# Patent

## Title
Code synchronization in CDMA satellite wireless communications system using uplink channel detection

## Abstract

An uplink signal transmitted by a terminal is received by a satellite wireless communications system. The uplink signal includes a known information element, e.g., a reverse access channel (R-ACH) preamble, spread according to a spreading code specific to a component of a satellite wireless communications system, e.g., a pseudonoise (PN) sequence associated with a satellite beam. A correlation of the received uplink signal with the spreading code over a range of time shifts is determined. The known information element is detected from the determined correlation. The satellite wireless communications system is synchronized with the terminal responsive to detection of the known information element. For example, a delay may be assigned to a receiver of the satellite wireless communications system responsive to detection of the known information element.

## Background
RELATED APPLICATION
The present application claims priority from U.S. Provisional Application Ser. No. 60/551,526, entitled CDMA Code Synchronization Over Satellite Return Path, filed Mar. 9, 2004 and incorporated herein by reference in its entirety.


FIELD OF THE INVENTION
This invention relates to wireless communications systems and methods, and more particularly to satellite wireless communications systems and methods.
BACKGROUND OF THE INVENTION
CDMA cellular systems (such as IS-95 and CDMA2000 systems) typically require relatively precise timing between a base station and a mobile terminal (MT) to maintain proper synchronization. The MT downloads system timing information from the base transceiver station (BTS), and uses this to set the timing offset of its internal spreading code generators. At the BTS, the RAKE receiver adjusts its internally generated pseudonoise (PN) code offset to match that of the MT. Since terrestrial cells are typically about 1 km in radius, the path delay uncertainty between the MT and BTS typically requires a search range of a few chip periods for the gateway receiver to precisely synchronize to the MT's spreading code.
Compared to the terrestrial environment, CDMA operation using a satellite may introduce a much longer path delay, and also a much greater delay variability due to the larger spot beam coverage areas. For example, beam sizes typical of geosynchronous mobile communications satellites may produce a round-trip delay dispersion on the order of 5 msec within beams located over the northern continental United States (CONUS). Given a CDMA chip period of 0.814 msec, this may require the gateway receiver (or other portion of the satellite system that processes signals from MTs) to search over more than ±3000 chips to synchronize, which may be beyond the capability of conventional receivers.
SUMMARY OF THE INVENTION
In some embodiments of the present invention, methods of synchronizing a satellite wireless communications system with a terminal are provided. An uplink signal transmitted by the terminal is received, the uplink signal including a known information element, e.g., a reverse access channel (R-ACH) preamble, spread according to a spreading code specific to a component of a satellite wireless communications system, e.g., a pseudonoise (PN) sequence associated with a satellite beam. A correlation of the received uplink signal with the spreading code over a range of time shifts is determined. The known information element is detected from the determined correlation. The satellite wireless communications system is synchronized with the terminal responsive to detection of the known information element. For example, a delay may be assigned to a RAKE or other type CDMA receiver used in the satellite wireless communications system responsive to detection of the known information element.
In some embodiments, determining a correlation of the received uplink signal with the spreading code over a range of time shifts may include generating respective sets of correlation measures for respective ones of a plurality of time segments, the sets of correlation measures including respective correlation measures for respective time shifts of the range of time shift, and averaging the correlation measures for the respective time shifts over the plurality of sets of correlation measures to generate a set of average correlation measures. Detecting the known information element from the determined correlation may include detecting a peak value in the set of average correlation measures. Generating respective sets of correlation measures for respective ones of a plurality of time segments may include correlating respective sets of samples of the received uplink signal for the respective time segments with multiple time shifts of the spreading code to generate respective sets of correlation values (e.g., using a fast Fourier transform (FFT) correlator), and generating respective sets of magnitude measures for the respective time segments from the respective sets of correlation values. Averaging the correlation measures for the respective time shifts over the plurality of sets of correlation measures may include averaging the magnitude measures for the respective time shifts over the sets of magnitude measures to generate the set of average correlation measures.
In further embodiments of the present invention, a radio signal is received at a satellite wireless communications system. A preamble of a transmitted R-ACH message in the received radio signal is detected. The satellite wireless communications system is synchronized with a terminal that transmitted the R-ACH message responsive to detection of the preamble of the R-ACH message. Detection of the preamble of the transmitted R-ACH message may include determining a correlation of the received radio signal with a reference PN sequence and detecting the preamble of a transmitted R-ACH message from the determined correlation.
According to additional embodiments of the present invention, an apparatus is provided for synchronizing a satellite wireless communications system with a terminal that transmits an uplink signal including a known information element spread according to a spreading code specific to a component of a satellite wireless communications system. The apparatus includes a receiver configured to receive the uplink signal transmitted by the terminal, to determine a correlation of the received uplink signal with the spreading code over a range of time shifts, to detect the known information element from the determined correlation and to synchronize with the terminal responsive to detection of the known information element. In yet further embodiments, an apparatus for synchronizing a satellite wireless communications system with a terminal includes a receiver configured to receive a radio signal at the satellite wireless communications system, to detect a preamble of a R-ACH message transmitted by a terminal and to synchronize with the terminal responsive to detection of the preamble of the R-ACH message.
In further embodiments, a satellite wireless communications system includes a satellite configured to receive an uplink signal from a terminal, the uplink signal including a known information element spread according to a spreading code specific to a component of a satellite wireless communications system. The system further includes means for determining a correlation of the received uplink signal with the spreading code over a range of time shifts, means for detecting the known information element from the determined correlation and means for synchronizing with the terminal responsive to detection of the known information element. In additional embodiments, a satellite wireless communications system includes a satellite configured to receive radio signal from a terminal, means for detecting a preamble of a R-ACH message transmitted by a terminal from the radio signal, and means for synchronizing with the terminal responsive to detection of the preamble of the R-ACH message.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates a format of a conventional random access channel (R-ACH) message.
FIG. 2 is a schematic diagram illustrating exemplary spread-spectrum encoding in a conventional wireless communications system.
FIG. 3 is a schematic diagram illustrating generation of vectors of radio signal samples according to some embodiments of the present invention.
FIG. 4 is a schematic diagram illustrating generation of correlation measures according to further embodiments of the present invention.
FIG. 5 is a graph illustrating probabilities of missed and false detection of a R-ACH preamble according to some embodiments of the present invention.
FIG. 6 is a schematic diagram illustrating detection of a R-ACH preamble and control of a RAKE receiver according to some embodiments of the present invention.
FIG. 7 is a graph illustrating error probabilities as a function of number of correlated time segments according to further embodiments of the present invention.
FIGS. 8 and 9 are schematic diagrams of satellite wireless communications systems according to further embodiments of the present invention.



