The invention relates to receivers for multiuser communication such as UWB multiuser communication.
In many multiuser communication system studies, the multiuser interference (MUI), also called multiple-access interference (MAI), has conventionally been modeled as a Gaussian process which is justified by a central limit theorem (CLT). However, there are certain cases where the MUI cannot be approximated by a Gaussian distribution. Multiuser interference in pulse based UWB (ultra wideband) communication is one such scenario where the CLT is known to have very slow convergence even in an environment with equal power independent interferers. Several non-Gaussian models have been proposed for the MUI in the context of performance analysis and receiver design. A few models have also been proposed for the accurate statistical characterization of the MUI as a function of simple random variables (commonly functions of uniform and binomial random variables) in the additive white Gaussian noise (AWGN) channel. In general, these models may not be suitable for economical receiver design due to their complexity, although they are tractable for exact or close-to-exact bit error rate (BER) analysis.
A Laplacian model(LM), generalized Gaussian (GGM) model, Gaussian mixture model (GMM) and a hidden Markov model (HMM) have been used for approximating the distribution of the MAI. These distributions are generally heavy tailed and have a positive excess kurtosis, which is desirable because it is known that the MUI in UWB systems is impulsive. All the models mentioned are known to fit the distribution of the MAI better than the Gaussian approximation (GA).
According to one broad aspect, the invention provides a method comprising: receiving a signal, the signal comprising a plurality of representations of an information bit, multiple-access interference from other signals, and noise; processing the received signal using a receiver that is configured to generate decision statistics based on a symmetric alpha-stable distribution assumption for the multiple-access interference and noise, to generate at least one decision statistic.
In some embodiments, the method further comprises generating a decision of a value for the information bit based on the at least one decision statistic.
In some embodiments, the signal comprises a UWB signal carrying said information bit.
In some embodiments, processing the received signal comprises: generating a plurality of samples for the information bit, each sample corresponding to a respective time-hopped representation of the bit in the desired signal; processing the plurality of samples using a first myriad filter detector to produce a first decision statistic; processing the plurality of samples using a second myriad filter detector to produce a second decision statistic; combining the first decision statistic and the second decision statistic to produce the overall decision statistic.
In some embodiments, each sample is a correlator output sample.
In some embodiments, processing the plurality of samples using a first myriad filter detector to produce a first decision statistic comprises determining:
processing the plurality of samples using a second myriad filter detector to produce a second decision statistic comprises determining:
where γi,b are the plurality of samples, K is a tuning parameter, and s represents a magnitude of a signal component.
In some embodiments, receiving a signal comprises receiving a signal comprising a plurality of information bits inclusive of said information bit; wherein the step of processing the received signal is performed for each information bit.
In some embodiments, the method further comprises adapting a value for K.
In some embodiments, adapting a value for K comprises: determining a plurality of samples of an empirical characteristic function of the multiple access interference; determining K from the plurality of samples of the empirical characteristic function.
In some embodiments, the method further comprises: approximating the characteristic function as Φ1(ω)≅exp(−ζ|ω|α), where α and ζ are parameters to be estimated; estimating α and ζ from the plurality of samples of the empirical characteristic function; using an empirical relationship for K to determine K from α and ζ.
In some embodiments, using an empirical relationship for K to determine K from α and ζ comprises using:
to determine K from α and ζ, where C is a constant and σ2 is variance of a noise component ni.
According to another broad aspect, the invention provides an apparatus comprising: at least one antenna for receiving a signal, the signal comprising an information bit, multiple-access interference from other signals, and noise; a receiver that is configured to generate decision statistics based on a symmetric alpha-stable distribution assumption for the multiple-access interference and noise, to generate at least one decision statistic.
In some embodiments, the receiver is further configured to make a decision based on the at least one decision statistic.
