fig1 illustrates a wireless local area network ( lan ) embodiment of the invention , which is referred to herein by the general reference numeral 100 . such embodiment is preferably based on orthogonal frequency division multiplexing ( ofdm ), and quadrature amplitude modulated ( qam ) of signals transmitted in the license - free 5 ghz frequency band . the wireless lan 100 typically includes a wireless network 101 connected to the internet , a phy - transmitter 102 , and a phy - receiver 103 . such all conform to the ieee - 802 . 11a specification for a physical layer ( phy ) interface in a wireless local area network which allows mobile clients . the transmitter 102 comprises a digital signal processor ( dsp ) 104 which implements a forward error correction ( fec ) coder 106 , an interleaving and mapping process 108 , an inverse fast fourier transform processor 110 , and a symbol wave shaper 112 . the dsp 104 outputs in - phase ( i ) and quadrature - phase ( q ) signals that are input to an iq modulator 114 driven by a local oscillator 116 . the modulated output is sent to a mixer 118 for upconversion to the five ghz band . a second local oscillator 120 provides the necessary carrier frequency . a high power amplifier ( hpa ) 122 drives a transmitter antenna 124 . a radio up - link 125 is received by the wireless network 101 . in general , the transmitter 102 can be implemented with conventional methods and components . the receiver 103 receives a radio down - link 126 that is typically transmitted in packets . each packet is begun with a training sequence , e . g , a short and long preamble . the receiver 103 includes a receiver antenna 128 followed by a low - noise amplifier ( lna ) 130 . a local oscillator 132 and a first mixer 134 produce an intermediate frequency ( if ). an automatic gain control ( agc ) amplifier 136 smoothes out signal - strength variations and drives an iq - detector 138 . a second local oscillator 140 provides the carrier necessary to derive the i / q samples , e . g . 16 - bit binary at 20 . 0 mhz . in all embodiments of the present invention , no automatic frequency control ( afc ) clock recovery is needed because any frequency offset errors are corrected in later digital processing . a receiver - dsp 142 comprises a fast fourier transform process 144 , a demapping and deinterleaving process 146 , and an fec decoder 148 . the receiver - dsp 142 further includes the necessary digital logic needed for carrier frequency offset determination and correction . the higher levels of the mobile client are represented by a media access controller ( mac ) 150 and a client agent software 152 . a first embodiment of the invention for timing misalignment detection and correction works with the short preamble . a real signal constructed from the complex time - domain signal associated with the short preamble is discrete fourier transform processed to gather timing misalignment information . the short preamble is comprised of ten 0 . 