DETAILED DESCRIPTION
Specific exemplary embodiments of the invention now will be described with reference to the accompanying drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, like numbers refer to like elements. It will be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. Furthermore, “connected” or “coupled” as used herein may include wirelessly connected or coupled. As used herein the term “and/or” includes any and all combinations of one or more of the associated listed items.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless expressly stated otherwise. It will be further understood that the terms “includes,” “comprises,” “including” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
As used herein, a “wireless terminal” includes cellular and/or satellite communications devices with or without a multi-line display; Personal Communications System (PCS) terminals that may combine a voice and data processing, facsimile and/or data communications capabilities; Personal Digital Assistants (PDA) that can include a radio frequency transceiver and a pager, Internet/Intranet access, Web browser, organizer, calendar and/or a global positioning system (GPS) receiver; and/or conventional laptop and/or palmtop computers or other appliances, which include a radio frequency transceiver. As used herein, “wireless terminal” also includes “mobile terminals” that may be portable, transportable, installed in a vehicle (aeronautical, maritime, or land-based), or situated and/or configured to operate locally and/or in a distributed fashion at any other location(s) on earth and/or in space, as well as terminals designed for operation from a fixed location.
According to some exemplary embodiments of the invention, rapid code synchronization over a wide range of satellite path delays may be provided by searching for a unique information element in a spread-spectrum satellite uplink signal. For example, the known information element may include a PN-sequence transmitted during the preamble of an MT's Reverse Access Channel (R-ACH) transmission. Exemplary embodiments using detection of a PN-sequence in R-ACH transmission of a MT communicating according to IS-95 or CDMA2000 protocols will now be described, but those skilled in the art will appreciate that techniques described herein may be extended to other transmission formats within the scope of the present invention.
The structure of an MT's exemplary R-ACH transmission 100 compliant with IS-95 and CDMA2000 protocols is shown in FIG. 1. It includes an access channel preamble 110 of all-zero bits followed by a message capsule 120 transmitted at an information rate of 4800 bps. For example, the length of the preamble 110 may be an integer number equal to (1+PAM_SZs) 20-msec. frames, where the parameter PAM_SZs is downloaded to the MT from the BTS, and is therefore network-configurable.
The preamble and message capsule bits in FIG. 1 may be processed through a series of encoding and interleaving steps that increase the raw symbol rate to, in the instant example, 307.2 ksps, followed by spreading code modulation that produces the final chip rate of 1.2288 Mcps. However, during preamble transmission, the symbol stream input to the spreader is all zeros, so the process flow may be simplified to the block diagram shown in FIG. 2.
A Long Code 206 produced by a Long Code generator 205 in FIG. 2 is a PN-sequence of length 242−1(≈2.4×1012) bits. For the R-ACH, a Long Code mask 204 used to set the timing offset of the Long Code generator 205 is calculated as a function of BTS-related parameters only, so all MTs use the same Long Code mask 204 for a given R-ACH. A Short Code PN-sequence of 32768 chips overlays the Long Code-modulation but does not produce any additional signal spreading. Different Short Code sequences 207, 208 modulate I- and Q-channels. For all MT transmissions in the instant example, the Short Code offset index is set to zero. The offset indices for the Long and Short Codes 104, 207, 208 are defined with respect to the MT's internal system time, which for satellite operation is delayed from true system time by the amount of the satellite path delay (e.g., around 250 msec.). After Short Code modulation, the resulting signals are mapped to bipolar values (+1) for QPSK modulation.
From FIG. 2, it can be seen that the PN-sequence transmitted during the R-ACH preamble is the modulo-2 sum of the Long and Short Codes (in FIG. 2, the “+” symbols indicate modulo-2 addition). The PN-timing offset observed at the gateway is a function of the MT's PN-generator offset indices (which may be known to the network) plus the unknown path delay between the gateway and the MT. By detecting the R-ACH message preamble at the gateway and measuring the timing offset of its spreading code, the path delay to the transmitting MT can be precisely determined.
In some embodiments of the invention, detecting a R-ACH transmission preamble at a satellite gateway (e.g., via a bent-pipe path through a satellite) involves performing a correlation of the received CDMA signals against a range of R-ACH spreading code timing offsets that could be received from MTs located anywhere within the given spot beam coverage. If each R-ACH uses its own unique Long Code mask, separate correlators may be required for each R-ACH. One possible implementation is described below with reference to FIGS. 3 and 4.
Referring to FIG. 3, the received CDMA signals plus channel noise are down-converted by the nominal carrier frequency coo to complex baseband by a downconverter 310. The I- and Q-components thus produced are then low-pass filtered in a filter 320 to remove image frequency components, yielding a complex baseband input signal y(t). The signal y(t) is then sampled by a sampler 330 at approximately the chipping rate to form a discrete complex sequence y(m). Groups of M complex samples of y(m) may be collected to form time segment vectors vk, where index “k” denotes the “kth” time segment.
The number of samples M in the vector vk may be limited by the maximum Doppler shift of the received MT signals. Any difference between the down-conversion frequency coo and the MT's actual received carrier frequency may produce a phase rotation across the complex samples of vk. When the total phase rotation over the time segment exceeds π radians, the correlation peak should begin to diminish, and at 2π, the peak should disappear. Thus, it may be advantageous to limit the time segment duration to approximately one-half period of the maximum Doppler shift frequency. For a land-mobile case at L-band transmission frequencies, the maximum Doppler shift due to vehicle motion for the instant example may be about 350 Hz, assuming that the MT's local oscillator is locked to the forward carrier, and that the Doppler component due to satellite motion is negligible. Therefore, the time duration of each vk may be limited in this exemplary case to a maximum of about 1.4 msec. At a sampling rate of 1.2288 MHz, this may constrain the maximum value of M to about 1700 time samples.
In FIG. 4, each sample segment vk is correlated with internally generated complex reference sequence gk. A fast Fourier transform (FFT) correlator 410 may be used to maximize computational efficiency. This FFT can use the correspondence between multiplication in the frequency domain and convolution in the time domain to produce a very computationally efficient correlation in some embodiments. The real and imaginary parts of the gk elements correspond to the complex conjugate of the I- and Q-channel PN-sequences transmitted by the MT during the R-ACH preamble, so both I- and Q-channels can be processed simultaneously. While such an FFT-based correlator may be preferred, it will be appreciated that other correlators and/or correlation techniques may be used with the present invention.
For each time segment k, the reference sequence gk may be advanced so that the midway point of the sequence matches the PN-timing offset that would be received from a MT transmitting at the center of the beam footprint. The reference sequence gk preferably spans the full range of possible delay offsets plus the duration of the input segment vk. For the instant example, this requires a total time span of about 6.5 msec., and a total number of samples N equal to about 8000 (sampling at the chipping rate). Setting N=8192 provides a convenient correlator implementation using an 8192-point FFT.
The FFT-correlation process produces an output vector xk whose elements xk(n)(1≦n≦N) correspond to the cross-correlation of input vector vk with the “nth” circular shift of the reference vector gk. The complex elements xk(n) are converted to magnitude-squared values in a magnitude-squared converter 420 to combine the I- and Q-terms. The resulting values are then summed element-by-element over the “K” most recent time segments in a moving averager 430 to produce the vector zk. The presence of a R-ACH preamble should produce a correlation peak at the element zk(n) whose index n matches the PN-timing offset of the received R-ACH preamble. Concurrent R-ACH transmissions should produce multiple peaks, each corresponding to its own timing offset. Since the true correlation peaks should occur at the same offset in each successive |x|2k segment, but false peaks due to noise should change randomly from segment to segment, the moving average process shown in FIG. 4 can enhance the ratio of true-peak to false-peaks in zk.
As shown in FIG. 4, each element in zk includes K elements from the prior |x|2k segments as follows:




  
    
      z
      k
    
    ⁡
    
      (
      n
      )
    
  
  =
  
    
      ∑
      
        j
        =
        
          k
          -
          K
          +
          1
        
      
      k
    
    ⁢
    
      
        
        
          
            x
            j
          
          ⁡
          
            (
            n
            )
          
        
        
