase the number of averaging operations, making the template less affected by noise. To this end, the invention proposes a Frame-level Noise suppression (Frame-level Noise)Supression, FNS) concept. Frame-level noise suppression is to reduce the period of the averaging operation to the frame level, where the training sequence bits cannot be introduced into the TH code. Three functions of analyzing the TH code in UWB communication are as follows: 1) providing multiple-access (MA) for information bits; 2) whitening the spectrum to reduce interference with other communication means; 3) low Probability of Interception (LPI) of the data is supported. Since the training sequence is only a small part of the whole bit stream, this scheme will not affect the three points.
The NT constructed by the frame-level noise suppression method is shown as follows:
wherein
Then will be
By TfFor periodic continuation, the length is extended to TsThe NT of (1) can collect energy. The new structure of NT is as follows
If M is adopted1Averaging over symbols, each symbol comprising NfFrame, then symbol level average mode, noise variance is sigma2/M1(ii) a While the frame-level averaging can reduce the noise variance to sigma2/(M1Nf) From FIG. 2, it can be seen that in an environment of lower signal-to-noise ratio, the frame levelThe noise suppression capability of the averaging operation is much stronger than that of the symbol-level averaging operation.
After NT construction is complete, parameter estimation using the preamble sequence and NT can begin. Except for the previously mentioned M1Besides the full "+ 1" sequence used to construct NT, a set of post-synchronization sequences consisting of two mutually exclusive subsets is additionally configured for the requirement of parameter estimation: s+：＝{s[n]＝s[n-1]And S-：＝{s[n]＝-s[n-1]In which M is2And M3Are respectively a set S+And S-The potential of (c).
The explicit expression of y [ n ] is derived from [1] appendix A as:
y[n]＝Aξ(s[n](Nf-nf-λξ)+s[n-1](nf+λξ))+w[n] (11)
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</mrow></math> Representing the energy of a frame. (11) Indicating that y n is due to the presence of a delay]The collected energy is the energy of two consecutive symbols, and the CML algorithm estimates the delay by using the energy of the two consecutive symbols.
[5]Parameter A is derived by a CML methodξEstimated analytic expressionsThe formula is as follows:
observing the above formula, for AξEssentially by using the set S+The full "+ 1" sequence estimate within results in the energy of one frame. Estimate AξWhether it is accurate or not directly affects nfThe accuracy of the estimation of. Therefore, the invention provides a mode of noise template Cross-correlation Estimation (NTCE) to estimate AξFurther, the influence of noise is suppressed.
Noise template cross-correlation estimation method As shown in FIG. 3(b), two noise uncorrelated templates NT are generated using a preamble sequence1And NT2And estimating A using the cross-correlation of NTξI.e. by
It can be seen that after changing the design of the estimator, both components of the correlation operation are processed for frame-level noise suppression, whereas the original CML algorithm aξEstimate, see formula (12), where y [ n ]]Only a small number of symbol-level noise suppression processes are performed, thus AξThe estimation performance of (a) is significantly inferior to the noise template cross-correlation estimation.
AξSubstituting into n after estimation is completedfThe estimated expression is used to obtain a delay estimate for the coarse synchronization, i.e.
When the signal-to-noise ratio of the original CML algorithm is higher than a certain level, the mean square error has a performance lower limit, and the reason for the performance lower limit is that the finally obtained delay estimation is adopted <math><mrow>
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Front and back 2TfStep search in the range, which step is adopted to search the area can be adjusted according to the requirement of precision; for NT, a step cyclic shift is used to match the sliding of the correlation window over r (t) to achieve a sliding correlation operation.
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After the synchronization is completed, by
The starting position of the symbol can be determined and, at the same time, willThe frame-level noise template is loaded to carry out time domain correction inside the frame, and a demodulation template with TH codes can be constructed by introducing time-hopping continuation. Considering the Inter-frame Interference (IFI) introduced by TH code, the construction of each frame template needs to be accumulated beforeThe effect of one frame or even the first two (depending on the channel length, here it is assumed that <math><mrow>
<msub>
<mi>τ</mi>
<mi>L</mi>
</msub>
<mo>+</mo>
<msub>
<mi>T</mi>
<mi>c</mi>
</msub>
<msub>
<mi>max</mi>
<mrow>
<mi>k</mi>
<mo>∈</mo>
<mrow>
<mo>[</mo>
<mn>1</mn>
<mo>,</mo>
<msub>
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</msub>
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</mrow>
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<mrow>
<mo>(</mo>
<msub>
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</msub>
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</mrow>
<mo>≤</mo>
<mn>2</mn>
<mrow>
<msub>
<mi>T</mi>
<mi>f</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow></math> The method of constructing the demodulated NT is then as follows.