8 μs duration , i . e . 16 - sample long at sampling frequency = 20 mhz , sequences . the short preamble is mainly used for packet detection and coarse frequency offset estimation . in the absence of any frequency offset or other distorting effect , the short preamble is characterized by its imaginary ( quadrature - phase ) part which corresponds to its real ( in - phase ) part in almost every particular . the principle difference is the imaginary ( quadrature - phase ) part is delayed 0 . 4 μs ( eight sample times ) with respect to the real ( in - phase ) part . such phenomenon can be taken advantage of to decrease signal waveform processing complexity by simply adding real ( in - phase ) and imaginary ( quadrature - phase ) parts together . the resulting signal is characterized by a repeating 0 . 4 μs duration , eight - sample waveform δ ( t ). then a 3 . 2 μs duration , i . e . 64 - sample sequence is extracted from the short preamble . spectrum - wise , this signal exhibits three equidistant , equal - amplitude frequency peaks . assuming that the beginning of thee first 8 - sample sequence of δ ( t ) coincides with that of δ ( t ), timing offset information embedded within the phase of each of these frequency peaks can be represented with , φ 1 ⁢ ( t ) = π 4 ⁢ ( 1 + t t s ) φ 2 ⁢ ( t ) = π 4 ⁢ ( 1 + 2 ⁢ ⁢ t t s ) φ 3 ⁢ ( t ) = 3 ⁢ π 4 ⁢ ( - 1 + t t s ) the phase of such frequency peaks φ 1 , φ 2 and φ 3 varies with the timing offset and depend on any misalignment existing between δ ( t ) and δ ( t ). an intra - baud timing offset , or timing misalignment , τ ( ) can be derived from φ 1 , φ 2 and φ 3 . for example , a received signal can be represented by , ψ ⁡ ( t ) = φ 1 ⁡ ( t ) + 2 ⁢ φ 2 ⁡ ( t ) + φ 3 ⁡ ( t ) = π 4 ⁢ ( 1 + t t s ) + 2 ⁢ ⁢ π 4 ⁢ ( 1 + 2 ⁢ ⁢ t t s ) + 3 ⁢ π 4 ⁢ ( - 1 + t t s ) = 2 ⁢ π ⁢ ⁢ t t s . in practice , ψ =( x 8 p 1 )( x 16 p 2 ) 2 ( x 24 p 3 ), where x k and p n respectively designate 64 - point fast fourier transform frequency components and the phase correcting coefficients needed compensate for phase offset errors cause by a misalignment between δ ( t ) and δ ( t ). plotting this results in a sawtooth waveform that reflects timing misalignment independent of timing offset . the timing misalignment τ is expressed as a fraction of t s , and is in general , preferred implementations of the present invention are designed to compute a 64 - point fast fourier transform rather than a three - point discrete fourier transform . fig2 is a diagram representing the sampling of the short preamble used in training sequences for the physical layer ( phy ) of a wireless local area network ( lan ) conforming to the ieee - 802 . 11a specification . fig3 is a diagram representing the structure of the synchronizing plcp preamble , signal , and data fields used for the physical layer ( phy ) of a wireless local area network ( lan ) conforming to the ieee - 802 . 