The invention relates to receivers and methods for performing reception of UWB (ultra-wide bandwidth) signals.
Ultra-wide bandwidth (UWB) wireless is a promising communication technology which is proposed as a valid solution for high-speed wireless communication systems. Several transmitters can viably coexist in the coverage area in an UWB system because of its robustness to severe multipath conditions. A time-hopping (TH) sequence is introduced to UWB systems to avoid the catastrophic collisions. Multiple access interference (MAI) for TH systems has been analyzed in M. Z. Win and R. A. Scholtz, “Ultra-Wide Bandwidth Time-Hopping Spread-Spectrum Impulse Radio for wireless Multiple-Access Communications,” IEEE Trans. Commun., vol. 48, pp. 679-691, April 2000 and A. Taha and K. M. Chugg, “A theoretical study on the effects of interference on UWB multiple access impulse radio,” in Proc. IEEE conf. on Signals, Systems and Computers, pp. 728-732, Nov. 3-6, 2002, where the MAI has been approximated as a Gaussian random variable (RV) based on the Central Limit Theorem and the conventional matched filter is used as the receiver detector. The conventional matched filter is optimal for a signal embedded in additive white Gaussian noise (AWGN) since it maximizes the output signal-to-noise ratio (SNR), J. G. Proakis, Digital Communications, 4th ed. New York: McGraw-Hill, 1995, pp. 243, but the MAI in UWB systems is not Gaussian distributed. It is shown in B. Hu and N. C. Beaulieu, “Exact bit error rate of TH-PPM UWB systems in the presence of multiple access interference,” IEEE Communications Letters, vol. 7, pp. 572-574, December 2003, B. Hu and N. C. Beaulieu, “Accurate performance evaluation of time-hopping and direct-sequence UWB systems in multi-user interference,” IEEE Trans. Commun., vol. 53, pp. 1053-1062, June 2005, G. Durisi and G. Romano, “On the validity of Gaussian approximation to characterize the multiuser capacity of UWB TH-PPM,” in Proc. IEEE Conf. on Ultra Wideband Systems and Technologies, Baltimore, USA, May 20-23, 2002 and G. Durisi and S. Benedetto, “Performance evaluation of TH-PPM UWB systems in the presence of multiple access interference,” IEEE Commun. Lett., vol. 7, pp. 224-226, May 2003 that the “Gaussian approximation” (GA) is not accurate enough to predict the UWB system performance and it highly underestimates the BER of an UWB system when the MAI is the dominant disturbance. Therefore, the conventional matched filter UWB receiver is not necessarily an optimal receiver.
According to one broad aspect, the invention provides a method of receiving a signal comprising: receiving a signal over a wireless channel; adaptively selecting a shaping parameter p over time; generating a first set of partial statistics by, for each of a plurality N of observations per symbol, using a receiver model based on an assumption that the noise plus MAI has a PDF f(x)=c·exp{−γ|x−Sm|p} where p is the shaping parameter, Sm is the mean, and parameter γ is used to adjust the second moment of the RV, and c is a constant to ensure
to generate a respective partial decision statistic of the first set of partial statistics; summing the partial decision statistics to produce a first sum; making a decision on a symbol contained in the signal based on the first sum; outputting the decision.
In some embodiments, for each of a plurality N of observations per symbol, using a receiver model based on an assumption that the noise plus MAI has a PDF f(x)=c·exp{−γ|x−Sm|p} where the parameter p is adaptive, Sm is the mean, and parameter γ is used to adjust the second moment of the RV, and c is a constant to ensure that
to generate a respective partial decision statistic comprises: transforming each observation according to:
where rm is the mth observation.
In some embodiments, the method further comprises generating each of the plurality N of observations by performing a respective correlation between the received signal at a particular time and a pulse shape.
In some embodiments, adaptively selecting p over time comprising adapting p as a function of SNR.
In some embodiments, adaptively selecting p over time comprises using kurtosis matching.
In some embodiments, adaptively selecting p over time comprises: measuring a channel condition; updating p by determining the new value for p as a function of the channel condition.
