COMPLEX SIGNAL LIMITING

Abstract: Each complex signal sample a(k)+jb(k) of a frequency modulated signal is limited in order to reduce co-channel interference. The limiting is performed efficiently in a digital signal processor by determining a ratio r with a magnitude less than one, equal to b(k)/a(k) in a first case and a(k)/b(k) in a second case, determining from a look-up table a variable p with a magnitude equal to 1/ 2ROOT (1+r<2>), and determining a number equal to sgn(a(k))p(1 + jr) in the first case and sgn(b(k))p(r + j) in the second case as the limited output signal sample.

Description: COMPLEX SIGNAL LIMITING This invention relates to limiting complex signals, and is particularly applicable to complex signal limiting for reducing co-channel interference (CCI) in communications systems. Background of the Invention CCI is constituted by one or more interfering signals within the frequency band of a desired signal in a communications system, and is a key factor that limits the frequency reuse capacity of mobile communications systems. The CCI can not be reduced by conventional filtering techniques, because it falls within the bandwidth of the desired signal. One technique, described in the copending application referred to above, for reducing CCI is limiting of a received complex signal which comprises a mixture of a desired FM (frequency modulated) signal and an independent weaker (i.e. lower average power) CCI. The desired signal has a constant envelope, whereas the received signal has a non-constant envelope due to the CCI. The complex signal limiter converts the input mixture to a constant envelope signal, transforming at least half of the CCI energy outside the bandwidth of the desired signal so that it can be filtered out by a low pass filter. As described in the copending application, the complex signal limiting is carried out in a DSP (digital signal processor) on each sample x(k) of the received complex signal, typically at a sampling rate of about 48 kHz, and consists of a calculation of the function ι,\ _ x ( ) _ x ( k ) Xta( '- | χ (kr (x( ) X *(k)) 0 - 5 where x*(k) is the complex conjugate of x(k) and xiim(k) is the ouφut of the complex signal limiter. As can be appreciated, the calculation of this non-linear function for each sample requires significant DSP resources. An object of this invention is to provide an improved method for calculating this function which reduces the required DSP resources, and hence to provide an improved method of limiting a complex signal representing a received signal in a communications system. Summary of the Invention One aspect of this invention provides a method of limiting a complex signal sample x(k) = a(k)+jb(k) to produce a limited signal sample xiim(k), comprising the steps of: determining a ratio r which has a magnitude less than one and which in a first case is equal to b(k)/a(k) and in a second case is equal to a(k)/b(k); determining a variable p with a magnitude equal to l/V(l+r 2 ); and determining a complex value equal to sgn(a(k))p(l + jr) in the first case and equal to sgn(b(k))p(r + j) in the second case to constitute the limited signal sample xii m (k). The invention also provides a method of reducing co-channel interference in a frequency modulated signal, comprising the steps of: sampling the frequency modulated signal to produce signal samples represented by a complex number a(k)+jb(k) where a and b are real numbers and k is an integer which identifies each sample; and limiting each sample to produce a limited output signal sample by the steps of: determining a ratio r which has a magnitude less than one and which in a first case is equal to b(k)/a(k) and in a second case is equal to a(k)/b(k); determining a variable p with a magnitude equal to l/v(l+r 2 ); and determining a number equal to sgn(a(k))p(l + jr) in the first case and equal to sgn(b(k))p(r + j) in the second case representing the limited ouφut signal sample. Preferably the variable p is determined from a look-up table in dependence upon the ratio r. Another aspect of this invention provides a complex signal sample limiter responsive to a complex input signal sample x(k) = a(k)+jb(k) to produce a limited ouφut signal sample, comprising a digital signal processor programmed and arranged to: determine a ratio r which has a magnitude less than one and which in a first case is equal to b(k)/a(k) and in a second case is equal to a(k)/b(k); determine a variable p with a magnitude equal to l/V(l+r 2 ); and determine a complex value equal to sgn(a(k))p(l + jr) ia the first case and equal to sgn(b(k))p(r + j) in the second case to constitute the limited ouφut signal sample. The invention further provides apparatus for reducing co-channel interference in a frequency modulated signal, comprising: a sampler for sampling the frequency modulated signal to produce signal samples represented by a complex number a(k)+jb(k) where a and b are real numbers and k is an integer which identifies each sample; and a limiter for limiting each sample to produce a limited ouφut signal sample, the limiter comprising a digital signal processor which is programmed and arranged to: determine a ratio r which has a magnitude less than one and which in a first case is equal to b(k)/a(k) and in a second case is equal to a(k)/b(k); determine a variable p with a magnitude equal to l/V(l+r 2 ); and determine a number equal to sgn(a(k))p(l + jr) in the first case and equal to sgn(b(k))p(r + j) in the second case representing the limited ouφut signal sample. Preferably the digital signal processor is programmed and arranged to determine the variable p from a look-up table in dependence upon the ratio r. Brief Description of the Drawings The invention will be further understood from the following description with reference to the accompanying drawings, in