      
      2
    
  




FIG. 5 illustrates two possible probability distribution outcomes for zk(n). In the absence of a R-ACH correlation peak, the xj(n) terms are uncorrelated zero-mean random variables, so the sum of squared magnitudes comprising zk(n) produces a chi-squared probability distribution with 2K degrees of freedom (where the factor of 2 comes from the contribution of both real and imaginary parts of xj(n)). If a R-ACH correlation peak occurs at the given offset index “n”, then the xj(n) terms are no longer zero-mean (but they are still uncorrelated), and the probability distribution of zk(n) becomes a non-central chi-squared distribution.
As shown in FIG. 5, a decision threshold zT may be established to provide a desired compromise between missed-detection and false-detection errors. In FIG. 6, such a decision threshold may be applied to each element zk(n) of a vector zk in a decision unit 610. If the R-ACH preamble is detected by the presence of a correlation peak, the decision unit 610 assigns one of a plurality of RAKE receivers 620-1, 620-2, . . . , 620L to that MT's transmission. The index of the correlation peak is used to compute the satellite path delay, which is applied to offset the RAKE receiver's internal PN generator. This can reduce the receiver's search process to a very small number of chip periods around this initial offset. Once code synchronization is achieved, the RAKE receiver may de-spread and demodulate the MT's R-ACH message in a conventional manner. Several RAKE receivers can be assigned to the same R-ACH, because delay dispersion within the satellite beam footprint may allow multiple MTs to transmit simultaneously on the same R-ACH without causing collisions. As a call progresses from set-up to the in-call phase, the path delay PN offset calculated for the MT's R-ACH transmission may be applied to facilitate synchronization to the MT's reverse traffic channel. In this way, the system can compensate for the satellite path delay over the full call duration. It will be appreciated that although the receivers 620-1, 620-2, . . . , 620L are indicated as being RAKE receivers, i.e., receivers capable of processing multiple delay paths, other types of CDMA receivers may be used with the present invention. For example, a single path demodulator may be used in applications that typically have less severe multipath fading, such as satellite applications.
A probability analysis that indicates how rapidly the correlation method described above can reliably detect a R-ACH preamble according to some embodiments of the invention will now be described. It will be understood that this analysis provides a theoretical explanation pointing to potential advantages of some embodiments of the present invention, and does not limit the present invention to the mathematical models and/or assumptions described in the analysis.
Probability Analysis of an Exemplary R-ACH Preamble Detection Method
Some simplifying assumptions for an analytical model may include:


    
    
        1. Sampling rate=chip rate (1.2288 MHz);
        2. Optimum sampling=No intersymbol interference (ISI);
        3. Co-frequency CDMA interference modeled as additive white Gaussian noise (AWGN);
        4. No received Doppler shift of desired MT signal;
        5. Noise+interference assumed statistically independent between time samples; and
        6. MT's transmission is modeled as quaternary phase shift keying (QPSK).

Referring to FIG. 3, define the received RF signal plus noise r(t) as:

r(t)=s(t)+w(t)  (1)

where

        s(t)=desired CDMA R-ACH preamble signal.
        w(t)=aggregate CDMA self-interference plus channel noise, modeled as AWGN.

The desired signal s(t) may be modeled as:

s(t)=sI(t)cos(ω0t+θ)+sQ(t)sin(ω0t+θ)  (2)

where:

        sI(t)=I-channel PN spreading modulation (±1);
        sQ(t)=Q-channel PN spreading modulation (±1);
        θ=arbitrary received phase angle (constant); and
        ω0=received carrier frequency.

PN-sequences sI(t) and sQ(t) may be modeled as zero-mean random processes with variance=1.

    
    


Letting C represent the power in s(t), it follows from equation (2) that:




  
    
      
        C
        =
        
          
            
              lim
              
                T
                ->
                ∞
              
            
            ⁢
            
              
                1
                T
              
              ⁢
              
                
                  ∫
                  0
                  T
                
                ⁢
                
                  
                    
                      s
                      2
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                  ⁢
                  
                    d
                    t
                  
                
              
            
          
          =
          1.
        
      
    
    
      
        (
        3
        )
      
    
  




Using quadrature noise representation for the aggregate interference and thermal noise term w(t):

w(t)=wc(t)cos(ω0t)+ws(t)sin(ω0t)  (4)

where wc(t) and ws(t) are statistically independent normal random processes with mean μ=0 and variance σw2. Letting I represent the time average power of w(t), then:

σw2=I  (5)

Forming the product 2r(t)ejω0t (complex down-conversion), low-pass filtering to remove double-frequency terms, and sampling at the chip rate produces a discrete-time complex baseband sequence y(m). It can be shown that the expression for y(m) is given by:

y(m)=ejθ[sI(m)−jsQ(m)]+wc(m)−jws(m),  (6)

where sI(m), sQ(m), wc(m), and ws(m) are modeled as statistically independent zero-mean random variables having variances 1, 1, I, and I, respectively.

Sequence y(m) may be divided into time segments, each containing M samples, where vector vk represents the “kth” segment, containing samples y(kM) through y([k+1]M−1).
Referring to FIG. 4, letting g(n) denote the receiver's internal reference sequence, defined as the complex conjugate of the R-ACH PN-sequence that would be received from a MT transmitting from the middle of the beam footprint, yields:

g(m)=i(m)+jq(m)  (7)

where:

    
    
        i(m)=I-channel reference PN-sequence (±1), synchronized to beam mid-point; and
        q(m)=Q-channel reference PN-sequence (±1), synchronized to beam mid-point.

For each input segment vk, a reference code vector gk may be generated having N=2D+M elements, where ±D is the maximum code search offset relative to the beam mid-point.

    
    


Defining xk(n) as the correlation of input vector vk with an offset version of gk that is time-shifted by n samples yields:




  
    
      
        
          
            x
            k
          
          ⁡
          
            (
            n
            )
          
        
        =
        
          
            ∑
            
              m
              =
              kM
            
            
              
                
                  (
                  
                    k
                    +
                    1
                  
                  )
                
                ⁢
                M
              
              -
              1
            
          
          ⁢
          
            
              y
              ⁡
              
                (
                m
                )
              
            
            ⁢
            
              g
              ⁡
              
                (
                
                  n
                  +
                  m
                
                )
              
            
          
        
      
    
    
      
        (
        8
        )
      
    
  




In evaluating (8), two cases may be considered as follows.

Case 1: Offset Index n is Aligned with Received R-ACH Preamble PN-offset

In this case, the reference sequence g(n+m) is aligned with the received R-ACH preamble PN-sequences sI(m) and sQ(m) in vk, such that:

i(n+m)=sI(m)  (9)

q(n+m)=sQ(m)  (10)

Substituting equations (6) and (7) into equation (8), with sI(m) and sQ(m) replacing i(n+m) and q(n+m), yields:





  
    
      
        
          
            x
            k
          
          ⁡
          
            (
            n
            )
          
        
        =
        
          
            ∑
            
              m
              =
              kM
            
            
              
                
                  (
                  
                    k
                    +
                    1
                  
                  )
                
                ⁢
                M
              
              -
              1
            
          
          ⁢
          
            
              
                {
                
                  
                    
                      e
                      
                        j
                        ⁢
                        
                          
                        
                        ⁢
                        θ
                      
                    
                    ⁡
                    
                      [
                      
                        
                          
                            s
                            I
                          
                          ⁡
                          
                            (
                            m
                            )
                          
                        
                        -
                        
                          
                            js
                            Q
                          
                          ⁡
                          
                            (
                            m
                            )
                          
                        
                      
                      ]
                    
                  
                  +
                  
                    
                      w
                      c
                    
                    ⁡
                    
                      (
                      m
                      )
                    
                  
                  -
                  
                    
                      jw
                      s
                    
                    ⁡
                    
                      (
                      m
                      )
                    
                  
                
                }
              
              ⁡
              
                [
                
                  
                    
                      s
                      i
                    
                    ⁡
                    
                      (
                      m
                      )
                    
                  
                  +
                  
                    
                      js
                      Q
                    
                    ⁡
                    
                      (
                      m
                      )
                    
                  
                
                ]
              
            
            .
          