In some embodiments, the receiver comprises: a sample generator that generates a set of samples for the information bit; a decision statistic generator configured to perform processing of the samples based on a symmetric alpha-stable distribution assumption for the multiple-access interference and noise to produce at least one decision statistic; and a decision generator that produces a decision of a value for the information bit based on the at least one decision statistic.
In some embodiments, the signal comprises a UWB signal carrying said information bit.
In some embodiments, the sample generator generates a respective sample for each of a plurality of time-hopped representations of the information bit in the signal; the decision statistic generator comprises: a) a first myriad filter detector configured to process the plurality samples to produce a first decision statistic; b) a second myriad filter detector configured to process the plurality of samples to produce a second decision statistic.
In some embodiments, the apparatus further comprises: a combiner that generates an overall decision statistic from the first decision statistic and the second decision statistic, the decision generator configured to make a decision based on the overall decision statistic.
In some embodiments, the first myriad filter detector produces the first decision statistic according to:
the second myriad filter detector produces the second decision statistic according to:
where γi,b are the plurality of samples, K is a tuning parameter, and s represents a magnitude of a signal component.
In some embodiments, the apparatus further comprises: a parameter estimator that estimates a value of K.
In some embodiments, the parameter estimator is configured to estimate the value of K by: determining a plurality of samples of an empirical characteristic function of the multiple access interference; determining K from the plurality of samples of the empirical characteristic function.
In some embodiments, the parameter estimator is further configured to estimate the value of K by: approximating the characteristic function as Φ1(ω)≅exp(−ζ|ω|α), where α and ζ are the parameters to be estimated; estimating α and ζ from the plurality of samples of the empirical characeristic function; using an empirical relationship for K to determine K from α and ζ.
In some embodiments, the parameter estimater uses the following empirical relationship for K
to determine K from α and ζ, where C is a constant and σ2 is the variance of a noise component ni.
Embodiments of the invention will be described with reference to the attached drawings in which:
A receiver based on a symmetric alpha-stable model for the MUI is provided. Referring now to
In some embodiments, the at least one decision statistic is an overall statistic that is a combination of a respective decision statistic for each of two possible decisions. This can involve for example, generating a plurality of samples for the information bit, each sample corresponding to a respective time-hopped representation of the bit in the desired signal; processing the plurality of samples using a first myriad filter detector to produce a first decision statistic; processing the plurality of samples using a second myriad filter detector to produce a second decision statistic; combining the first decision statistic with the second decision to produce an overall decision statistic upon which the decision is based for example by comparing the overall decision statistic to a threshold. In another embodiment, the at least one decision statistic includes the first decision statistic and the second decision statistic, and the decision is made on the basis of the two decision statistics without first generating an overall decision statistic for example by performing a comparison operation between the two decision statistics as detailed below.
In some embodiments, each “sample” is a correlator output of a correlation operation between a portion of a received signal containing a representation of the bit with a template signal.
In some embodiments, the approximated parameter(s) is updated/adapted for each information bit. This can, for example involve adapting a value for K for each information bit as detailed below. Alternatively, the approximated parameter(s) can be adapted on some other basis, for example periodically, for example after each set of Nadapt bits, where Nadapt is the adaptation period, in bits, or on some other basis.
An apparatus configured to implement the above-described method is shown in
The transmitted signal of the kth user in a TH-UWB (time-hopped UWB) system with pulse amplitude modulation (PAM) can be written as
where p(t) is the transmitted UWB pulse with unit energy, Es is the energy of a symbol, and Tf is the length of a frame. One symbol consists of Ns pulses and hence a symbol duration is equal to NsTf. The bth transmitted data symbol is denoted by db where db can be −1 or +1 and └x┘denotes the largest integer not greater than x. The time-hopped sequence is denoted by cikε{0,1, . . . Nh}, where the integer Nh satisfies the condition NhTc≦Tf, and Tc is the TH step size. Assuming that the system contains Nu active asynchronous users the received signal can be written as
where hk and τk are respectively the channel gain and the asynchronous delay of the kth user, and n(t) is additive white Gaussian noise (AWGN) from the channel. Assuming h0=1 the sample generated by a correlation receiver can be written as
and it is assumed that the bth bit of the 0th user is being detected. The signal component S in (2) is given by √{square root over (EsNs)} and n denotes the filtered Gaussian noise. The MAI component I can be written as
Similarly, one can express the partial correlation from a single frame, γi,b, as γi,b=dbsi+Ii+ni where si=s=√{square root over (Es/Ns)}, and where Ii is given by
and
where N0/2 is the two-sided power spectral density of the AWGN.