In some embodiments, adaptively selecting p over time comprises: maintaining a table lookup of p as a function of a channel condition; measuring the channel condition; updating p by looking up the new value for p using the table lookup and the measured channel condition.
In some embodiments, the method further comprises adapting a value for Sm used in the partial decision statistics over time.
In some embodiments, adapting a value for Sm used in the partial decision statistics over time comprises adapting a value Topt for Sm based on estimated channel conditions or error rate monitoring.
In some embodiments, the method is employed within a rake receiver.
In some embodiments, the method comprises: generating a respective set of partial statistics for each of a plurality of multi-path components of the received signal, one of the sets of partial statistics being said first set of partial statistics, by for each of a plurality N of observations per symbol, using a receiver model based on an assumption that the noise plus MAI has a PDF f(x)=c·exp{−γ|x−Sm|p} where p is the shaping parameter, Sm is the mean, and parameter γ is used to adjust the second moment of the RV, and c is a constant to ensure that
to generate a respective partial decision statistic; for each multi-path component, summing the partial decision statistics to produce a respective decision statistic, one of the sums being the first sum; combining the sums to produce an overall decision statistic; wherein making a decision on a symbol contained in the signal based on the sum comprises making a decision based on the overall decision statistic.
In some embodiments, making a decision on a symbol contained in the signal based on the sum comprises making a decision based on the overall decision statistic comprises performing maximum ratio combining.
In some embodiments, receiving a signal comprises receiving a signal having a signal bandwidth that is greater than 20% of the carrier frequency, or receiving a signal having a signal bandwidth greater than 500 MHz.
In some embodiments, receiving a signal comprises receiving a signal having a signal bandwidth greater than 15% of the carrier frequency.
In some embodiments, receiving a signal comprises receiving a signal having pulses that are 1 ns in duration or shorter.
In some embodiments, receiving a signal comprises receiving a UWB signal.
In some embodiments, receiving a signal comprises receiving a TH UWB signal.
In some embodiments, receiving a signal comprises receiving a DS UWB signal.
In some embodiments, a receiver operable to implement the method as summarized above.
In some embodiments, a computer readable medium having instructions stored thereon for implementing the method as summarized above.
According to another broad aspect, the invention provides a receiver comprising: a correlator configured to generate a first set of partial statistics by, for each of a plurality N of observations per symbol, using a receiver model based on an assumption that the noise plus MAI has a PDF f(x)=c·exp{−γ|x−Sm|p} where p is a shaping parameter, Sm is the mean, and parameter γ is used to adjust the second moment of the RV, and c is a constant to ensure that
to generate a respective partial decision statistic of the first set of partial statistics; a channel estimator configured to adapt the shaping parameter over time; an accumulator configured to sum the partial decision statistics to produce a first sum; a decision block configured to make a decision on a symbol contained in the signal based on the first sum; an output for outputting the decision.
In some embodiments, the receiver further comprises at least one antenna.
In some embodiments, the receiver further configured to adapt the mean Sm over time.
In some embodiments, a rake receiver comprises the receiver as summarized above.
According to another broad aspect, the invention provides a method of receiving a signal using a rake receiver, the method comprising: receiving a signal over a wireless channel; adaptively selecting a shaping parameter p over time; generating a first set of partial statistics by, for each of a plurality N of observations per symbol, using a receiver model based on an assumption that the noise plus MAI has a PDF f(x)=c·exp{−γ|x−Sm|p} where p is the shaping parameter, Sm is the mean, and parameter γ is used to adjust the second moment of the RV, and c is a constant to ensure that
to generate a respective partial decision statistic of the first set of partial statistics; generating a respective set of partial statistics for each of a plurality of multi-path components of the received signal, one of the sets of partial statistics being said first set of partial statistics, by for each of a plurality N of observations per symbol, using a receiver model based on an assumption that the noise plus MAI has a PDF f(x)=c·exp{−γ|x−Sm|p} where p is the shaping parameter, Sm is the mean, and parameter γ is used to adjust the second moment of the RV, and c is a constant to ensure that
to generate a respective partial decision statistic; combining the partial decision statistics to produce an overall decision statistic; wherein making a decision on a symbol contained in the signal based on the sum comprises making a decision based on the overall decision statistic.