        
      
    
    
      
        (
        11
        )
      
    
  




Multiplying out the factors in equation (11) and simplifying yields:




  
    
      
        
          
            x
            k
          
          ⁡
          
            (
            n
            )
          
        
        =
        
          
            2
            ⁢
            M
            ⁢
            
              
            
            ⁢
            
              e
              
                
                  
                
                ⁢
                
                  j
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
              
            
          
          +
          
            
              ∑
              
                m
                =
                kM
              
              
                
                  
                    (
                    
                      k
                      +
                      1
                    
                    )
                  
                  ⁢
                  M
                
                -
                1
              
            
            ⁢
            
              
                
                  s
                  I
                
                ⁡
                
                  (
                  m
                  )
                
              
              ⁢
              
                
                  w
                  c
                
                ⁡
                
                  (
                  m
                  )
                
              
            
          
          -
          
            
              
                js
                Q
              
              ⁡
              
                (
                m
                )
              
            
            ⁢
            
              
                w
                c
              
              ⁡
              
                (
                m
                )
              
            
          
          -
          
            
              
                js
                I
              
              ⁡
              
                (
                m
                )
              
            
            ⁢
            
              
                w
                s
              
              ⁡
              
                (
                m
                )
              
            
          
          -
          
            
              
                s
                Q
              
              ⁡
              
                (
                m
                )
              
            
            ⁢
            
              
                
                  w
                  s
                
                ⁡
                
                  (
                  m
                  )
                
              
              .
            
          
        
      
    
    
      
        (
        12
        )
      
    
  




Collecting the real and imaginary terms in equation (12) together yields:




  
    
      
        
          
            
              x
              k
            
            ⁡
            
              (
              n
              )
            
          
          =
          
            
              
                w
                k
                ′′
              
              ⁢
              
                
                   
                  Re
                
                ⁢
                
                  (
                  n
                  )
                
              
            
            +
            
              
                jw
                k
                ′′
              
              ⁢
              
                
                   
                  Im
                
                ⁢
                
                  (
                  n
                  )
                
              
            
          
        
        ,
        
          where
          ⁢
          
            :
          
        
      
    
    
      
        (
        13
        )
      
    
  
  
    
      
        
          
            
              w
              k
              ′′
            
            ⁢
            
              
                 
                Re
              
              ⁢
              
                (
                n
                )
              
            
          
          =
          
            
              2
              ⁢
              M
              ⁢
              
                
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              θ
            
            +
            
              
                ∑
                
                  m
                  =
                  kM
                
                
                  
                    
                      (
                      
                        k
                        +
                        1
                      
                      )
                    
                    ⁢
                    M
                  
                  -
                  1
                
              
              ⁢
              
                
                  
                    s
                    I
                  
                  ⁡
                  
                    (
                    m
                    )
                  
                
                ⁢
                
                  
                    w
                    c
                  
                  ⁡
                  
                    (
                    m
                    )
                  
                
              
            
            -
            
              
                
                  s
                  Q
                
                ⁡
                
                  (
                  m
                  )
                
              
              ⁢
              
                
                  w
                  s
                
                ⁡
                
                  (
                  m
                  )
                
              
            
          
        
        ,
        and
      
    
    
      
        (
        14
        )
      
    
  
  
    
      
        
          
            w
            k
            ′′
          
          ⁢
          
            
               
              Im
            
            ⁢
            
              (
              n
              )
            
          
        
        =
        
          
            2
            ⁢
            M
            ⁢
            
              
            
            ⁢
            sin
            ⁢
            
              
            
            ⁢
            θ
          
          +
          
            
              ∑
              
                m
                =
                kM
              
              
                
                  
                    (
                    
                      k
                      +
                      1
                    
                    )
                  
                  ⁢
                  M
                
                -
                1
              
            
            ⁢
            
              
                
                  s
                  Q
                
                ⁡
                
                  (
                  m
                  )
                
              
              ⁢
              
                
                  w
                  c
                
                ⁡
                
                  (
                  m
                  )
                
              
            
          
          +
          
            
              
                s
                I
              
              ⁡
              
                (
                m
                )
              
            
            ⁢
            
              
                
                  w
                  s
                
                ⁡
                
                  (
                  m
                  )
                
              
              .
            
          
        
      
    
    
      
        (
        15
        )
      
    
  




It may be recalled that wc(m) and ws(m) are zero-mean normal random variables having variance I, and are statistically independent for all values of “m,” and that sI(m) and sQ(m) are independent zero-mean random variables that take on values of ±1. Then, it follows from equations (14) and (15) that wk′′Re(n) and wk′′Im(n) are also normal random variables having the following properties:

wk′′Re(n) ̃μ=2M cos θ,σ2=2MI); and  (16)

wk′′Im(n) ̃μ=2M sin θ,σ2=2MI).  (17)

Case 2: Offset Index n is Not Aligned with Received R-ACH Preamble PN-offset:

In this case, the reference sequences i(n+m) and q(n+m) are uncorrelated with received PN-sequences sI(m) and sQ(m). Consequently, the analysis can be simplified by approximating both signal and noise terms in y(m) by an equivalent AWGN process as follows:

y(m)≈wc′(m)−jws′(m),  (18)

    
    
        where:

wc′(m)=sI(m)+wc(m); and  (19)

ws′(m)=sQ(m)+ws(m)  (20)

In a CDMA channel, the received power of the noise+self-interference terms, represented by wc(m) and ws(m), is typically much greater than the desired signal power, represented by sI(m) and sQ(m). Thus, the summations in equations (19) and (20) may still be approximately Gaussian. Therefore, wc′(m) and ws′(m) can be modeled as normal random variables, having variances equal to the sum of the component variances:

wc′(m) ̃μ=0, σ2=I+1); and  (21)

ws′(m) ̃μ=0, σ2=I+1).  (22)

Substituting equations (18) and (7) into equation (8) yields:

    
    






  
    
      
        
          
            x
            k
          
          ⁡
          
            (
            n
            )
          
        
        =
        
          
            ∑
            
              m
              =
              kM
            
            
              
                
                  (
                  
                    k
                    +
                    1
                  
                  )
                
                ⁢
                M
              
              -
              1
            
          
          ⁢
          
            
              [
              
                
                  
                    w
                    c
                    ′
                  
                  ⁡
                  
                    (
                    m
                    )
                  
                
                -
                
                  
                    jw
                    s
                    ′
                  
                  ⁡
                  
                    (
                    m
                    )
                  
                
              
              ]
            
            ⁡
            
              [
              
                
                  i
                  ⁡
                  
                    (
                    
                      n
                      +
                      m
                    
                    )
                  