which: Fig. 1 illustrates a block diagram of part of a wireless digital communications receiver including a complex signal limiter in accordance with this invention; and Fig. 2 is a flow chart illustrating steps of the complex signal limiting method of the invention. Detailed Description Referring to Fig. 1, a block diagram illustrates parts of a wireless communications receiver, in which an FM communications signal is received by an RF (radio frequency) receiver circuit and down converter 10 to produce a signal which is sampled and the samples converted into digital form by a sampler and A-D (analog-to-digital) converter 11. For reducing co-channel interference (CCI) signals which are within the bandwidth of the desired signal, the digital samples are supplied to a complex signal limiter 12. The ouφut of the complex signal limiter 12 is supplied, optionally via further CCI reducing units, to an FM demodulator (not shown). Where the receiver system is part of a cellular radio communications system, the CCI may for example be due to frequency reuse in other cells of the system, and/or it may originate from sources extemal to the communications system. The complex signal limiter 12 is implemented in a DSP (digital signal processor) integrated circuit, which desirably also implements other processing functions in the receiver system. As explained in the introduction, the complex signal limiter 12 serves to produce an ouφut sample xii (k) from each input sample x(k) in accordance with the function x lim (k) = i . ., |x(k)| As described below, the complex signal limiter 12 determines this function in accordance with this invention in a manner which is particularly convenient to implement in the DSP, using much less processing time than is required for a conventional calculation of this function. Using Cartesian and polar forms for x(k) gives: x(k) = a + jb = Re jφ Consequentiy, the invention recognizes that the above function of the complex signal limiter 12 can be expressed in the following two forms: x lim(k) = + jtan(φ(k)))cos(φ(k)) (1) In addition, it is recognized in conjunction with equation (1) that and in conjunction with equation (2) that From the similar form of the equations (3) and (4), the invention recognizes that the relationship between cos(φ(k)) and the ratio b(k)/a(k) (i.e. tan(φ(k))) for values of this ratio between 0 and 1 is exactly the same as the relationship between sin(φ(k)) and the ratio a(k)/b(k) (i.e. cot(φ(k))) for values of this ratio between 0 and 1. Thus the same calculation or, more desirably, a single look-up table can be used to determine either cos(φ(k)) from the ratio b(k)/a(k) or sin(φ(k)) from the ratio a(k)/b(k). Furthermore, the invention recognizes that the sign of cos(φ(k)) is the same as the sign of a(k), and that the sign of sin(φ(k)) is the same as the sign of b(k). Combining all of these recognitions, the method of the invention comprises the steps shown in the flow chart of Fig. 2 to determine the ouφut of the complex signal limiter 12. As indicated above, these steps are all carried out by a DSP which implements the complex signal limiter 12. Referring to Fig. 2, the DSP determines in a decision block 13 whether the magnitude of the real part a(k) of the complex signal sample x(k) is greater than the magnitude of the imaginary part b(k), if so calculates in a block 14 the ratio b(k)/a(k) which represents tan(<p(k)), and if not calculates in a block 15 the ratio a(k)/b(k) which represents cot(φ(k)). It is observed that this corresponds to a conventional division in a DSP, in which the numerator and denominator are interchanged to provide a division result in the range from 0 to 1. The DSP then performs a table look-up as shown by a block 16 of the magnitude of cos(φ(k)) using the ratio b(k)/a(k) for the former case when this ratio is less than one, or as shown by a block 17 of the magnitude of sin(φ(k)) using the ratio a(k)/b(k) for the latter case when this ratio is less than one. As indicated above, the table look-ups represented by both of the blocks 16 and 17 are identical processes using a single look up table. The input ratio to the look-up table is in the range from 0 to 1, and the ouφut is a number in the range from 1 down to 1/V2. In the former case, the DSP determines in a block 18 the sign of cos(φ(k)) as being the same as the sign of a(k), so that cos(φ(k)) = sgn(a(k)) lcos(φ(k))l, and in the latter case the DSP determines in a block 19 the sign of sin(φ(k)) as being the same as the sign of b(k), so that sin(φ(k)) = sgn(b(k)) lsin(φ(k))l. Finally, in the former case the DSP performs the calculation in equation (1) above to determine the complex value of xii m (k) from the determined values of tan(φ(k)) and cos(φ(k)), and in the latter case the DSP performs the calculation in equation (2) above to determine the complex value of xii m (k) from the determined values of cot(φ(k)) and sin(φ(k)). It can be seen that, if r is a ratio whose magnitude is less than or equal to one and which is equal to b(k)/a(k) in the former case and a(k)/b(k) in the latter case, and if p is a variable equal to l V(l+r 2 ) and hence corresponding to equations (3) and (4) above, then equations (1) and (2) above can be rewritten without using trigonometric functions as equations (la) and (2a) below. For la(k)l > lb(k)l, x lim (k) = sgn(a(k))p(l + jr) (la) For la(k)l < lb(k)l, x lim (k) = sgn(b(k))p(r + j) (2a) It can be appreciated from the description above that this invention enables a DSP to provide the function of the complex signal limiter 12 with minimal processing and memory resources. It should be appreciated that numerous changes, variations, and adaptations may be made to the particular embodiment of the invention described above without departing from the scope of the invention as defined in the claims.