A new UWB receiver is provided which is based on the assumption that the MAI has a symmetric alpha-stable distribution.
In order to construct a symmetric alpha-stable model for the UWB MUI, it will be useful to first consider an adaptation of an empirical probability density function (PDF) of the MUI as determined by simulation. The rationale for this adaptation is the following. Any estimate of the actual PDF of the MAI by simulation is an estimate of a locally averaged version of the actual PDF. Let fIa (I) denote the actual PDF of the MAI, I, and fIs (I) denote a PDF estimate by simulation, we can write E{fIs(x)}=PIa(x−δ<I<x+δ)/2δ, where 2δ denotes the length of a small segment in the x axis. In
It is noted that a PDF with singularities is difficult to capture with a simple mathematical model. However, the area under singularities are small, hence considering a smoothed PDF will not be much different from considering the PDF with singularities for detection purposes. Locally averaging also occurs in the receiver due to filtering, sampling and quantizing.
A symmetric alpha-stable RV, Z, has the following characteristic function
ΦZ(ω)=exp(−ζ|ω|a+jωβ)0≦α≦2 (6)
where α is the characteristic exponent which determines the heaviness of the tail of the PDF of Z, ζ is the shaping parameter, and β is the location parameter of the distribution. The location parameter is the mean of the random variable, or the point where the PDF is symmetric on both sides. In this case it is the signal that is to be detected and as such, the location parameter is the same as the signal level. One can note that both the Gaussian distribution and the Cauchy distribution are special cases of the symmetric alpha-stable distribution with α=2 and α=1, respectively. Also, a larger value of α represents a smooth (or non-impulsive distribution) and a smaller value of α represents a heavy tailed (impulsive) distribution. Note that closed-form expressions for the corresponding PDFs are only known for the cases α=0.5, α=1 and α=2. Even though one can express the PDF for αε[0,1)∪(1,2) in series expansions, the resulting expressions are not well suited for the purpose of receiver design.
In accordance with an embodiment of the invention, a myriad filter location estimator is adapted for use in an adaptive receiver, for application, for example, to UWB signals. A myriad filter location estimator is used to estimate the location parameter, β, of a symmetric alpha-stable distribution. Based on an observation set (or samples) {xi}i=1N the myriad filter location estimator's estimate of the location is given by
where one has to select a suitable value of K known as the tuning or linearity parameter. In some embodiments, K is selected using an α˜K relationship that attempts to minimize detection error probability.
If the problem is binary signal detection with perfect channel information, the location parameter β is restricted such that βε{−s,s} where s represents the magnitude of the signal component in the decision variable. A myriad filter location estimator for binary detection is provided according to
The decision rule is to test
using a suitable value of K.
By adapting K over time, for example as detailed below, Equation (9) can be used to implement an adaptive receiver rule for detection of signals contaminated by symmetric alpha-stable noise. Now, one can note that the distribution of the term Ii+ni in (2) can be more closely approximated by a Gaussian distribution in the following cases, when E{ni2} is dominant, or when there is a large number of interferers, or when Ii is weak. On the other hand, it can be closely approximated (see
dominance of E{ni2};
number of interferers;
strength of Ii.