Embodiments of the invention will now be described with reference to the attached drawings in which:
Some new UWB receiver structures which outperform the conventional matched filter UWB receiver have been proposed recently. A soft-limiting UWB receiver proposed in N. C. Beaulieu and B. Hu, “A Soft-limiting receiver structure for timehopping UWB in multiple access interference,” in Proc. 9th International Symposium on Spread Spectrum Techniques and Applications (ISSSTA), Manaus, Brazil, Aug. 28-31, 2006 was shown to achieve better performance than the conventional matched filter UWB receiver when only MAI is present in the channel. When both MAI and AWGN are present, the soft-limiting UWB receiver underperforms the conventional matched filter UWB receiver for small and moderate SNR, but achieves 1 dB gain for large SNR. A more complex receiver based on the soft-limiting UWB receiver was proposed in N. C. Beaulieu and B. Hu, “An Adaptive Threshold Soft-Limiting UWB Receiver with Improved Performance in Multiuser Interference”, to be presented at 2006 International Conference on Ultra-Wideband (ICUWB), Massachusetts, USA, Sep. 24-27, 2006. This adaptive threshold soft-limiting UWB receiver improves the performance of the soft-limiting UWB receiver by employing an adaptive threshold and it always meets or outperforms the conventional matched filter UWB receiver when both MAI and AWGN are present in the channel.
A new UWB receiver structure referred to herein as the “p-order metric” receiver (p-omr) is provided. In practical mixed multiuser plus Gaussian noise environments, the p-omr can meet or outperform both the conventional matched filter UWB receiver and the adaptive threshold soft-limiting UWB receiver for all SNR values and all signal-to-interference (SIR) values. Another new UWB receiver structure referred to herein as the “p-order metric adaptive threshold limiting receiver” (p-omatlr) is also provided which is on the p-omr structure. It will be shown that the p-omatlr UWB receiver design meets or surpasses the performance of all of, the conventional matched filter UWB receiver, the soft-limiting UWB receiver, the adaptive threshold soft-limiting UWB receiver, and the p-omr.
A specific example of the form of a UWB time-hopping binary phase shift keying (TH-BPSK) signal can be described as
where s(k)(t) is the signal of the kth user, t is the transmitter clock time, Eb is the bit energy, Ns is the number of frames which are used to transmit a single information bit, and dj(k) is the jth information bit of the kth user, which takes values from {+1, −1} with equal probabilities. The function p(t) is the transmitted UWB pulse with unit energy, which means it satisfies the condition
Each time frame with duration Tf is divided into chips with duration T. The sequence WI is the time-hopping sequence for each bit of the kth user, and the product cj(k)Tc adds an additional time shift to the TH pulses to avoid catastrophic collisions. The sequence {cj(k)} takes integer values in the range 0≦cj(k)<Nh, where Nh is the number of hops which satisfies the condition NhTc≦Tf. It is to be clearly understood that while the embodiments described in here assume the form of the UWB signal presented above, the methods have application to other forms of UWB signals. Examples of these are given below.