First of all introduceTo pair
Carry out cyclic shift, then
Then to
The time-hopping process is carried out, because the influence of the current frame and the previous frame needs to be considered, so the time-hopping process is carried out
Finally, performing time domain expansion to obtain
MATLAB simulation was performed for the BPSK-UWB system. CM in improved S-V model1Channel (LOS 0-4m), channelThe parameter is (1/Λ, 1/λ, Γ, γ) ═ 43, 0.4, 7.1, 4.3) ns. The pulse waveform used is a second-order Gaussian pulse with unit energy and the pulse width is 1 ns. The basic parameters are as follows: n is a radical off＝20，Tf50 ns. Configuring training sequence M1＝M2＝M 320. When SCS algorithm is added, let step length delta be Tf/20. The three improvements herein were individually loaded onto the CML algorithm for optimization, using Normalized mean square error (Normalized MSE, <math><mrow>
<mi>NMSE</mi>
<mo>=</mo>
<mi>E</mi>
<mo>{</mo>
<msup>
<mrow>
<mo>|</mo>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>τ</mi>
<mo>^</mo>
</mover>
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</msub>
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<msub>
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</mrow>
<mo>/</mo>
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</msub>
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</mrow>
<mn>2</mn>
</msup>
<mo>}</mo>
<mo>)</mo>
</mrow></math> the synchronization performance is analyzed, and the simulation result is shown in fig. 4.
Simulation results show that FNS and NTCE indeed improve the synchronization accuracy under the condition of low signal-to-noise ratio to a certain extent, however, under the condition of high signal-to-noise ratio, the algorithm aims at coarse synchronization, the accuracy is about one frame range, and therefore the FNS and NTCE have no capability of breaking through the lower limit existing in theory; when a first-level SCS fine synchronization estimation is added, the lower limit of the mean square performance is broken by about one order of magnitude. However, it can be seen from fig. 4 that SCS cannot optimize the mean square performance in low signal-to-noise ratio cases, because the overall delay estimate <math><mrow>
<msub>
<mover>
<mi>τ</mi>
<mo>^</mo>
</mover>
<mn>0</mn>
</msub>
<mo>=</mo>
<msub>
<mi>T</mi>
<mi>f</mi>
</msub>
<msub>
<mover>
<mi>n</mi>
<mo>^</mo>
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</msub>
<mo>+</mo>
<mover>
<mi>ξ</mi>
<mo>^</mo>
</mover>
<mo>,</mo>
</mrow></math> Wherein
Takes a great proportion once
A large deviation is present which is such that,
does not contribute much to the estimation of the total delay, so the SCS is enabled on the premise that the correct delay estimation is obtained at the frame level.
The above description is a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily made by those skilled in the art within the technical scope of the present invention will be covered by the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Reference to the literature
[1]Zhi Tian and G B.Giannakis，“A GLRT Approach to Data-Aided Timing Acquisitionin UWB Radios-Part I：Algorithms”，IEEE Transactions on wireless communications，Vol.4，No.6，pp.2956-2967，Nov.2005
Claims (3)
1. A synchronization method of an ultra-wideband communication system based on conditional maximum likelihood estimation is characterized in that: firstly, a group of training sequences is constructed, wherein the training sequences are composed of a front synchronization sequence and a rear synchronization sequence, and the front synchronization sequence M1+M2For the generation of noise templates NT, post-synchronisation sequences, M3For estimating the amount of frame-level timing deviation nf；
The specific steps of the synchronization process are as follows:
(1) using preamble M in preamble sequence1Noise template constructed by symbol sequenceNT1Suppressing the influence of noise generation by a frame-level waveform averaging operation, noise template NT1The structure formula is as follows:
wherein
NfNumber of frames in a single symbol, TfIs the frame interval, r (t) is the received waveform loaded with the timing deviation, t is the time variable;
then will be
By TfExtended to length T for cycle continuationsNT of (2)1NT of novel construction1The following formula:
wherein T iss＝Nf×TfRepresenting a single symbol interval;
(2) reusing last M in a preamble sequence2Noise template NT constructed by symbol sequence2Suppressing the influence of noise generation by a frame-level waveform averaging operation, template NT2The structure formula is as follows:
wherein
Then will be
By TfExtended to length T for cycle continuationsNT of (2)2NT of structure2The following formula:
(3) for the generated NT1And NT2Averaging is performed to obtain the noise template NT, as shown in the following formula:
(4) for the generated NT1And NT2Performing noise template cross-correlation estimation to obtain parameter estimation representing one frame energyAs shown in the following formula:
(5) according to the CML algorithm, utilizing the estimation in (4)
(3) The noise template NT, the post-synchronization sequence M3 and other known parameters constructed in (1) calculate an estimate of the amount of frame-level timing deviation
As shown in the following formula:
wherein
s[n]E { +/-1 } is a transmission information symbol; s-is a subset of the transmitted information symbols and satisfies the condition S-that the symbols of adjacent information symbols are opposite: is { s [ n ]]＝-s[n-1]}；
(6) Obtaining an estimate of the amount of timing deviation at the frame level
On the basis of (1), define
And adding a region sliding correlation search, estimating xi by capturing xi values corresponding to correlation peaks, namely:
wherein xi is
Front and rear span of 2TfStep search in the region, step size delta tau, delta tau epsilon (0, T)f]Adjusting according to the requirement of precision; for the noise template NT, a step cyclic shift is adopted to match the sliding of the correlation window on r (t) to realize a sliding correlation operation;
(7) finally, the total delay estimation is obtained
2. The ultra-wideband communication system synchronization method based on conditional maximum likelihood estimation as claimed in claim 1, wherein in step (1), the preamble sequence is composed of a set of all "+ 1" sequences, and the modulation scheme is BPSK.
3. The ultra-wideband communication system synchronization method based on conditional maximum likelihood estimation as claimed in claim 1, wherein in step (6), the post-synchronization sequence is composed of a set of sequences alternately arranged as +1 and-1: "+ 1, -1, +1, -1 …".
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