11a specification . fig4 represents an embodiment of the invention for timing misalignment determination in a radio receiver , and is referred to herein by the general reference numeral 400 . the embodiment 400 comprises a step element 402 for correcting a frequency offset and determining a boundary between a short preamble and a long preamble in a received radio signal ; exemplary embodiments of these functions are described in “ coarse frequency offset estimation — patent disclosure ”, alain chiodini , john reagan , nband communications , 2000 and “ ofdm data demodulator timing synchronization — patent disclosure ”, john reagan , alain chiodini , nband communications , 2000 . a step element 404 constructs a real signal from a complex time - domain signal associated with the short preamble . a step element 406 extracts a n - sample ( n is preferably a power of 2 or 4 so that radix - 2 or radix - 4 fft may be used subsequently ) sequence from a portion of the short preamble to obtain a plurality of equidistant equal amplitude frequency peaks . a step element 408 determines a timing misalignment estimate by inspecting the relative phases of the plurality of equidistant equal amplitude frequency peaks . the objective is to thereafter be able to demodulate data encoded in the received radio signal . the step element 404 may include in - phase and quadrature - phase sampling of the received radio signal to obtain a real part and an imaginary part . the real and imaginary parts are assumed to be similar to one another except for a fixed time - skew between them . the step element 404 may also include a simple addition of the real and imaginary parts to obtain the real signal . the step element 408 can be such that phase of a set of three frequency peaks φ 1 , φ 2 and φ 3 is assumed to vary with timing misalignment between δ ( t ) and δ ( t ), and an intra - baud timing offset τ can be derived from φ 1 , φ 2 and φ 3 , wherein , a received signal can be represented by , ψ ⁡ ( t ) = ⁢ φ 1 ⁡ ( t ) + 2 ⁢ φ 2 ⁡ ( t ) + φ 3 ⁡ ( t ) = π 4 ⁢ ( 1 + t t s ) + 2 ⁢ ⁢ π 4 ⁢ ( 1 + 2 ⁢ ⁢ t t s ) + 3 ⁢ π 4 ⁢ ( - 1 + t t s ) = 2 ⁢ π ⁢ ⁢ t t s and , ψ =( x 8 p 1 )( x 16 p 2 ) 2 ( x 24 p 3 ), where x k and p n respectively designate 64 - point fast fourier transform frequency components and the phase correcting coefficients needed compensate for phase offset errors cause by a misalignment between δ ( t ) and δ ( t ), and the timing misalignment τ is expressed as a fraction of t s , and is the step of determining preferably computes a 64 - point fast fourier transform rather than a three - point discrete fourier transform . a step element 410 is then able to demodulate the transmitted data . a second embodiment of the invention for timing misalignment and correction works with the long preamble rather than the short preamble . it is assumed that the position of the boundary between short and long preambles has been accurately determined . the two 64 - sample