Assuming ideal free-space propagation, when there are Nu transmitters in the same coverage area, the received signal can be written as
where the sequences {Ak}k−1N
For the purpose of this analysis, it is assumed that the signal from the first user is the desired signal and d0(1) is the transmitted symbol. Of course the receiver has general applicability to any user, and to any transmitted symbol for that user. Without loss of generality, the TH sequence for the desired user, cj(1), is set to be 0, for all j. Of course the time hopped sequence can be any appropriate value or set of values. At the receiver side, assuming perfect time synchronization, the conventional single-user matched filter, which adopts the p(t−τ1−mTf) as the correlation waveform for the mth frame, is used to coherently detect the signal to be recovered, the correlator output is
where m is the frame index of the information bit to be recovered, and S=A1√{square root over (EbNsd0(1))} is desired signal component where d0(1) is the information bit transmitted by the desired user. The RV N is Gaussian distributed with zero mean and variance N0Ns/2. The parameter I, which represents the total MAI originating from all Ns frames, can be written as
where I(k) can be expressed as
Substituting (1) into (5) and denoting the autocorrelation function of the UWB pulse waveform p(t) as
I(k) can be rewritten as
where τs(k) is the time shift difference between different users which can be modeled in the same way as in M. Z. Win and R. A. Scholtz, “Ultra-Wide Bandwidth Time-Hopping Spread-Spectrum Impulse Radio for wireless Multiple-Access Communications,” IEEE Trans. Commun., vol. 48, pp. 679-691, April 2000, namely
τs(k)=τ1−τk=mkTfαk (7)
where mk is the value of the time uncertainty rounded to the nearest integer, and αk is the fractional part which is uniformly distributed in the region (−Tf/2,Tf/2]. Then the argument of (R·) is
(m+mk−j)Tf−cj(k)Tc+αk. (8)
Based on the assumption NhTc<Tf/2−2Tp, which means that the pulse can only hop over an interval of one-half of a frame time, Eq. (6) can be rewritten as
Putting (9) back into (4) and rearranging the order of summation, the total interference term can be represented in terms of the interference originating from a single frame, Im, as
where Im is given by
Then the final receiver decision statistic can be expressed as a summation of statistics in each frame
where Sm=A1√{square root over (Eb/Nsd0(1))} is the desired signal component in the mth frame, Nm is a Gaussian distributed RV with variance N0/2, and Im is the total interference component in the mth frame from all interferers given in (11). The RV Ym is the overall disturbance (MAI plus AWGN) in the mth frame.
The conventional matched filter is the optimal receiver structure when a signal is corrupted by AWGN, while the soft-limiting UWB receiver is optimal for a signal embedded in additive Laplace noise.
Observe in
Note that the pdf of a Gaussian distributed RV is
where Sm and σ are the mean and the standard deviation of the RV, respectively. The pdf of a Laplacian distributed RV is
where the mean of the RV is Sm and the variance is 2b2. Observe that both pdfs have the form f(x)=c·exp{−γ|x−Sm|p}, while the pdf of a Gaussian RV is with p=2 and the pdf of a Laplacian RV is with p=1. A new form of approximation for the pdf of Ym is provided as
f(x)=c·exp{−γ|x−Sm|p} (15)
where the parameter p is adaptive. The adaptation rate is implementation specific. It may be adapted, for example, every transmission. In the above, c is a constant to ensure that
The parameter γ is used to adjust the second moment of the RV to some certain value. For example, the parameter might be selected according to:
where σ2 is the variance of the RV, p is the shape parameter, and Γ(·) is the Gamma function. However, this parameter γ will not affect the structure of the UWB receiver as shown below. Different values of p are selected adaptively to fit the pdf of Ym for different SNRs. Within the region where the SNR is small and the RV Ym is approximately Gaussian distributed, f(x) can be used to approximate the pdf of Ym by setting p to 2, while in the region where the SNR values are moderate and the pdf can be approximated by pdf of the Laplace distribution, f(x) with p=1 becomes a good approximation of the pdf of the RV Ym. Note that the new approximated pdf f(x) changes in the same manner with the decreasing p as the pdf of Ym changes with the increasing values of the SNR. When the SNR grows large enough that neither the GA nor the LA is a good approximation of the pdf of Ym, f(x) with p less than 1 fits the actual pdf of Ym better than the Gaussian and Laplacian pdfs as shown in
H
0
:=r
m
=S
m
+Y
m
H
1
:=r
m
=−S
m
+Y
m m=0, . . . , Ns−1 (16)
where rm is the chip correlator output, Ns denotes the number of chips to transmit one single information bit, Sm is the sampled signal value in a single frame, {Ym}m=1N
Note that the function f(x) has the same form as the pdf of the generalized Gaussian distribution defined in S. M. Kay, Fundamentals of Statistical Signal Processing: Detection Theory, Englewood Cliffs: Prentice Hall 1998,
where the parameter Sm is the mean of the RV, the function
is a scaling factor which ensures that var(x)=σ2,Γ(·) is the Gamma function, and p is the shape parameter. Observe that the pdfs of the Gaussian and Laplacian distributions are special cases of the generalized Gaussian distribution, the Gaussian pdf having p=2 and the Laplacian pdf having p=1.
