US 20100002752 A1
A method implemented in a communication device for tracking a spread spectrum signal having an associated code at a receiver is claimed. Components of the spread spectrum signal are despread using locally generated versions of the associated code, each component having a different code phase. A tracking error is determined based on a quadratic function of the components and a weighting factor relating the signal to the tracking error. The weighting factor is a function of a time shift. A minimum in the tracking error is determined by adjusting the time shift.
1. A method implemented in a communication device for tracking a spread spectrum signal having an associated code at a receiver, the method comprising:
despreading a plurality of components of the spread spectrum signal using locally generated versions of the associated code, each of the plurality of components having a different code phase than all others of the plurality of code phases;
determining a tracking error based on:
a quadratic function of the components, and
a weighting factor relating the signal to the tracking error; the weighting factor being a function of a time shift; and
determining a minimum in the tracking error by adjusting the time shift.
2. The method of
a slope of the error signal in the neighborhood of the value of the time shift yielding the minimum to
an average noise power.
3. The method of
4. The method of
5. The method of
a vector representing the components,
a matrix, and
a transpose of the vector,
wherein elements of the matrix are adjusted to maximize the ratio.
6. The method of
This application is a continuation of U.S. patent application Ser. No. 10/788,209, filed Feb. 26, 2004, which is a continuation of U.S. patent application Ser. No. 10/071,899, filed on Feb. 8, 2002 and issued on Jun. 1, 2004 as U.S. Pat. No. 6,744,809, which is a continuation of U.S. patent application Ser. No. 09/261,689, filed on Mar. 3, 1999 and issued on Apr. 30, 2002 as U.S. Pat. No. 6,381,264 which is a continuation of U.S. patent application Ser. No. 08/669,771 filed on Jun. 27, 1996 and issued on Jun. 15, 1999 as U.S. Pat. No. 5,912,919, which claim the benefit of U.S. Provisional Patent Application No. 60/000,775, filed Jun. 30, 1995, which are incorporated by reference as if fully set forth.
The present disclosure is related to wireless communications.
The present invention generally pertains to code sequence tracking in Code Division Multiple Access (CDMA) communication systems, also known as spread-spectrum communication systems. More particularly, the present invention pertains to a system and method for efficient tracking of multipath signal components allowing for combining of multipath signal components to improve data signal detection and despreading by reducing effects of multipath interference, and increase CDMA communication system efficiency by reducing the required transmit power.
Providing quality telecommunication services to user groups which are classified as remote, such as rural telephone systems and telephone systems in underdeveloped countries, has proved to be a challenge over recent years. The past needs created by these services have been partially satisfied by wireless radio services, such as fixed or mobile frequency division multiplex (FDM), frequency division multiple access (FDMA), time division multiplex (TDM), time division multiple access (TDMA) systems, combination frequency and time division systems (FD/TDMA), and other land mobile radio systems. Usually, these remote services are faced with more potential users than can be supported simultaneously by their frequency or spectral bandwidth capacity.
Recognizing these limitations, recent advances in wireless communications have used spread spectrum modulation techniques to provide simultaneous communication by multiple users. Spread spectrum modulation refers to modulating a information signal with a spreading code signal; the spreading code signal being generated by a code generator where the period, Tc, of the spreading code is substantially less than the period of the information data bit or symbol signal. The code may modulate the carrier frequency upon which the information has been sent, called frequency-hopped spreading, or may directly modulate the signal by multiplying the spreading code with the information data signal, called direct-sequence spreading (DS). Spread-spectrum modulation produces a signal with bandwidth substantially greater than that required to transmit the information signal. The original information is recovered by synchronously demodulating and despreading of the signal at the receiver. The synchronous demodulator uses a reference signal to synchronize the despreading circuits to the input spread-spectrum modulated signal to recover the carrier and information signals. The reference signal may be a spreading code which is not modulated by an information signal. Such use of a synchronous spread-spectrum modulation and demodulation for wireless communication is described in U.S. Pat. No. 5,228,056 entitled SYNCHRONOUS SPREAD-SPECTRUM COMMUNICATIONS SYSTEM AND METHOD by Donald L. Schilling, which is incorporated herein by reference.