                
                +
                
                  jq
                  ⁡
                  
                    (
                    
                      n
                      +
                      m
                    
                    )
                  
                
              
              ]
            
          
        
      
    
    
      
        (
        23
        )
      
    
  




As with Case 1, the product terms in equation (23) can be collected into a single real and imaginary terms as follows:




  
    
      
        
          
            
              
                x
                k
              
              ⁡
              
                (
                n
                )
              
            
            =
            
              
                
                  w
                  k
                  ′
                
                ⁢
                
                  
                     
                    Re
                  
                  ⁢
                  
                    (
                    n
                    )
                  
                
              
              +
              
                
                  jw
                  k
                  ′
                
                ⁢
                
                  
                     
                    Im
                  
                  ⁢
                  
                    (
                    n
                    )
                  
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            where
            ⁢
            
              :
            
          
        
        ⁢
        
          
        
      
    
    
      
        (
        24
        )
      
    
  
  
    
      
        
          
            
              w
              k
              ′
            
            ⁢
            
              
                 
                Re
              
              ⁢
              
                (
                n
                )
              
            
          
          =
          
            
              
                ∑
                
                  m
                  =
                  kM
                
                
                  
                    
                      (
                      
                        k
                        +
                        1
                      
                      )
                    
                    ⁢
                    M
                  
                  -
                  1
                
              
              ⁢
              
                
                  
                    w
                    c
                    ′
                  
                  ⁡
                  
                    (
                    m
                    )
                  
                
                ⁢
                
                  i
                  ⁡
                  
                    (
                    
                      n
                      +
                      m
                    
                    )
                  
                
              
            
            +
            
              
                
                  w
                  s
                  ′
                
                ⁡
                
                  (
                  m
                  )
                
              
              ⁢
              
                q
                ⁡
                
                  (
                  
                    n
                    +
                    m
                  
                  )
                
              
            
          
        
        ;
        and
      
    
    
      
        (
        25
        )
      
    
  
  
    
      
        
          
            w
            k
            ′
          
          ⁢
          
            
               
              Im
            
            ⁢
            
              (
              n
              )
            
          
        
        =
        
          
            
              ∑
              
                m
                =
                kM
              
              
                
                  
                    (
                    
                      k
                      +
                      1
                    
                    )
                  
                  ⁢
                  M
                
                -
                1
              
            
            ⁢
            
              
                
                  w
                  c
                  ′
                
                ⁡
                
                  (
                  m
                  )
                
              
              ⁢
              
                q
                ⁡
                
                  (
                  
                    n
                    +
                    m
                  
                  )
                
              
            
          
          -
          
            
              
                w
                s
                ′
              
              ⁡
              
                (
                m
                )
              
            
            ⁢
            
              
                i
                ⁡
                
                  (
                  
                    n
                    +
                    m
                  
                  )
                
              
              .
            
          
        
      
    
    
      
        (
        26
        )
      
    
  




Using similar arguments to those for Case #1, wk′Re(n) and wk′Im(n) can be modeled as normal random variables having the following properties:

wk′′Re(n) ̃(μ=0, σ2=2M[I+1]); and  (27)

wk′Im(n) ̃(μ=0, σ2=2M[I+1])  (28)

Having derived expressions for xk(n) in (13) and (24) corresponding to Case #1 and Case #2, respectively, these complex terms can be converted to magnitude-squared values, and then summed over the prior K time segments to produce:





  
    
      
        
          
            
              
                z
                k
              
              ⁡
              
                (
                n
                )
              
            
            =
            
              
                ∑
                
                  j
                  =
                  
                    k
                    -
                    K
                    +
                    1
                  
                
                k
              
              ⁢
              
                
                  
                  
                    
                      x
                      j
                    
                    ⁡
                    
                      (
                      n
                      )
                    
                  
                  
                
                2
              
            
          
          ,
          
            

          
          ⁢
          
            where
            ⁢
            
              :
            
          
        
        ⁢
        
          
        
      
    
    
      
        (
        29
        )
      
    
  
  
    
      
        
          
            
            
              
                x
                j
              
              ⁢
              
                (
                n
                )
              
            
            
          
          2
        
        =
        
          
            
              x
              j
            
            ⁡
            
              (
              n
              )
            
          
          ⁢
          
            
              
                x
                j
              
              ⁡
              
                (
                n
                )
              
            
            *
          
        
      
    
    
      
        (
        30
        )
      
    
  




The two possible outcomes can be treated separately, as follows.
Case 1: Offset Index “n” Aligned with Received R-ACH Preamble PN-offset
For this case, equation (13) provides an applicable expression for xk(n). Then:

|xj(n)|2=wj′′Re2(n)+wj′′Im2(n)  (31)

For the derivation that follows, the random variables wj′′Re(n) and wj′′Im(n) are treated as being statistically independent. This may be the case between different time segments j, but may not be rigorously correct within the same time segment. This is because both wj′′Re(n) and wj′′Im(n) share the same component terms, but multiplied in different combinations as shown in equations (14) and (15). However, since there are a large number of product terms comprising wj′′Re(n) and wj′′Im(n), and these product terms are uniquely different between the two random variables, it is expected that wj′′Re(n) and wj′′Im(n) will appear uncorrelated, so that the independence assumption appears reasonable.

Substituting equation (31) into equation (29) yields:




  
    
      
        
          
            z
            k
          
          ⁡
          
            (
            n
            )
          
        
        =
        
          
            ∑
            
              j
              =
              
                k
                -
                K
                +
                1
              
            
            k
          
          ⁢
          
            
              [
              
                
                  
                    w
                    j
                    ′′
                  
                  ⁢
                  
                    
                       
                      Re
                      2
                    
                    ⁢
                    
                      (
                      n
                      )
                    
                  
                
                +
                
                  
                    w
                    j
                    ′′
                  
                  ⁢
                  
                    
                       
                      Im
                      2
                    
                    ⁢
                    
                      (
                      n
                      )
                    
                  
                
              
              ]
            
            .
          
        
      
    
    
      
        (
        32
        )
      
    
  




Assuming statistical independence of the wj′′Re(n) and wj′′Im(n) terms, then the sum-of-squares in equation (32) produces a non-central chi-squared probability distribution with 2K degrees-of-freedom. The distribution is “non-central” because the component wj′′Re(n) and wjΔIm(n) terms are not zero-mean, as shown in equations (16) and (17). The “non-centrality parameter” λ for this distribution is defined as:





  
    
      
        
          λ
          =
          
            
              ∑
              
                i
                =
                1
              
              
                2
                ⁢
                K
              
            
            ⁢
            
              
                μ
                i
                2
              
              
                σ
                2
              
            
          
        
        ,
      
    
    
      
        (
        33
        )
      
    
  




where μi and σ2 are the mean and variance of the ith random variable term (wj′′Re(n) or wj′′Im(n)), respectively. From equations (16) and (17) we have:

μi=2M cos θ for wj′′Re(n) terms,

=2M sin θ for wj′′Im(n) terms, and  (34)

σ2=2MI for both wj′′Re(n) and wj′′Im(n) terms.  (35)

Substituting equations (34) and (35) into equation (33) and simplifying yields:

λ=2KM/I  (36)

Then the conditional probability density function of zk(n) given that the received R-ACH preamble is aligned with offset index n, is given by the following expression for a non-central chi-squared distribution with 2K degrees of freedom:





  
    
      
        
          
            
              f
              z
            
            ⁢
            
              〈
              
                z
                |
                aligned
              
              〉
            
          
          =
          
            
              
                
                  
                    e
                    
                      
                        -
                        
                          (
                          
                            
                              z
                              /
                              
                                σ
                                2
                              
                            
                            +
                            λ
                          
                          )
                        
                      
                      /
                      2
                    
                  
                  ⁡
                  
                    (
                    
                      z
                      /
                      
                        σ
                        2
                      
                    
                    )
                  
                
                
                  (
                  
                    K
                    -
                    
                      1
                      2
                    
                  
                  )
                
              
              ⁢
              
                (
                
                  λ
                
                )
              
              ⁢
              
                
              
              ⁢
              
                
                  I
                  
                    K
                    -
                    1
                  
                
                (
                
                  
                    λ
                    ⁢
                    
                      
                    
                    ⁢
                    
                      z
                      /
                      
                        σ
                        2
                      
                    
                  
                
                )
              
            
            
              2
              ⁢
              
                
              
              ⁢
              
                
                  
                    σ
                    2
                  
                  ⁡
                  
                    (
                    
                      λ
                      ⁢
                      
                        
                      
                      ⁢
                      
                        z
                        /
                        
                          σ
                          2
                        
                      
                    
                    )
                  
                
                
                  K
                  2
                
              
            
          
        
        ,
      
    
    
      
        (
        37
        )
      
    
  




where λ and σ2 are given in equations (36) and (35) respectively, and In(x) is the modified Bessel function of the first kind.

Case 2: Offset Index in Not Aligned Wraith Received R-ACH PN-offset

In this case, equation (24) provides an applicable expression for xk(n), and:

|xj(n)|2=wj′Re2(n)+wj′Im2(n).  (38)

Substituting equation (38) into equation (29) yields:





  
    
      
        
          
            z
            k
          
          ⁡
          
            (
            n
            )
          
        
        =
        
          
            ∑
            
              j
              =
              
                k
                -
                K
                +
                1
              
            
            k
          
          ⁢
          
            
              [
              
                
                  
                    w
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      Re
                    
                    
                      ′
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                  ⁡
                  
                    (
                    n
                    )
                  
                
                +
                
                  
                    w
                    
                      j
                      ⁢
                      
                        
                      
                      ⁢
                      Im
                    
                    
                      ′
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                  ⁡
                  
                    (
                    n
                    )
                  
                
              
              ]
            
            .
          
        
      
    
    
      
        (
        39
        )
      
    
  




As in Case 1, it may be assumed that random variables wj′Re(n) and wj′Im(n) are mutually independent, and independent across all time segments j. From equations (27) and (28), both wj′Re(n) and wj′Im(n) are zero-mean normal random variables with variance:

σ2=2M(I+1)  (40)

Because the random variables wj′Re(n) and wj′Im(n) are zero-mean, the sum-of-squares in equation (39) produces a (central) chi-squared probability distribution with 2K degrees of freedom. Thus, the conditional probability density function of zk(n), given that the received R-ACH preamble is not aligned with offset index n, may be given by the following expression for a chi-squared distribution:





  
    
      
        
          
            
              f
              z
            
            ⁢
            
              
            
            ⁢
            
              〈
              
                z
                |
                
                  not
                  ⁢
                  
                    
                  
                  ⁢
                  aligned
                
              
              〉
            
          
          =
          
            
              
                
                  e
                  
                    -
                    
                      (
                      
                        
                          z
                          /
                          2
                        
                        ⁢
                        
                          
                        
                        ⁢
                        
                          σ
                          2
                        
                      
                      )
                    
                  
                
                ⁡
                
                  (
                  
                    z
                    /
                    
                      σ
                      2
                    
                  
                  )
                
              
              
                (
                
                  K
                  -
                  1
                
                )
              
            
            
              
                2
                K
              
              ⁢
              
                
              
              ⁢
              
                
                  
                    σ
                    2
                  
                  ⁡
                  
                    (
                    
                      K
                      -
                      1
                    
                    )
                  
                
                !
              
              ⁢
              
                
              
              ⁢
              
                U
                ⁡
                
                  (
                  z
                  )
                
              
            
          
        
        ,
      
    
    
      
        (
        41
        )
      
    
  




where the value for σ2 is given by equation (40). A cumulative distribution function for zk(n) can also be expressed in closed-form as follows:





  
    
      
        
          
            F
            z
          
          ⁢
          
            
          
          ⁢
          
            〈
            
              z
              |
              
                not
                ⁢
                
                  
                
                ⁢
                aligned
              
            
            〉
          
        
        =
        
          1
          -
          
            
              e
              
                -
                
                  (
                  
                    
                      z
                      /
                      2
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      σ
                      2
                    
                  
                  )
                
              
            
            ⁢
            
              
            
            ⁢
            
              
                ∑
                
                  k
                  =
                  0
                
                
                  K
                  -
                  1
                
              
              ⁢
              
                
                  
                    (
                    
                      
                        z
                        /
                        2
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        σ
                        2
                      
                    
                    )
                  
                  k
                
                /
                
                  
                    k
                    !
                  
                  .
                
              
            
          
        
      
    
    
      
        (
        42
        )
      
    
  




A decision threshold for all zk(n), denoted zT, may be established. If zk(n)>zT, a R-ACH preamble aligned with offset index n may be declared to be present. As illustrated in FIG. 5, a value of zT may be chosen to provide a desirable compromise between missed-detection and false-detection errors:





  
    
      
        
          
            Pr
            ⁢
            
              {
              Missed
              }
            
          
          =
          
            
              ∫
              0
              
                z
                T
              
            
            ⁢
            
              
                f
                z
              
              ⁢
              
                〈
                
                  z
                  |
                  aligned
                
                〉
              
              ⁢
              
                
              
              ⁢
              
                d
                z
              
            
          
        
        ,
        and
      
    
    
      
        (
        43
        )
      
    
  
  
    
      
        
          
            Pr
            ⁢
            
              {
              False
              }
            
          
          =
          
            1
            -
            
              
                F
                z
              
              ⁢
              
                〈
                
                  
                    z
                    T
                  
                  |
                  
                    not
                    ⁢
                    
                      
                    
                    ⁢
                    aligned
                  
                
                〉
              
            
          
        
        ,
      
    
    
      
        (
        44
        )
      
    
  




where fz(z|aligned) and Fz(z|not aligned) are given in equations (37) and (42), respectively. The integration in (43) may be performed by means of numerical integration of equation (37).

The definitions of Pr{Missed} and Pr{False} above pertain to a single zk(n) sample. However, for the instant example, because there may be over 6000 possible offsets n to be evaluated and, typically, at most a few R-ACH preambles being transmitted at any given time, then there are far more opportunities for Pr{False} to occur than for Pr{Missed} to occur. Consequently, it may be more useful to define a new false-detection probability, denoted {False}, as the conditional probability that one or more zk(n) samples, over the entire range of (N−M) valid offset values of n, exceeds the threshold zT, given that no R-ACH preamble is present. Then {False} is related to Pr{False} for a single zk(n) sample by:

{False}=1−[1−Pr{False}](N−M).  (45)

For this analysis, the decision threshold zT was determined iteratively by simultaneously minimizing Pr{Missed} in equation (43) and {False} in equation (45).