long sequences that constitute the long preamble are linearly combined using least squares techniques to obtain an improved signal . this method captures the essential characteristics of the received signal and minimizes the impact of residual frequency offset and other distortions on the quality of estimation . the absolute value of any timing misalignment is estimated by computing a normalized dot product of the resulting signal and the ideal on - baud sequence whose derivative is used to determine the sign through the calculation of a second dot product . the minimization of the cost function ( in the least square sense ) described hereafter leads to two complex coefficients ( also called weighting coefficients ) that are used to combine the two 64 - sample long sequences mentioned above into one idealized 64 - sample sequence . c ⁡ ( α 1 , α 2 ) = ⁢  r → on - [ x → 1 x → 2 ] ⁡ [ α 1 α 2 ]  2 = ⁢ ( r → on - [ x → 1 x → 2 ] ⁡ [ α 1 α 2 ] ) h ⁢ ( r → on - [ x → 1 x → 2 ] ⁡ [ α 1 α 2 ] ) = ⁢ ( r → on h - α 1 * ⁢ x → 1 h - α 2 * ⁢ x → 2 h ) ⁢ ( r → on - α 1 ⁢ x → 1 - α 2 ⁢ x → 2 ) = ⁢  r → on  2 - 2 ⁢ re ⁡ ( α 1 * ⁢ x → 1 h ⁢ r → on ) - 2 ⁢ re ⁡ ( α 2 * ⁢ x → 2 h ⁢ r → on ) + ⁢ 2 ⁢ re ⁡ ( α 1 * ⁢ α 2 ⁢ x → 1 h ⁢ x → 2 ) +  α 1  2 ⁢  x → 1  2 +  α 2  2 ⁢  x → 2  2 { right arrow over ( x )} 1 ={ right arrow over ( c )} 1 · x { right arrow over ( r )} off +{ right arrow over ( n )} 1 is the first sequence of the long preamble , { right arrow over ( x )} 2 ={ right arrow over ( c )} 2 · x { right arrow over ( r )} off +{ right arrow over ( n )} 2 is the second one , { right arrow over ( r )} on and { right arrow over ( r )} off respectively designate the on - baud and off - baud sampled reference sequence , α 1 and α 2 are the weighting coefficients , c → 1 =  ⅇ j ⁢ ⁢ φ 1 ⅇ j2π ⁢ ⁢ v f s + j ⁢ ⁢ φ 1 ⋮ ⅇ j2π ⁢ ⁢ v f s ⁢ ⁢ 63 + j ⁢ ⁢ φ 1 , ⁢ ⁢ c → 2 =  ⅇ j ⁢ ⁢ φ 2 ⅇ j2π ⁢ ⁢ v f s + j ⁢ ⁢ φ 2 ⋮ ⅇ j2π ⁢ ⁢ v f s ⁢ ⁢ 63 + j ⁢ ⁢ φ 2 , and minimizing c ( α 1 , α 2 ) with respect to α 1 and α 2 , ∂ c ∂ α 1 = ⁢ - r → on h ⁢ x → 1 + α 2 * ⁢ x → 2 h ⁢ x → 1 + α 1 * ⁢  x → 1  2 = ⁢ - ∑ n = 0 63 ⁢ r on * ⁡ ( n ) ⁢ r off ⁡ ( n ) ⁢ ⅇ j2π ⁢ ⁢ v f s ⁢ ⁢ n + j ⁢ ⁢ φ 1 + ⁢ α 2 * ⁢ ⅇ j ⁡ ( φ 1 - φ 2 ) ⁢ ∑ n = 0 63 ⁢  r off ⁡ ( n )  2 + α 1 * ⁡ (  r → off  2 + σ n 2 ) = ⁢ - ⅇ jφ 1 ⁢ p + α 1 * ⁡ ( s + σ n 2 ) + α 2 * ⁢ ⅇ j ⁡ ( φ 1 - φ 2 ) ⁢ s ∂ c ∂ α 2 = ⁢ - r → on h ⁢ x → 2 + α 1 * ⁢ x → 1 h ⁢ x → 2 + α 2 * ⁢  x → 2  2 = ⁢ - ∑ n = 0 63 ⁢ r on * ⁡ ( n ) ⁢ r off ⁡ ( n ) ⁢ ⅇ j2π ⁢ ⁢ v f s ⁢ ⁢ n + j ⁢ ⁢ φ 2 + ⁢ α 1 * ⁢ ⅇ j ⁡ ( φ 2 - φ 1 ) ⁢ ∑ n = 0 63 ⁢  r off ⁡ ( n )  2 + α 2 * ⁡ (  r → off  2 + σ n 2 ) = ⁢ - ⅇ jφ 2 ⁢ p + α 1 * ⁢ ⅇ j ⁡ ( φ 2 - φ 1 ) ⁢ s + α 2 * ⁡ ( s + σ n 2 ) ⁢ s = ∑ n = 0 63 ⁢ ⁢  r off ⁡ ( n )  2 ⁢ ⁢ and ⁢ ⁢ p = ∑ n = 0 63 ⁢ ⁢ r on * ⁡ ( n ) ⁢ r off ⁡ ( n ) ⁢ ⅇ - j2π ⁢ ⁢ v f s ⁢ ⁢ n . in preferred embodiments of the invention , it is assumed that { right arrow over ( n )} 1 h { right arrow over ( n )} 2 ={ right arrow over ( n )} 