One area in which spread-spectrum techniques are used is in the field of mobile cellular communications to provide personal communication services (PCS). Such systems desirably support large numbers of users, control Doppler shift and fade, and provide high speed digital data signals with low bit error rates. These systems employ a family of orthogonal or quasi-orthogonal spreading codes, with a pilot spreading code sequence that is synchronized to the family of codes. Each user is assigned one of the spreading codes from the family as a spreading function. Related problems of such a system include handling multipath fading effects. Solutions to such problems include diversity combining of multipath signals. The problems associated with spread spectrum communications, and methods to increase capacity of a multiple access, spread-spectrum system are described in U.S. Pat. No. 4,901,307 entitled SPREAD SPECTRUM MULTIPLE ACCESS COMMUNICATION SYSTEM USING SATELLITE OR TERRESTRIAL REPEATERS by Gilhousen et al. which is incorporated herein by reference.
The problems associated with the prior art systems focus around reliable reception and synchronization of the receiver despreading circuits to the received signal. The presence of multipath fading introduces a particular problem with spread spectrum receivers in that a receiver must somehow track the multipath components to maintain code-phase lock of the receiver's despreading means with the input signal. Prior art receivers generally track only one or two of the multipath signals, but this method may not be satisfactory because the combined group of low-power multipath signal components may actually contain far more power than the one or two strongest multipath components. The prior art receivers track and combine only the strongest components to maintain a predetermined Bit Error Rate (BER) of the receiver. Such a receiver is described, for example, in U.S. Pat. No. 5,109,390 entitled DIVERSITY RECEIVER IN A CDMA CELLULAR TELEPHONE SYSTEM by Gilhousen et al. which is incorporated herein by reference. A receiver that combines all multipath components, however, is able to maintain the desired BER with a signal power that is lower than that of prior art systems because more signal power is available to the receiver. Consequently, there is a need for a spread spectrum communication system employing a receiver that tracks substantially all of the multipath signal components, so that substantially all multipath signals may be combined in the receiver. This would reduce the required transmit power of the signal for a given BER.
A spread spectrum signal having an associated code is tracked at a receiver. A plurality of components of the spread spectrum signal are despread using the associated code. Each of the plurality of components has a different code phase than all others of the plurality of code phases. Each of the plurality of components is weighted based on a phase difference between that component and a center code phase associated with the plurality of components. A tracking error is determined based on the weighted components.
Three CDMA spreading-code tracking methods in multipath fading environments are described which track the code phase of a received multipath spread-spectrum signal. The first is the prior art tracking circuit which simply tracks the spreading code phase with the highest detector output signal value, the second is a tracking circuit that tracks the median value of the code phase of the group of multipath signals, and the third, the system and method of the present invention, is the centroid tracking circuit which tracks the code-phase of an optimized, least mean squared weighted average of the multipath signal components. The following describes the methods by which the spreading code phase of the received CDMA signal is tracked.
A tracking circuit has operating characteristics that reveal the relationship between the time error and the control voltage that drives a Voltage Controlled Oscillator (VCO) of a spreading-code phase tracking circuit. When there is a positive timing error, the tracking circuit generates a negative control voltage to offset the timing error. When there is a negative timing error, the tracking circuit generates a positive control voltage to offset the timing error. When the tracking circuit generates a zero value, this value corresponds to the perfect time alignment called the ‘lock-point’.
In a CDMA system, the signal, s(t), shown in Equation (1) transmitted by the reference user is written in the low-pass representation as,
where ck represents the spreading code coefficients, PTc (t) represents the spreading code chip waveform, and Tc is the chip duration. Assuming that the reference user is not transmitting data, only the spreading code modulates the carrier. Referring to
In Equation (2), ai is an attenuation factor due to fading effect of the multipath channel on the i-th path and τi is the random time delay associated with the same path. The receiver passes the received signal through a matched filter, which is implemented as a correlation receiver and is described below. This operation is done in two steps: first the signal is passed through a chip matched filter and sampled to recover the spreading code chip values, then this spreading sequence is correlated with the locally generated code sequence.
Here, hR (t) is the impulse response of the chip matched filter and “*” denotes convolution. By changing the order of the summations, Equation (3) can be rewritten as Equation (5),
In the multipath channel described above, the sampler samples the output signal of the matched filter to produce x(nT) at the maximum power level points of g(t). In practice, however, the waveform g(t) may be distorted due to the multipath signal reception, and a perfect time alignment of the signals may not be available.