Using the probability expressions derived above, a calculation of Pr{Missed} and {False} versus number of summed time segments K was performed using values of M=1500 and N=8192. The total interference+noise power I was calculated as the sum of channel thermal noise, intra-beam self-interference, and adjacent-beam interference values, shown in Table 1:










TABLE 1








Interference


Return Link
Ebi/10
C/I (channel
Power


Interference
(info. rate =
noise BW =
“I” (linear units,


Component:
4800 bps) − dB
1.25 MHz) − dB
relative to C = 1)


















Intra-beam self-
9.0
−15.2
32.8


interference:


Adjacent beam
11.3
−12.9
19.3


interference:


Channel thermal
2.0
−22.2
164.3


noise:









Total interference + thermal noise power I:
216.4









Using M=1500, N=8192, and I=216.4 as inputs, the calculated values of Pr{Missed} and {False} are plotted as functions of K in FIG. 7.

Table 2 summarizes the major parameter values used in the analytical model:








TABLE 2





Parameter
Value







Num. Input Samples “M” per Time Segment yk (see FIG. 3):
1500


Duration of Input Time Segment yk:
1.2 msec.


Num. Samples “N” per Reference PN-Segment gk 
8192


(see FIG. 4):


MT EIRP:
−23 dBW


CDMA Channel Loading:
32 MTs


Frequency Reuse Factor:
  3









To simplify the analysis, zero Doppler shift of the MT's received carrier is assumed (although an arbitrary constant phase shift is applied).

The number of time segments K that are summed to form the output vector zk as shown in FIG. 4 is treated as the variable in this analysis. Missed-detection and false-detection probabilities as a function of K are determined, where these two probabilities are defined as follows:

    
    
        Pr{Missed}=conditional probability that a given zk(n) value does not exceed the decision threshold, given that a R-ACH preamble was received whose PN-offset corresponds to index 12. The mathematical expression for Pr{Missed} is given in equation (43).
        {False}=conditional probability that one or more zk(n) values within a given vector zk exceeds the decision threshold, given that no R-ACH preamble was received. The mathematical expression for {False} is given in equation (45).
    
    


Given the parameter values in Table 2, the missed-detection and false-detection probabilities defined above were calculated using standard equations for the chi-squared and non-central chi-squared distributions. The results are shown in FIG. 7 as a function of the number of summed time segments K.
FIG. 7 shows that at K=14, both missed-detection and false-detection probabilities have fallen to 1×10−6. Assuming a time segment duration of 1.2 msec., the total observation time would then be 14×1.2=16.8 msec. Thus, these exemplary analytical results indicate that the R-ACH preamble can be detected with high probability under within the time span of a single 20 msec preamble frame.
FIG. 8 illustrates a satellite wireless communications system 800 according to some embodiments of the present invention. The system 800 includes a satellite 810 configured to communicate with a wireless terminal 10. The satellite 810 relays transmissions from the terminal 10 to a ground-based antenna 820 associated with a receiver 840 of a gateway 830. As shown, the receiver 840 includes a downconverter 842 that converts radio signals received via the antenna 820 to baseband signals. A R-ACH preamble detector 844 detects a preamble of a R-ACH transmission by the terminal 10 using, for example, the detection techniques discussed above. As shown, the R-ACH transmission from the terminal 10 may be compatible with R-ACH transmission formats (such as IS-95, CDMA2000, or similar) recognized by a terrestrial wireless infrastructure, e.g., the R-ACH message may be encoded according to a spreading code format compatible with the CDMA standards implemented by terrestrial cellular base stations 20. The R-ACH preamble detector 844 is configured to provide an appropriate code delay to a RAKE receiver 846 responsive to detection of a R-ACH preamble, such that operation of the receiver 840 is synchronized to the terminal 10. It will be appreciated that the RAKE receiver 846 may include, for example, a combination of correlator fingers, one or more combiners for combining the outputs of the correlator fingers, and a symbol estimator that generates estimates of information in a received spread spectrum signal. Operations and configurations of RAKE receivers are known to those skilled in the art, and will not be discussed in greater detail herein. It will also be appreciated that CDMA receivers other than RAKE receivers may be used.
As illustrated in FIG. 9, a mobile satellite communications system 800′ according to further embodiments of the present invention may include a gateway 830′ with a receiver 840′ including a R-ACH preamble detector 844′ including a correlator 910, an averager 920, and a delay determiner 930. The correlator 910 may provide functions similar to those of the FFT correlator 410 and magnitude-squared converter 420 of FIG. 4, and the averager 920 may perform functions similar to those of the averager 410 of FIG. 4. The delay determiner 930 may perform functions similar to those described for the delay determiner 610 of FIG. 6.
It will be appreciated that the implementations shown in FIGS. 8 and 9 are exemplary, and that other implementations fall within the scope of the present invention. For example, although FIGS. 8 and 9 show implementation of R-ACH preamble detection in a satellite gateway, it will be understood that such functions may be implemented in other system components, e.g., in a satellite or some other component of a satellite wireless communications system. It will be further understood that, although exemplary embodiments described above relate to determining signal timing by detecting a known information element in the form of a R-ACH preamble, similar timing determination could be achieved within the scope of the invention by detecting other known information elements in terminal transmissions.
CDMA deployment over satellite generally requires that the system accommodate the longer path delay and increased delay variability of the satellite channel. According to some embodiments of the invention, a satellite gateway receiver is synchronized to mobile terminal (MT) transmissions on the return link using a correlation process at the gateway to detect the preamble of the MT's Reverse Access Channel (R-ACH) transmission during call setup. By measuring the time offset of the preamble's spreading PN-sequence, the precise path delay from the gateway to the MT can be determined. This time offset can be used to adjust the initial timing of the RAKE receiver's de-spreading sequence, which can greatly reduce the code phase search range to synchronize and de-spread the MT's signal.
In the drawings and specification, there have been disclosed exemplary embodiments of the invention. Although specific terms are employed, they are used in a generic and descriptive sense only and not for purposes of limitation, the scope of the invention being defined by the following claims.

## Claims

1. A method of synchronizing a satellite wireless communications system with a terminal, the method comprising:
receiving an uplink signal transmitted by the terminal, the uplink signal including a known information element spread according to a spreading code specific to a component of a satellite wireless communications system;
determining a correlation of the received uplink signal with the spreading code over a range of time shifts, wherein determining a correlation of the received uplink signal with the spreading code over a range of time shifts comprises:
generating respective sets of correlation measures for respective ones of a plurality of time segments, the sets of correlation measures including respective correlation measures for respective time shifts of the range of time shifts; and
averaging the correlation measures for the respective time shifts over the plurality of sets of correlation measures to generate a set of average correlation measures; and


detecting the known information element from the determined correlation, wherein detecting the known information element from the determined correlation comprises detecting a peak value in the set of average correlation measures; and
synchronizing the satellite wireless communications system with the terminal responsive to detection of the known information element.

2. A method according to claim 1, wherein the spreading code comprises a pseudonoise (PN) sequence associated with a satellite beam.

3. A method according to claim 1, wherein the known information element comprises a fixed value data sequence.

4. A method according to claim 1, wherein the uplink signal comprises a reverse access channel (R-ACH) message, and wherein the known information element comprises a preamble of the R-ACH message.