1 h { right arrow over ( x )} 2 ={ right arrow over ( n )} 2 h { right arrow over ( x )} 1 ={ right arrow over ( n )} 1 h { right arrow over ( r )}={ right arrow over ( n )} 2 h { right arrow over ( r )}= 0 . such assumption may not be exactly true in reality , but dramatically simplifies the equations and therefore the computer processing required . this proceeds as , { ∂ c ∂ α 1 = 0 ∂ c ∂ α 2 = 0 ⇒ [ s + σ n 2 ⅇ j ⁡ ( φ 1 - φ 2 ) ⁢ s ⅇ j ⁡ ( φ 2 - φ 1 ) ⁢ s s + σ n 2 ] ⁡ [ α 1 * α 2 * ] = [ ⅇ jφ 1 ⁢ p ⅇ jφ 2 ⁢ p ] ⁢ ⇔ [ α 1 α 2 ] = 1 ( s + σ n 2 ) 2 - s 2 ⁡ [ s + σ n 2 - ⅇ j ⁡ ( φ 2 - φ 1 ) ⁢ s - ⅇ j ⁡ ( φ 1 - φ 2 ) ⁢ s s + σ n 2 ] ⁡ [ ⅇ - jφ 1 ⁢ p * ⅇ - jφ 2 ⁢ p * ] ⁢ ⇔ [ α 1 α 2 ] = p * 2 ⁢ s + σ n 2 ⁡ [ ⅇ - jφ 1 ⅇ - jφ 2 ] . in the absence of any timing misalignment , frequency offset or gaussian noise , the weighting coefficients are simply , [ α 1 α 2 ] = 1 2 ⁡ [ ⅇ - jφ 1 ⅇ - jφ 2 ] . z → = α 1 ⁢ x → 1 + α 2 ⁢ x → 2 = p * 2 ⁢ s + σ n 2 ⁢ ( ⅇ - jφ 1 ⁡ ( c → 1 · × r → off + n → 1 ) + ⅇ - jφ 2 ⁡ ( c → 2 · × r → off + n → 2 ) ) = p * 2 ⁢ s + σ n 2 ⁢ ( 2 ⁢ c → · × r → off + n → ) with : ⁢ ⁢ c → = ❘ 1 ⅇ j2π ⁢ ⁢ v f s ⋮ ⅇ j2π ⁢ ⁢ v f s ⁢ ⁢ 63 , p * = ∑ n = 0 63 ⁢ ⁢ r off * ⁡ ( n ) ⁢ r on ⁡ ( n ) ⁢ ⅇ - j2π ⁢ ⁢ v f s ⁢ ⁢ n = ∑ n = 0 63 ⁢ ⁢ ( r on ⁢ ( n ) + δ ⁢ ( n ) ) * ⁢ r on ⁢ ( n ) ⁢ ⅇ - j2π ⁢ ⁢ v f s ⁢ ⁢ n = p on * + ∑ n = 0 63 ⁢ ⁢ δ * ⁢ ( n ) ⁢ r on ⁢ ( n ) ⁢ ⅇ - j2π ⁢ ⁢ v f s ⁢ ⁢ n = p on * + p δ * . because r on ( 32 − n )= r on ( 32 + n ) for n = 1 . . . 31 and r on ( 0 )=− r on ( 32 ), p * on can be rewritten as , p on * =  r on ⁢ ( 0 )  2 + (  r on ⁢ ( 32 )  2 + 2 ⁢ ∑ n = 1 31 ⁢ ⁢  r on ⁢ ( 32 + n )  2 ⁢ cos ⁡ ( 2 ⁢ π ⁢ ⁢ v f s ⁢ ⁢ n ) ) ︸ γ ⁢ ( v ) ⁢ ⅇ - j2π ⁢ ⁢ v f s ⁢ ⁢ 32 . because γ ( ν ) is real and much greater than | r on ( 0 )| 2 , the result is ∠ ⁢ ⁢ p on * ≅ - 2 ⁢ π ⁢ ⁢ v f s ⁢ ⁢ 32 ⁢ ⁢ radian . thus , p * is composed of two phase coefficients , a first one ( p * on ) centers the frequency offset related phase component around z ( 32 ), and the second one ( p * δ ) contains timing - misalignment information . once { right arrow over ( z )} has been computed , the absolute value and sign of the timing misalignment are determined by computing dot products , as in , γ value =  z → h ⁢ r → on   r → on  2 ⁢ λ max λ max - λ min where : { λ max , λ min }= eig ( m h m ) with m =[{ right arrow over ( x )} 1 { right arrow over ( x )} 2 ]. γ sign = re ( z → h ⁢ ∂ r → on ∂ t ) . because λ = m h m is a 2 × 2 matrix , det ( λ )= λ max λ min and trace ( λ )= λ max + λ min . it is then easy to get back to λ max and λ min . the timing misalignment is deduced from γ value and γ sign , e . g . τ = f ⁡ ( γ value , γ sign ) = sign ⁡ ( γ sign ) ⁢ - 332 791 ⁢ log ⁡ ( γ value ) . results in a symmetrical heap function that peaks with a γ value of 1 . 00 at a zero timing misalignment , and drops to γ value of 0 . 55 at a normalized timing misalignment of ± 0 . 