When the multipath distortion in the channel is negligible and a perfect estimate of the timing is available, i.e., a1 a1=1, τ1=0, and ai=0, i=2, . . . , M, the received signal is r(t)=s(t). Then, with this ideal channel model, the output of the chip matched filter becomes
When there is multipath fading, however, the received spreading code chip value waveform is distorted, and has a number of local maxima that can change from one sampling interval to another depending on the channel characteristics.
For multipath fading channels with quickly changing channel characteristics, it is not practical to try to locate the maximum of the waveform f(t) in every chip period interval. Instead, a time reference can be obtained from the characteristics of f(t) that may not change as quickly. Three tracking methods are described based on different characteristics of f(t).
Prior art tracking methods include a code tracking circuit in which the receiver attempts to determine the maximum matched filter output value of the chip waveform and sample the signal at that point. However, in multipath fading channels, the receiver despread spreading-code waveform can have a number of local maxima, especially in a mobile environment. In the following, f(t) represents the received signal waveform of the spreading code chip convolved with the channel impulse response. The frequency response characteristic of f(t) and the timing of its maximum correlation can change rather quickly making it impractical to track the maximum of f(t).
Define τ to be the time estimate that the tracking circuit calculates during a particular sampling interval. Also, define the following error function
The tracking circuits of the prior art calculate a value of the input signal that minimizes the error ε. One can write
Assuming f(t) has a smooth frequency response characteristic in the values given, the value of τ for which f(t) is maximum minimizes the error ε, so the tracking circuit tracks the maximum point of f(t).
The Median Weighted Tracking Method minimizes the absolute weighted error, defined as,
This tracking method calculates the “median” signal value of f(t) by collecting information from all paths, where f(t) is as in Equation (6). In a multipath fading environment, the waveform f(t) can have multiple local maxima, but only one median.
To minimize ε, the derivative of Equation (10) is taken with respect to τ and is equated it to zero, which yields Equation (11).
The value of τ that satisfies (11) is called the “median” of f(t). Therefore, the Median Tracking Method of the present embodiment tracks the median of f(t).
Tracking the median of a group of multipath signals keeps the received energy of the multipath signal components equal on the early and late sides of the median point of the correct locally generated spreading-code phase Cn. The tracking circuit consists of an A/D converter 401 which samples an input signal x(t) to form the half chip offset samples. The half chip offset samples are alternatively grouped into even samples called an early set of samples x(nT+τ) and odd samples called a late set of samples x(nT+(T/2)+τ). The first correlation bank adaptive matched filter 402 multiplies each early sample by the spreading-code phases c(n+1), c(n+2), . . . , c(n+L), where L is small compared to the code length and approximately equal to number of chips of delay between the earliest and latest multipath signal. The output of each correlator is applied to a respective first sum-and-dump bank 404. The magnitudes of the output values of the L sum-and-dump circuits are calculated in the calculator 406 and then summed in summer 408 to give an output value proportional to the signal energy in the early multipath signals. Similarly, a second correlation bank adaptive matched filter 403 operates on the late samples, using code phases c(n−1), c(n−2), . . . , c(n−L), and each output signal is applied to a respective sum-and-dump circuit in an integrator 405. The magnitudes of the output signals of the L sum-and-dump circuits are calculated in calculator 407 and then summed in summer 409 to give a value for the late multipath signal energy. Finally, the adder 410 calculates the difference and produces error signal ε(τ) of the early and late signal energy values.
The tracking circuit adjusts by means of error signal ε(τ) the locally generated code phases c(t) to cause the difference between the early and late values to tend toward 0.
The optimal spreading-code tracking circuit of one embodiment of the present invention is called the squared weighted tracking (or centroid) circuit. Defining τ to denote the time estimate that the tracking circuit calculates, based on some characteristic of .function.(t), the centroid tracking circuit minimizes the squared weighted error defined as
This function inside the integral has a quadratic form, which has a unique minimum. The value of τ that minimizes ε can be found by taking the derivative of the above equation with respect to τ and equating to zero, which gives
Therefore, the value of τ that satisfies
is the timing estimate that the tracking circuit calculates, and .beta. is a constant value.
Based on these observations, a realization of the tracking circuit of the present invention minimizing the squared weighted error is shown in
The value that satisfies ε(τ)=0 is the perfect estimate of the timing.