Claims: WHAT IS CLAIMED IS: 1. A method of limiting a complex signal sample x(k) = a(k)+jb(k) to produce a limited signal sample xiim(k), comprising the steps of: determining a ratio r which has a magnitude less than one and which in a first case is equal to b(k)/a(k) and in a second case is equal to a(k)/b(k); determining a variable p with a magnitude equal to l/V(l+r 2 ); and determining a complex value equal to sgn(a(k))p(l + jr) in the first case and equal to sgn(b(k))p(r + j) in the second case to constitute the limited signal sample xii m (k). 2. A method as claimed in claim 1 wherein the variable p is determined from a look- up table in dependence upon the ratio r. 3. A method of reducing co-channel interference in a frequency modulated signal, comprising the steps of: sampling the frequency modulated signal to produce signal samples represented by a complex number a(k)+jb(k) where a and b are real numbers and k is an integer which identifies each sample; and limiting each sample to produce a limited ouφut signal sample by the steps of: determining a ratio r which has a magnitude less than one and which in a first case is equal to b(k)/a(k) and in a second case is equal to a(k)/b(k); determining a variable p with a magnitude equal to l/V(l+r 2 ); and determining a number equal to sgn(a(k))p(l + jr) in the first case and equal to sgn(b(k))p(r + j) in the second case representing the limited ouφut signal sample. 4. A method as claimed in claim 3 wherein the variable p is determined from a look¬ up table in dependence upon the ratio r. 5. A complex signal sample limiter responsive to a complex input signal sample x(k) = a(k)+jb(k) to produce a limited ouφut signal sample, comprising a digital signal processor programmed and arranged to: determine a ratio r which has a magnitude less than one and which in a first case is equal to b(k)/a(k) and in a second case is equal to a(k)/b(k); determine a variable p with a magnitude equal to l/ (l+r 2 ); and determine a complex value equal to sgn(a(k))p(l + jr) in the first case and equal to sgn(b(k))p(r + j) in the second case to constitute the limited ouφut signal sample. 6. A complex signal sample limiter as claimed in claim 5 wherein the digital signal processor is programmed and arranged to determine the variable p from a look-up table in dependence upon the ratio r. 7. Apparatus for reducing co-channel interference in a frequency modulated signal, comprising: a sampler for sampling the frequency modulated signal to produce signal samples represented by a complex number a(k)+jb(k) where a and b are real numbers and k is an integer which identifies each sample; and a limiter for limiting each sample to produce a limited ouφut signal sample, the limiter comprising a digital signal processor which is programmed and arranged to: determine a ratio r which has a magnitude less than one and which in a first case is equal to b(k)/a(k) and in a second case is equal to a(k)/b(k); determine a variable p with a magnitude equal to l/V(l+r 2 ); and determine a number equal to sgn(a(k))p(l + jr) in the first case and equal to sgn(b(k))p(r + j) in the second case representing the limited ouφut signal sample. 8. Apparatus as claimed in claim 7 wherein the digital signal processor is programmed and arranged to determine the variable p from a look-up table in dependence upon the ratio r.

Inventors: TONG WEN, WANG RUI, TONG, WEN, WANG, RUI
Applicants: NORTHERN TELECOM LTD, NORTHERN TELECOM LIMITED
Application year: 1996
Main classification: G06F1
IPC codes: G06F1, G06F7, H03G11, H04B1