Based on this observation, an optimal receiver structure is provided that is based on the assumption that the pdf of the overall disturbance in a single frame, Ym, can be approximated as a RV with pdf f(x). In the optimal detector, the transformation of the single chip correlator output, rm, to the single sample log-likelihood ratio Lm(rm), is given by (See H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part I. New York: Wiley, 2001)
Eq. (17) defines a transform of the chip correlator output, rm, into a partial decision statistic, hm(rm). If the new approximation (15) of the pdf is adopted, the new partial decision statistic, hm(rm), is given by
where γ can be chosen to be 1 or other positive real values. The final decision statistic of the detector is represented as
The transmitted information bit d0(1) is detected based on the new decision statistic {tilde over (r)} according to the rule
{tilde over (r)}>0=>d0(1)=+1 (20a)
{tilde over (r)}<0=>d0(1)=−1 (20b)
If {tilde over (r)}=0, a fair coin maybe tossed to decide which information bit was transmitted, or d0(1)=1 can be decided, or d0(1)=−1 can be decided.
If p=2, eq. (18) becomes
and the final decision statistic {tilde over (r)} becomes
and the p-omr becomes exactly the same as the conventional matched filter UWB receiver. If p assumes the value of 1, eq. (18) becomes
and the p-omr becomes the same as the soft-limiting receiver.
Referring now to
In operation a received signal r(t) is processed by signal processing and timing function 10 to recover timing. As a function of this timing, the pulse generator 12 generates a pulse for use by correlator 14 in performing a correlation between the pulse and r(t). The output of the correlator rm is passed to the p-omr or p-omatlr output transform 16 where it is transformed as described in detail to produce the partial statistic {tilde over (r)}m, where {tilde over (r)}m=hm(rm) as defined in equation (18). The {tilde over (r)}m's relating to the same bit are summed in the accumulator 18 to produce {tilde over (r)} (this is equivalent to equation (19)), and a final decision on the sum is made by the threshold function 20.
It is emphasized that the design of the p-omr and p-omatlr structure is based on an approximation of the true pdf. That is, the p-omr and p-omatlr are not optimal. However, the discussion above shows that the p-omr becomes exactly the same as the conventional matched filter UWB receiver or the soft-limiting UWB receiver for certain values of p, which implies that if the parameter p is adaptive and optimized, the p-omr can always meet or outperform both the conventional matched filter UWB receiver and the soft-limiting UWB receiver. Meanwhile, the p-omatlr becomes exactly the same as the conventional matched filter UWB receiver or the adaptive threshold soft-limiting receiver for certain values of p and threshold Topt, which implies that if the parameter p and the threshold Topt are both adaptive and optimized, the p-omatlr can always meet or outperform both the conventional matched filter UWB receiver and the adaptive threshold soft-limiting UWB receiver.
In order to implement the p-omr for signal detection, the shape parameter p in the pdf f(x) of equation (15) needs to be estimated. Equivalently, the shape parameter for the generalized Gaussian pdf of equation (15b) can be estimated, and it is this form of the pdf that will be used in the analysis that follows. In
The kurtosis of RV X with pdf fgg(x) can be expressed as
Note that, shape parameter p is the only argument in eq. (25), and as a function of p, the kurtosis is monotonically decreasing. Thus, it is easy to obtain the shape parameter p once the kurtosis is determined. In some embodiments, the shape parameter p can be estimated from an estimated value for the kurtosis.