The early and late multipath signal energy on each side of the centroid point are equal. The centroid tracking circuit shown in
The weighted early multipath signal energy values are summed in sample adder 510 to give an output value proportional to the signal energy in the group of multipath signals corresponding to positive code phases which are the early multipath signals. Similarly, a second correlation bank adaptive matched filter 503 operates on the early and late samples, using the negative spreading phases c(n−1), c(n−2), . . . , c(n−L), each output signal is provided to a respective sum-and-dump circuit of discrete integrator 505. The magnitude value of the L sum-and-dump output signals is calculated by the respective calculator of calculator bank 507 and then weighted in weighting bank 509. The weighted late multipath signal energy values are summed in sample adder 511 to give an energy value for the group of multipath signals corresponding to the negative code phases which are the late multipath signals. Finally, the adder 512 calculates the difference between the early and late signal energy values to produce error sample value ε(τ).
The tracking circuit of
In another embodiment of the tracking method, the tracking circuit adjusts sampling phase to be “optimal” and robust to multipath. Let f(t) represent the received signal waveform as in Equation 16 above. The particular method of optimizing starts with a delay locked loop with an error signal ε(τ) that drives the loop. The function ε(τ) must have only one zero at τ=τ0 where τ0 is optimal. The optimal form for ε(τ) has the canonical form
where w(t, τ) is a weighting function relating f(t) to the error ε(τ), and the following holds
It follows from Equation 18 that w(t, τ) is equivalent to w(t−τ). Considering the slope M of the error signal in the neighborhood of a lock point τ0:
where w′(t, τ) is the derivative of w(t, τ) with respect to τ, and g(t) is the to average of |f(t)|2.
The error ε(τ) has a deterministic part and a noise part. Let z denote the noise component in ε(τ), then |z|2 is the average noise power in the error function ε(τ). Consequently, the optimal tracking circuit maximizes the ratio
The implementation of the Quadratic Detector is now described. The discrete error value e of an error signal ε(τ) is generated by performing the operation
where the vector y represents the received signal components yi, i=0, 1, . . . L−1, as shown in
The Quadratic Detector described above may be used to implement the centroid tracking system described above with reference to
To understand the operation of the Quadratic Detector, it is useful to consider the following. A spread spectrum (CDMA) signal, s(t) is passed through a multipath channel with an impulse response hc(t). The baseband spread signal is described by Equation (22).
where Ci is a complex spreading code symbol, p(t) is a predefined chip pulse and Tc is the chip time spacing, where Tc=1/Rc and Rc is the chip rate.
The received baseband signal is represented by Equation (23)
where q(t)=p(t))*hc (t), τ is an unknown delay and n(t) is additive noise. The received signal is processed by a filter, hR (t), so the waveform, x(t), to be processed is given by Equation (24).
where f(t)=q(t)*hR (t) and z(t)=n(t)*hR (t).
In the exemplary receiver, samples of the received signal are taken at the chip rate, that is to say, 1/Tc. These samples, x(mTc+τ′), are processed by an array of correlators that compute, during the rt
These quantities are composed of a noise component wk(r) and a deterministic component yk(r) given by Equation (26).
In the sequel, the time index r may be suppressed for ease of writing, although it is to be noted that the function f(t) changes slowly with time.
The samples are processed to adjust the sampling phase, τ′, in an optimum fashion for further processing by the receiver, such as matched filtering. This adjustment is described below. To simplify the representation of the process, it is helpful to describe it in terms of the function f(t+τ), where the time-shift, τ, is to be adjusted. It is noted that the function f(t+τ) is measured in the presence of noise. Thus, it may be problematical to adjust the phase τ′ based on measurements of the signal f(t+τ). To account for the noise, the function v(t): v(t)=f(t)+m(t) is introduced, where the term m(t) represents a noise process. The system processor may be derived based on considerations of the function v(t).
The process is non-coherent and therefore is based on the envelope power function |v(t+τ)|2. The functional e(τ′) given in Equation (27) is helpful for describing the process.
The shift parameter is adjusted for e(τ′)=0, which occurs when the energy on the interval (−∞,τ′−τ] equals that on the interval [τ′−τ, ∞). The error characteristic is monotonic and therefore has a single zero crossing point. This is the desirable quality of the functional. A disadvantage of the functional is that it is ill-defined because the integrals are unbounded when noise is present. Nevertheless, the functional e(τ′) may be cast in the form given by Equation (28).
where the characteristic function w(t) is equal to sgn(t), the signum function.