5. A method according to claim 1:
wherein generating respective sets of correlation measures for respective ones of a plurality of time segments comprises:
correlating respective sets of samples of the received uplink signal for the respective time segments with multiple time shifts of the spreading code to generate respective sets of correlation values; and
generating respective sets of magnitude measures for the respective time segments from the respective sets of correlation values; and

wherein averaging the correlation measures for the respective time shifts over the plurality of sets of correlation measures comprises averaging the magnitude measures for the respective time shifts over the sets of magnitude measures to generate the set of average correlation measures.

6. A method according to claim 5, wherein correlating respective sets of samples of the received uplink signal for the respective time segments with multiple time shifts of the spreading code to generate respective sets of correlation values comprises fast Fourier transform (FFT) correlating the respective sets of samples with the spreading code to generate the respective sets of correlation values.

7. A method according to claim 1, wherein synchronizing the satellite wireless communications system with the terminal responsive to detection of the known information element comprises assigning a delay to a receiver of the satellite wireless communications system responsive to detection of the known information element.

8. A method of synchronizing a satellite wireless communications system with a terminal, the method comprising:
receiving a radio signal at the satellite wireless communications system;
detecting a preamble of a transmitted R-ACH message in the received radio signal, wherein detecting a preamble of a transmitted R-ACH message comprises:
determining a correlation of the received radio signal with a PN sequence; and
detecting the preamble of a transmitted R-ACH message from the determined correlation; and

synchronizing the satellite wireless communications system with a terminal that transmitted the R-ACH message responsive to detection of the preamble of the R-ACH message;
wherein determining a correlation of the received radio signal with a PN sequence comprises determining a correlation of the received radio signal with the PN sequence over a range of time shifts;
wherein determining a correlation of the received radio signal with the PN sequence over a range of time shifts comprises:
generating respective sets of correlation measures for respective ones of a plurality of time segments, the sets of correlation measures including respective correlation measures for respective time shifts of the range of time shifts; and
averaging the correlation measures for the respective time shifts over the plurality of sets of correlation measures to generate a set of average correlation measures; and

wherein detecting a preamble of a R-ACH message comprises detecting a peak value in the set of average correlation measures.

9. A method according to claim 8, wherein the PN sequence comprises a PN sequence associated with a satellite beam.

10. A method according to claim 8:
wherein generating respective sets of correlation measures for respective ones of a plurality of time segments comprises:
correlating respective sets of samples of the received radio signal for the respective time segments with multiple time shifts of the PN sequence to generate respective sets of correlation values; and
generating respective sets of magnitude measures for the respective time segments from the respective sets of correlation values; and

wherein averaging the correlation measures for the respective time shifts over the plurality of sets of correlation measures comprises averaging the magnitude measures for the respective time shifts over the sets of magnitude measures to generate the set of average correlation measures.

11. A method according to claim 10, wherein correlating respective sets of samples of the received radio signal for the respective time segments with multiple time shifts of the PN sequence to generate respective sets of correlation values fast Fourier transform (FFT) correlating the respective sets of samples with the PN code to generate the respective sets of correlation values.

12. A method according to claim 8, wherein synchronizing the satellite wireless communications system with a terminal that transmitted the R-ACH message responsive to detection of the preamble of the R-ACH message comprises assigning a delay to a receiver of the satellite wireless communications system responsive to detection of the known information element.

13. A method according to claim 8, wherein receiving a radio signal at the satellite wireless communications system comprises receiving the radio signal at a satellite gateway.

14. An apparatus for synchronizing a satellite wireless communications system with a terminal that transmits an uplink signal including a known information element spread according to a spreading code specific to a component of a satellite wireless communications system, the apparatus comprising:
a receiver configured to receive the uplink signal transmitted by the terminal, to determine a correlation of the received uplink signal with the spreading code over a range of time shifts, to detect the known information element from the determined correlation and to synchronize with the terminal responsive to detection of the known information element, wherein the receiver comprises:
means for generating respective sets of correlation measures for respective ones of a plurality of time segments, the sets of correlation measures including respective correlation measures for respective time shifts of the range of time shifts;
means for averaging the correlation measures for the respective time shifts over the plurality of sets of correlation measures to generate a set of average correlation measures; and
means for detecting a peak value in the set of average correlation measures.

15. An apparatus according to claim 14, wherein the spreading code comprises a PN sequence associated with a satellite beam.

16. An apparatus according to claim 14, wherein the known information element comprises a fixed value data sequence.

17. An apparatus according to claim 14, wherein the uplink signal comprises a R-ACH message, and wherein the known information element comprises a preamble of the R-ACH message.

18. An apparatus according to claim 14:
wherein the means for generating respective sets of correlation measures for respective ones of a plurality of time segments comprises:
means for correlating respective sets of samples of the received uplink signal for the respective time segments with multiple time shifts of the spreading code to generate respective sets of correlation values; and
means for generating respective sets of magnitude measures for the respective time segments from the respective sets of correlation values; and

wherein the means for averaging the correlation measures for the respective time shifts over the plurality of sets of correlation measures to generate a set of average correlation measures comprises means for averaging the magnitude measures for the respective time shifts over the sets of magnitude measures to generate the set of average correlation measures.

19. An apparatus according to claim 18, wherein the means for correlating respective sets of samples of the received uplink signal for the respective time segments with multiple time shifts of the spreading code to generate respective sets of correlation values comprises a fast Fourier transform (FFT) correlator configured to correlate the respective sets of samples with the spreading code to generate the respective sets of correlation values.

20. An apparatus according to claim 14, wherein the receiver further comprises:
a receiver configured to estimate information included in the uplink signal; and
a delay determiner configured to assign a delay to the receiver responsive to detection of the known information element.

21. An apparatus for synchronizing a satellite wireless communications system with a terminal, the apparatus comprising:
a receiver configured to receive a radio signal at the satellite wireless communications system, to detect a preamble of a R-ACH message transmitted by a terminal and to synchronize with the terminal responsive to detection of the preamble of the R-ACH message, wherein the receiver is configured to determine a correlation of the received radio signal with a PN sequence, and to detect the preamble of the transmitted R-ACH message from the determined correlation, wherein the receiver is configured to determine a correlation of the received radio signal with the PN sequence over a range of time shifts, wherein the receiver comprises:
means for generating respective sets of correlation measures for respective ones of a plurality of time segments, the sets of correlation measures including respective correlation measures for respective time shifts of the range of time shifts;
means for averaging the correlation measures for the respective time shifts over the plurality of sets of correlation measures to generate a set of average correlation measures; and
means for detecting a peak value in the set of average correlation measures,
wherein the means for generating respective sets of correlation measures for respective ones of a plurality of time segments comprises:
means for correlating respective sets of samples of the received radio signal for the respective time segments with multiple time shifts of the PN sequence to generate respective sets of correlation values; and
means for generating respective sets of magnitude measures for the respective time segments from the respective sets of correlation values; and

wherein the means for averaging the correlation measures for the respective time shifts over the plurality of sets of correlation measures comprises means for averaging the magnitude measures for the respective time shifts over the sets of magnitude measures to generate the set of average correlation measures.

22. An apparatus according to claim 21, wherein the PN sequence comprises a PN sequence associated with a satellite beam.

23. An apparatus according to claim 21, wherein the receiver further comprises:
a receiver configured to estimate information included in the radio signal; and
a delay determiner configured to assign a delay to the receiver responsive to detection of the R-ACH preamble.

24. An apparatus according to claim 21, wherein the receiver is positioned at a satellite gateway.