Note that in eq. (11), the total interference in the mth frame can be expressed as
is the interference in the mth frame from the kth user. Note that mk is the value of the time shift difference between the desired user and the kth user, τs(k)=τ1−τk, measured in durations of one frame time rounded to the nearest integer, and αk is the fractional part which is uniformly distributed in
According to the assumption that the TH sequences are random, the pdf of cm+m
where δ(·) is the Dirac delta function. Then, the characteristic function (CF) of I(m,k) conditioned on d└(m+m
The conditional CF of I(m,k) can be further expressed using the theorem of total probability as
where lk=m+mk. Assuming the interfering symbol d└I
The fraction part of the time shift difference, αk, is assumed to be uniformly distributed in
as mentioned before, thus, the CF of I(m,k) can be represented as
The nth derivative of the CF Φx(ω) evaluated at ω=0 yields the nth moment of the RV X
Thus, when n is odd, the nth moment of the interference term, I(m,k), is
and when n is even, the nth moment can be expressed as
The first and third moments of I(m,k) are both 0, while the second and fourth moments are
respectively.
Note that the duration of the UWB pulse p(t) is τp, thus, the support of the autocorrelation function R(x) is [−τp,τp). Letting x=αk−hTc, the term for a particular value of h in eq. (36a) can be rewritten as
With the assumption NhTc<Tf/2−2τp, the region of the integration at the right side of eq. (37) is an interval covering the support of the integrand. Thus, the integration region can be extended to (−∞, +∞) without changing the integral, and the term for a particular h can be rewritten as
Note that these terms for all the possible values of h are the same. Thus, eq. (36a) can be expressed as
Note that eq. (38) represents the variance of the MAI from a single user in a single frame. Eq. (36b) can be simplified as
According to eq. (26), the first moment and the third moment of the total disturbance in the mth frame are 0. If equal power interferers are considered and it is assumed that the interference from different interferers are independent, the second moment of Im can be written as
The fourth moment of the RV Im is
When both MAI and AWGN are present in the channel, the GGA is used to model the total disturbance term Ym=Im+Nm. Assuming that the AWGN term and the MAI term both have zero means and are independent, the mean of the total disturbance term Ym=Im+Nm is also zero, and its variance can be written as
E(Ym2)=E(Im2)+E(Nm2) (42)
The fourth central moment of the RV Ym is
E(Ym4)=E(Im4)+6E(Im2)E(Nm2)+E(Nm4) (43)
The kurtosis of the RV Ym can be represented as
where E(Im2) and E(Im4) are the second and fourth moments of Im given by (40) and (41), respectively, and E(Nm2)=σn2 and E(Nm4)=3σn4 are the variance and the fourth moment of the AWGN component in the mth frame. The shape parameter p in this case can be estimated by matching eq. (44) and (25), and the estimated value for the shape parameter, {circumflex over (p)}, satisfies
In some embodiments, a table look-up mechanism is implemented that maps channel estimates for Im,Nm to the solution of equation 45. Alternatively, the solution to equation (45) or an approximation thereto can be implemented in hardware or software.
A very specific method of determining p based on kurtosis matching has been described. Other methods can be employed; for example, a computer search to determine values of p for respective sets of channel conditions may be employed. The results can be used to implement a table look-up mechanism. Interpolation may be employed to determine p for channel conditions not specifically covered.
In some embodiments, adapting p involves: measuring a channel condition; updating p as a function of the channel condition.
In some embodiments, adapting p involves: maintaining a table lookup of p as a function of a channel condition; updating p by measuring the channel condition, and looking up the new value for p using the table lookup.