To optimize the characteristic function w(t), it is helpful to define a figure of merit, F, as set forth in Equation (29).
The numerator of F is the numerical slope of the mean error characteristic on the interval [−TA, TA] surrounding the tracked value, τ0′. The statistical mean is taken with respect to the noise as well as the random channel, hc(t). It is desirable to specify a statistical characteristic of the channel in order to perform this statistical average. For example, the channel may be modeled as a Wide Sense Stationary Uncorrelated Scattering (WSSUS) channel with impulse response hc(t) and a white noise process U(t) that has an intensity function g(t) as shown in Equation (30).
The variance of e(τ) is computed as the mean square value of the fluctuation
where <e(τ)> is the average of e(τ) with respect to the noise.
Optimization of the figure of merit F with respect to the function w(t) may be carried out using well-known Variational methods of optimization.
Once the optimal w(t) is determined, the resulting processor may be approximated accurately by a quadratic sample processor which is derived as follows.
By the sampling theorem, the signal v(t), bandlimited to a bandwidth W may be expressed in terms of its samples as shown in Equation (32).
substituting this expansion into equation (z+6) results in an infinite quadratic form in the samples v(k/W+τ′−τ). Making the assumption that the signal bandwidth equals the chip rate allows the use of a sampling scheme that is clocked by the chip clock signal to be used to obtain the samples. These samples, vk are represented by Equation (33).
This assumption leads to a simplification of the implementation. It is valid if the aliasing error is small.
In practice, the quadratic form that is derived is truncated. An example normalized B matrix is given below in Table 2. For this example, an exponential delay spread profile g(t)=exp(−t/τ) is assumed with .tau. equal to one chip. An aperture parameter TA equal to one and one-half chips has also been assumed. The underlying chip pulse has a raised cosine spectrum with a 20% excess bandwidth.
Code tracking of the above form in a CDMA system employing a Pilot signal can be implemented via a loop phase detector that is implemented in a digital signal processing device (DSP) as follows. The vector y is defined as a column vector which represents the 11 complex output level values of the Pilot AVC 1711, and B denotes an 11×11 symmetric real valued coefficient matrix with pre-determined values to optimize performance with the non-coherent Pilot AVC output values y. The output signal of the phase detector is given by Equation (21).
The following calculations are then performed to implement a proportional plus integral loop filter and the VCO:
for β and α which are constants chosen from modeling the system to optimize system performance for the particular transmission channel and application, and where x[n] is the loop filter's integrator output value and z[n] is the VCO output value. The code phase adjustments are made by the modem controller the following C-subroutine:
The value of L in the previous section determines the minimum number of correlators and sum-and-dump elements. L is chosen as small as possible without compromising the functionality of the tracking circuit.
The multipath characteristic of the channel is such that the received chip waveform f(t) is spread over QTc seconds, or the multipath components occupy a time period of Q chips duration. The value of L chosen is L=Q. Q is found by measuring the particular RF channel transmission characteristics to determine the earliest and latest multipath component signal propagation delay QTc is the difference between the earliest and latest multipath component arrival time at a receiver.
The previous description of acquisition and tracking algorithm focuses on a non-coherent method because the acquisition and tracking algorithm described requires non-coherent acquisition following by non-coherent tracking because during acquisition a coherent reference is not available until the AMF, Pilot AVC, Aux AVC, and DPLL are in an equilibrium state. However, it is known in the art that coherent tracking and combining is always optimal because in non-coherent tracking and combining the output phase information of each Pilot AVC finger is lost. Consequently, another embodiment of the invention employs a two step acquisition and tracking system, in which the previously described non-coherent acquisition and tracking algorithm is implemented first, and then the algorithm switches to a coherent tracking method. The coherent combining and tracking method is similar to that described previously, except that the error signal tracked is of the form:
where y is defined as a column vector which represents the 11 complex output level values of the Pilot AVC 1711, and A denotes an 11.times.11 symmetric real valued coefficient matrix with pre-determined values to optimize performance with the coherent Pilot AVC outputs y. An exemplary A matrix is shown below.
While the present invention has been described in terms of exemplary embodiments, it is understood by one skilled in the art that it may be practiced as described above with variations within the scope of the following claims.