5 . embodiments of the invention all operate well at low signal - to - noise ratios and in the presence of a relatively large residual frequency offsets . the second embodiment of the invention presented herein is preferred for lower signal - to - noise ratio signals . any performance deterioration at high signal - to - noise ratios can probably be corrected by regularizing the covariance matrix , e . g . using tikhonov regularization . fig5 represents a second embodiment of the invention for timing misalignment determination in a radio receiver , and is referred to herein by the general reference numeral 500 . the embodiment 500 comprises a step element 502 for determining a boundary between a short preamble and a long preamble in a received radio signal ; an exemplary method of doing this is listed in “ ofdm data demodulator timing synchronization — patent disclosure ”, john reagan , alain chiodini , nband communications , 2000 . a step element 504 linearly combines samples of two long sequences from the long preamble to obtain an idealized sequence of samples . a step element 506 computes a normalized dot product of the idealized sequence of samples and an ideal on - baud sampled sequence to obtain a magnitude estimate of any timing misalignment . a step element 508 computes a dot product of the idealized sequence of samples and the time derivative of the ideal on - baud sampled sequence mentioned above to obtain the sign of the timing misalignment if any . thus data encoded in the received radio signal may thereafter be demodulated in step element 510 . the steps of linearly combining and computing can use a cost function , mathematically described by , c ⁡ ( α 1 , α 2 ) = ⁢  r → on - [ x → 1 ⁢ ⁢ x → 2 ] ⁡ [ α 1 α 2 ]  2 = ⁢ ( r → on - [ x → 1 ⁢ ⁢ x → 2 ] ⁡ [ α 1 α 2 ] ) h ⁢ ( r → on - [ x → 1 ⁢ ⁢ x → 2 ] ⁡ [ α 1 α 2 ] ) = ⁢ ( r → on h - α 1 * ⁢ x → 1 h - α 2 * ⁢ x → 2 h ) ⁢ ( r → on - α 1 ⁢ x → 1 - α 2 ⁢ x → 2 ) = ⁢  r → on  2 - 2 ⁢ re ⁡ ( α 1 * ⁢ x → 1 h ⁢ r → on ) - 2 ⁢ re ⁡ ( α 2 * ⁢ x → 2 h ⁢ r → on ) + ⁢ 2 ⁢ re ⁡ ( α 1 * ⁢ α 2 ⁢ x → 1 h ⁢ x → 2 ) +  α 1  2 ⁢  x → 1  2 +  α 2  2 ⁢  x → 2  2 { right arrow over ( x )} 1 ={ right arrow over ( c )} 1 · x { right arrow over ( r )} off +{ right arrow over ( n )} 1 is the first sequence of the long preamble , { right arrow over ( x )} 2 ={ right arrow over ( c )} 2 · x { right arrow over ( r )} off +{ right arrow over ( n )} 2 is the second one , { right arrow over ( r )} on and { right arrow over ( r )} off respectively designate the on - baud and off - baud sampled reference sequence , α 1 and α 2 are the weighting coefficients , c → 1 =  ⅇ j ⁢ ⁢ φ 1 ⅇ j ⁢ ⁢ 2 ⁢ π ⁢ ⁢ v f s + j ⁢ ⁢ φ 1 ⋮ ⅇ j ⁢ ⁢ 2 ⁢ ⁢ π ⁢ ⁢ v f s ⁢ ⁢ 63 + j ⁢ ⁢ φ 1 , ⁢ ⁢ c → 2 =  ⅇ j ⁢ ⁢ φ 2 ⅇ j ⁢ ⁢ 2 ⁢ π ⁢ ⁢ v f s + j ⁢ ⁢ φ 2 ⋮ ⅇ j ⁢ ⁢ 2 ⁢ ⁢ π ⁢ ⁢ v f s ⁢ ⁢ 63 + j ⁢ ⁢ φ 2 , and and , minimizing c ( α 1 , α 2 ) with respect to α 1 and α 2 yields , ∂ c ∂ α 1 = ⁢ - r → on h ⁢ x → 1 + α 2 * ⁢ x → 2 h ⁢ x → 1 + α 1 * ⁢  x → 1  2 = ⁢ - ∑ n = 0 63 ⁢ r on * ⁡ ( n ) ⁢ r