The soft-limiting UWB receiver N. C. Beaulieu and B. Hu, “A soft-limiting receiver structure for time-hopping UWB in multiple access interference,” in Proc. IEEE International Symposium on Spread Spectrum Techniques and Application (ISSSTA 2006), September 2006, pp. 417-421 underperforms the CMF UWB receiver in practical mixed MAI-plus-AWGN environments for small to moderate values of SNR. The adaptive threshold soft-limiting UWB receiver in N. C. Beaulieu and B. Hu, “An adaptive threshold soft-limiting UWB Receiver with improved performance in multiuser interference”, in Proc. IEEE International Conference on Ultra-Wideband (ICUWB 2006), September 2006, pp. 405-410 based on the soft-limiting UWB receiver achieves better performance and outperforms the CMF UWB receiver for all the SNR values in such environments by adopting an adaptive limiter threshold Topt instead of Sm. In similar fashion, an extra degree of freedom Topt can also be introduced to the p-omr. That is, as in eq. (18),
h
m(rm)=γ|rm+Topt|p−γ|rm−Topt|p (46)
where p can, for example, be determined by the kurtosis matching method described above, and the threshold Topt is adaptive and optimized to gain the best BER performance. The parameter γ can be chosen to be 1 or other positive real values. Note that when p=1 and Topt is adaptive, the receiver becomes exactly the adaptive threshold soft-limiting UWB receiver. Theoretically, if the shape parameter p is estimated and threshold Topt are optimized to minimize the BER, the new receiver referred to herein as the “p-order metric adaptive threshold limiting receiver” (p-omatlr) must always meet or outperform the CMF UWB receiver, the adaptive threshold soft-limiting UWB receiver, and the p-omr. This will be true for arbitrary additive signal disturbances, including MAI, AWGN, and MAI-plus-AWGN.
In some embodiments, bit error monitoring at the bit level or the packet level is performed, or table look-up using channel state conditions measurement is performed, and a mapping transformation between SNR, SIR and or SINR to {circumflex over (p)}, Topt, σn2, σn4 and BER is used to determine the shaping parameter and the optimal adaptive threshold.
The previous embodiments have considered an AWGN channel model. Now a more practical scenario, the multipath fading channel is considered. Although many multipath components are present in UWB systems, the total disturbance is not always Gaussian. Even if the total disturbance is Gaussian distributed, this may not be the case for the chip correlator output in each Rake finger. This is why the superiority of the p-omr and p-omatlr designs still exists even in highly dense multipath UWB channels as subsequent results will show. Note that the robustness of UWB signals to multipath fading is due to their fine delay resolution, and high diversity order can be achieved with the adoption of a Rake receiver in UWB systems. It has already been shown that the p-omr and p-omatlr can achieve better BER performance in ideal free-space propagation (AWGN) channels. A new Rake receiver adopting the p-omr or p-omatlr in each finger is provided for signal detection. This new Rake receiver can achieve larger SINR than the standard matched filter based Rake receiver.
The Rake receiver of
The operation of the Rake receiver of
and the cumulative density function (cdf) can be written as
where the mean of rm,i is E(rm,i)=Sm, and the variance is var(rm,i)=2b2. The decision statistic, ri, in this finger of the matched filter based Rake receiver can be represented
The mean of ri is
and the variance is
var(ri)=Ns·var(rm,i)=2NsB2. (51)
Noting that the SINR of the decision statistic X in a transmission system is given by SINR=E2(X)σx2, the SINR in ith finger of the matched filter based Rake receiver can be expressed as
Consider now the new Rake receiver structure shown in
The mean of the new chip correlator output {tilde over (r)}m,i is
and its variance is
The decision statistic in ith finger of the new Rake receiver can be represented as
and, therefore, the mean of the new decision statistic {tilde over (r)}i is
and the variance is
var({tilde over (r)}i)=Ns·var({tilde over (r)}m,i) (58)
where E({tilde over (r)}m,i) and var({tilde over (r)}m,i) are given by (54) and (55), respectively. The SINR in the ith finger of the new Rake receiver can, thus, be expressed as
Eq. (52) gives the SINR in each finger of the CMF based Rake receiver, while that of the new Rake receiver adopting the p-omr is given in (59). These two SINRs are compared in
Since the value of SINRi,new is between 2 times and 8/3 times SINRi,mf for all values of i,
Thus, when measured in dB, the SINR gains of the final decision statistic of the new Rake receiver based on the design of p-omr over the standard matched filter Rake receiver are lower bounded by 3 dB and upper bounded by 4.26 dB. In practical UWB systems with small to medium SINR values, the SINR gains will be around 3 dB when p is close to 1. The preceding discussion valid for p=1 clarifies the mechanism of the SINR improvement. There is also a SINR gain for the p-omr for other values of p, as shown by the results in
Note that, as long as the multipath components in UWB channels are resolvable so that the Rake receiver is viable, the new design of the Rake receiver based on the p-omr or p-omatlr always performs at least as well as the matched filter based Rake receiver (when {circumflex over (p)}=2, the SINR gain is 0 dB, and the new Rake receiver becomes exactly the same as the CMF based Rake receiver). The fact that the new Rake receiver adopting the p-omr or p-omatlr in each Rake finger can achieve larger SINR values than the CMF based Rake receiver makes the designs of the p-omr and p-omaltr valuable not only in ideal free-space propagation (AWGN) channels, but also in multipath UWB channels.