In some embodiments, the following empirical relationship for K is employed:
where C is a constant, which might be experimentally determined for example, and σ2 is the variance of ni and α and ζ are parameters to be approximated. It is noted that this is an empirical relationship, and that other relationships for K may alternatively be used. This particular expression does not represent an optimal solution. The data bit db is detected as
while using the expression in eq. (10) for K2.
The characteristic function (CF) of the MAI (Ii) is defined by E{ejωI
where
is the CF of ni. Noisy samples of Ii may, for example, be obtained by subtracting s or −s from the samples γi,b. Samples of Īi can, for example, be collected over many symbols during a pilot sequence transmission.
The samples are referred to as “noisy samples” because it is difficult to sample Ii alone. In practical situations, samples of Ii+ni can be obtained, where ni is an AWGN component. While Ii is referred to in the above, based on the assumption that the MAI in each frame is identically distributed, the calculations do not need to be repeated for all i, and the values of α and ζ determined, and ultimately the value of K determined, are applicable for all i over an adaptation period.
In some embodiments, in order to estimate the parameters α and ζ, the empirical CF is calculated over Nω equally spaced sample points of ω given by the vector ω={Δω, . . . , Ω} where Δω=Ω/Nω. The CF of Ii is now approximated by
ΦI
where α and ζ are the parameters to be estimated. By taking natural logarithms twice on both sides of (12) the following linear relation is obtained
ln(−ln(ΦI
If In(−ln(ΦI
α=a2 and
ζ=ea
A block diagram of an example implementation of a UWB receiver is shown in
The parameters K and s, and the correlator outputs γi,b are fed into myriad filter calculators 22 and 24 which produce respective outputs 23, 25 corresponding to each possible value of the bit being estimated. The parameter “+s” and “−s” in the two myriad filter calculators 22, 24 represent the two possible values for the signal. The difference between outputs 23, 25 is produced in adder 26, and thresholding is performed based on this difference in threshold detector 28.
In
The specific examples described herein relate to time-hopping binary phase shift keying (TH-BPSK). However, the analysis and results are similar for a binary pulse position modulation (PPM) scheme and other binary schemes using an appropriate template.
The detailed examples above assume the myriad filter detector receiver approach is applied to the reception of a UWB signal. In some embodiments, the UWB signals are as defined in some literature to be any signal having a signal bandwidth that is greater than 20% of the carrier frequency, or a signal having a signal bandwidth greater than 500 MHz. In some embodiments, the myriad filter detector approach is applied to signals having a signal bandwidth greater than 15% of the carrier frequency. In some embodiments, the myriad filter detector receiver approach is applied to signals having pulses that are 1 ns in duration or shorter. These applications are not exhaustive nor are they mutually exclusive. For example, many UWB signals satisfying the above literature definition will also feature pulses that are 1 ns in duration or shorter.
The myriad filter detector receiver approach is applied to signals for which a plurality of correlations are to be performed in a receiver. In a specific example, the method might be applied for a plurality of correlations determined by the repetition code in a UWB receiver.
Values of BER are compared for the following set of parameters, Ns=8, Nh=8, Tf=20, Tc=0.9, τm=0.575 and Nu=4or 16. A 2nd-order Gaussian monocycle is used for signaling and the SIR is set at 10 dB. Table I shows a comparison of the different detectors. In Table I, ζ denotes the scaling parameter and α denotes the shaping parameter of the distribution models. In the Cauchy receiver a FLOM of order 0.5 is used to estimate the parameter ζ. The simplified Gaussian-Laplacian mixed model receiver (SGLM) uses a Laplacian model for the MAI and is adaptive to the current ambient noise level. In
Numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.
It should also be appreciated that the foregoing description and the drawings referenced therein are intended solely for the purposes of illustration. For example, different results than those shown in
This application claims the benefit of prior U.S. Provisional Application No. 60/980,930 filed Oct. 18, 2007, hereby incorporated by reference in its entirety.
Number | Date | Country | |
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60980930 | Oct 2007 | US |