off ⁡ ( n ) ⁢ ⅇ j2π ⁢ ⁢ v f s ⁢ ⁢ n + j ⁢ ⁢ φ 1 + α 2 * ⁢ ⅇ j ⁡ ( φ 1 - φ 2 ) ⁢ ∑ n = 0 63 ⁢  r off ⁡ ( n )  2 + α 1 * ⁡ (  r → off  2 + σ n 2 ) = ⁢ - ⅇ j ⁢ ⁢ φ 1 ⁢ p + α 1 * ⁡ ( s + σ n 2 ) + α 2 * ⁢ ⅇ j ⁡ ( φ 1 - φ 2 ) ⁢ s ∂ c ∂ α 2 = ⁢ - r → on h ⁢ x → 2 + α 1 * ⁢ x → 1 h ⁢ x → 2 + α 2 * ⁢  x → 2  2 = ⁢ - ∑ n = 0 63 ⁢ r on * ⁡ ( n ) ⁢ r off ⁡ ( n ) ⁢ ⅇ j2π ⁢ ⁢ v f s ⁢ ⁢ n + j ⁢ ⁢ φ 2 + α 1 * ⁢ ⅇ j ⁡ ( φ 2 - φ 1 ) ⁢ ∑ n = 0 63 ⁢  r off ⁡ ( n )  2 + α 2 * ⁡ (  r → off  2 + σ n 2 ) = ⁢ - ⅇ j ⁢ ⁢ φ 2 ⁢ p + α 1 * ⁢ ⅇ j ⁡ ( φ 2 - φ 1 ) ⁢ s + α 2 * ⁡ ( s + σ n 2 ) with ⁢ : ⁢ ⁢ σ n 2 = n → 1 h ⁢ n → 1 = n → 2 h ⁢ n → 2 , ⁢ s = ∑ n = 0 63 ⁢  r off ⁡ ( n )  2 ⁢ ⁢ and ⁢ ⁢ p = ∑ n = 0 63 ⁢ r on * ⁡ ( n ) ⁢ r off ⁡ ( n ) ⁢ ⅇ - j ⁢ ⁢ 2 ⁢ π ⁢ ⁢ v f s ⁢ ⁢ n the method preferably assumes that { right arrow over ( n )} 1 h { right arrow over ( n )} 2 ={ right arrow over ( n )} 1 h { right arrow over ( x )} 2 ={ right arrow over ( n )} 2 h { right arrow over ( x )} 1 ={ right arrow over ( n )} 1 h { right arrow over ( r )}={ right arrow over ( n )} 2 h { right arrow over ( r )}= 0 , although such is not exactly true in reality , and thereby reduces the overall computer processing required . thus , the process can continue with , { ∂ c ∂ α 1 = 0 ∂ c ∂ α 2 = 0 ⇒ [ s + σ n 2 ⅇ j ⁡ ( φ 1 - φ 2 ) ⁢ s ⅇ j ⁡ ( φ 2 - φ 1 ) ⁢ s s + σ n 2 ] ⁡ [ α 1 * α 2 * ] = [ ⅇ j ⁢ ⁢ φ 1 ⁢ p ⅇ j ⁢ ⁢ φ 2 ⁢ p ] ⁢ ⇔ [ α 1 α 2 ] = 1 ( s + σ n 2 ) 2 - s 2 ⁡ [ s + σ n 2 - ⅇ j ⁡ ( φ 2 - φ 1 ) ⁢ s - ⅇ j ⁡ ( φ 1 - φ 2 ) ⁢ s s + σ n 2 ] ⁡ [ ⅇ - j ⁢ ⁢ φ 1 ⁢ p * ⅇ - j ⁢ ⁢ φ 2 ⁢ p * ] ⁢ ⇔ [ α 1 α 2 ] = p * 2 ⁢ s + σ n 2 ⁡ [ ⅇ - j ⁢ ⁢ φ 1 ⅇ - j ⁢ ⁢ φ 2 ] in the absence of any timing misalignment , frequency offset or gaussian noise , the weighting coefficients are simply , [ α 1 α 2 ] = 1 2 ⁡ [ ⅇ - j ⁢ ⁢ φ 1 ⅇ - j ⁢ ⁢ φ 2 ] . the method is such that the steps of linearly combining and computing produce an γ ( ν ) that is real and much greater than | r on ( 0 )| 2 , and the result is ∠ ⁢ ⁢ p on * ≅ - 2 ⁢ π ⁢ ⁢ v f s ⁢ ⁢ 32 ⁢ ⁢ radian , and wherein , p * is composed of two phase coefficients , a first one ( p * on ) centers the frequency offset related phase component around z ( 32 ), and the second one ( p * δ ) contains timing - misalignment information . a result { right arrow over ( z )} is found , and the absolute value and sign of the timing misalignment can be determined by computing dot products , as in , γ value =  z → h ⁢ r → on   r → on  2 ⁢ λ max λ max - λ min where : { λ max , λ min }= eig ( m h m ) with m =[{ right arrow over ( x )} 1 { right arrow over ( x )} 2 ], and γ sign = re ⁡ ( z → h ⁢ ∂ r → on ∂ t ) . although the invention is described herein with reference to the preferred embodiment , one skilled in the art will readily appreciate that other applications may be substituted for those set forth herein without departing from the spirit and scope of the present invention . accordingly , the invention should only be limited by the claims included below .