The average bit error rate (BER) performance of the p-omr is evaluated and compared to the conventional matched filter UWB receiver, the soft-limiting UWB receiver which was recently proposed in N. C. Beaulieu and B. Hu, “A Soft-limiting receiver structure for timehopping UWB in multiple access interference,” in Proc. 9th International Symposium on Spread Spectrum Techniques and Applications (ISSSTA), Manaus, Brazil, Aug. 28-31, 2006, and the adaptive threshold soft-limiting UWB receiver proposed in N. C. Beaulieu and B. Hu, “An Adaptive Threshold Soft-Limiting UWB Receiver with Improved Performance in Multiuser Interference”, to be presented at 2006 International Conference on Ultra-Wideband (ICUWB), Massachusetts, USA, Sep. 24-27, 2006. The signal waveform is restricted to the second-order Gaussian monocyle with parameters given in Table I as follows:
The SIR and SNR are defined as
where σ12 defined as
and where R(t) is the autocorrelation function of the second-order Gaussian monocycle.
The above performance results are for the p-omr with shape parameter determined by computer search. The kurtosis matching method can also used to determine the optimal shape parameter for the p-omr.
The average bit error rate (BER) performances of the p-omr and the p-omatlr are evaluated and compared to the performances of the CMF UWB receiver, the soft-limiting UWB receiver, and the adaptive threshold soft-limiting UWB receiver. The signal waveform is restricted to the second-order Gaussian monocyle and the system parameters are the same as the first set given in Table I above.
As mentioned before,
Note that while the detailed embodiments described herein apply to TH-UWB, the receiver structure can also be applied to DS-UWB with appropriate modifications.
The detailed examples above assume the new receiver approaches are applied to the reception of a UWB signal. In some embodiments, the UWB signals are as defined in the 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 receiver approach is applied to signals having a signal bandwidth greater than 15% of the carrier frequency. In some embodiments, the 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, most UWB signals satisfying the literature definition will also feature pulses that are 1 ns in duration or shorter.
The receiver approach is applied to signals for which a plurality of correlations need 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. In other applications, the method might be applied for a plurality of correlations in a Rake receiver or a finger of a Rake receiver. That is to say, the correlations might be used across signal chips of a repetition code, across the fingers of a Rake receiver, or the new receiver might be used as a unit in each finger of a Rake receiver.
The embodiments described herein may be applied to wireless signals that physically come in any form. For example, they may be RF signals, or infrared signals to name a few specific examples.
Referring now to
f(x)=c·exp{−γ|x−Sm|p}
where p is the shaping parameter, Sm is the mean, and parameter γ is used to adjust the second moment of the RV, and c is a constant to ensure that
The method continues at block 15-4 with summing the partial decision statistics to produce a first sum, and making a decision on a symbol contained in the signal based on the first sum. Finally, in block 15-5, a decision is output.
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.
This application claims the benefit of U.S. Provisional Patent Application No. 60/716,033 filed May 4, 2007.
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/CA2008/000835 | 5/5/2008 | WO | 00 | 11/3/2009 |
Number | Date | Country | |
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60916033 | May 2007 | US |