Patent Publication Number: US-2004047284-A1

Title: Transmit diversity framing structure for multipath channels

Description:
[0001] This application is a continuation-in-part of U.S. patent application Ser. No. 10/099,556, “Transmit Multiplexing and Receive Processing for Delay Spread Channels,” filed Mar. 13, 2002, the entire contents of which is hereby incorporated by reference herein. 
    
    
     
       BACKGROUND OF THE INVENTION  
       [0002] 1. Field of the Invention  
       [0003] This invention generally relates to wireless communications links, and, more specifically, to frame structures for diverse antenna transmissions.  
       [0004] 2. Related Art  
       [0005] Virtually all wireless communication channels are limited in their ability to accurately communicate data by the signal-to-noise ratio (SNR) of the wireless channel. Antenna diversity is one category of techniques that may be used to enhance the effective SNR of communications channels, and thus enhance the ability to accurately transmit data.  
       [0006] Antenna diversity can be incorporated at the transmitter, or at the receiver, or both. However, for the cost-sensitive subscriber station, diversity is much cheaper if it is instantiated at the base station transmitter (where its benefits and costs may be shared by all subscribers), rather than at every subscriber station. In installations where a great deal of diversity is required for reliable service, multiplicities of diversity may be achieved if the base station transmitter and the subscriber station receiver both possess diversity. Mechanisms to realize transmit diversity are of great utility for wireless communications.  
       [0007] Many transmit diversity techniques have been proposed in the literature. One such technique is transmit delay diversity. At the transmitter, delay diversity is achieved by using two antennas that transmit the same signal, with the second antenna to transmitting a delayed replica of that transmitted by the first antenna. By so doing, the second antenna creates diversity by establishing a second set of independent multipath elements that may be collected at the receiver. If the multipath generated by the first transmitter fades, the multipath generated by the second transmitter may not, in which case an acceptable SNR will be maintained at the receiver. This technique is easy to implement, because only the composite TX0+TX1 channel is estimated at the receiver. Transmit delay diversity does not require the receiver to have special a-priori knowledge that the transmitter is using this type of diversity, because the receiver&#39;s equalizer compensates automatically for the additional multipath diversity induced by the second transmit antenna.  
       [0008] Both OFDM and single carrier modulation can easily implement a delay diversity scheme. The biggest drawback to transmit delay diversity is that it increases the effective delay spread of the channel, and can perform poorly when the multipath introduced by the second antenna falls upon, and interacts destructively with, the multipath of the first antenna, thereby reducing the overall level of diversity.  
       [0009] Another transmit diversity technique of low-to-moderate complexity is described in “A simple transmit diversity scheme for wireless communications,” S. Alamouti,  IEEE Journal on Select Areas in Communications , vol. 16, no. 8 Oct. 1998, pp. 1451-1458. This technique provides two-way maximal ratio-combining diversity. Unfortunately, the Alamouti transmit diversity scheme cannot be directly applied to systems experiencing delay spread, because it relies on an ability to isolate pairs of multiplexed symbols from each other, that is, the receiver must be able to process each pair of symbols without significant interaction from other pairs of symbols. In delay-spread channels, where symbol energy not only overlaps other symbols, but indeed may span hundreds of symbols, such absence of interaction cannot be relied upon. A transmit diversity technique that overcomes some of the limitations of the foregoing is described herein.  
       [0010] Transmit diversity techniques rely upon estimations of the symbol content of received signals. Estimating and compensating for transfer characteristics of the wireless channel, in turn, generally improves the symbol estimates. Irrespective of the basic transmit diversity technique used, techniques to enhance the symbol estimation will improve the overall ability of a communication system to accurately transfer data. Accordingly, there is a need for techniques to enhance the data transmission effectiveness of basic transmit diversity multiplexing techniques.  
       SUMMARY  
       [0011] Processing techniques and framing structures to enhance the effectiveness of transmit-diversity wireless communications, and systems employing such techniques and structures, are disclosed herein that may be used to enhance the effectiveness of communications transmitted by diverse antennas, particularly when the transmission channels have delay-spread characteristics. Multiplexing techniques to provide a plurality of signals for a corresponding plurality of transmit antennas are disclosed, as well as corresponding receiver combining and equalization techniques. Data structures are also disclosed for use in conjunction with diversity multiplexing techniques, particularly for delay-spread channels. Framing and processing techniques are disclosed that are applicable to single-carrier and/or OFDM transmit-diversity transmissions and receptions through delay-spread channels.  
       [0012] One embodiment is a method of transmitting dual signal-unit pairs from diverse antennas. It includes processing a plurality of N-point signal units each into a plurality of forms using time-domain techniques, and prepending a cyclic prefix on each of the resulting forms, before transmitting the prefixed forms of the signal units in concurrent pairs from the diverse antennas.  
       [0013] Another embodiment is a method of interpreting received signals that were transmitted in multiplexed forms from diverse transmit antennas. The method includes identifying received pilot words that include cyclically prefixed first and second pilot signal units. The method further includes ignoring the cyclic prefixes and combining forms of the first and second pilot signal units with first and second expected pilot symbol units to derive first and second channel estimates. The method further includes deriving estimates of transmitted payload signal units by combining forms of the channel estimates with forms of received payload signal units.  
       [0014] A further embodiment is a method of transmitting dual signal-unit pairs from diverse antennas. The method includes deriving a plurality of pilot signal units from portions of pilot data expected by a receiver, establishing a variant form of each signal unit, and cyclically prefixing the signal units and their variants. The method also includes transmitting, substantially concurrently, appropriate pairs of these various cyclically prefixed signal units. The method yet further includes transmitting a repetitive pilot signal unit by transmitting an appropriate signal unit pair one or more additional times, without cyclic prefixes, immediately after they have been transmitted with a cyclic prefixes.  
       [0015] Yet another embodiment is a system that may be used for transmitting dual signal-unit pairs from diverse antennas. The system includes first and second antennas and a signal-unit derivation block configured to derive N-point signal-units of time-domain samples from modulated source information. It also includes a diversity multiplexer block configured to multiplex pairs of the derived N-point signal units into multiplexed dual signal-unit pairs, each having first and second N-point multiplexed-signal-units (“MSUs”) for the first antenna, and first and second N-point MSUs for the second antenna, where the first N-point MSU for the first antenna is related to the second N-point MSU for the second antenna by complex conjugation and modulo-N sample time inversion, and the second N-point MSU for the first antenna is related to the first N-point MSU for the second antenna by complex conjugation, negation, and modulo-N sample time inversion. The system also includes a first output processing block configured to cyclically prefix the first and second N-point MSUs for the first antenna, and to process the prefixed MSUs for sequential transmission from the first antenna; and a second output processing block configured to cyclically prefix the first and second N-point MSUs for the second antenna, and to process the prefixed MSUs for sequential transmission from the second antenna substantially concurrently with the sequential transmission from the first antenna.  
       [0016] Yet a further embodiment is a receiver system that may be used for receiving paired multiplexed signals transmitted from plural antennas. The system of this embodiment includes a receive and alignment block configured to receive and align prefixed multiplexed-signal-units (“MSUs”) received sequentially in a frame structure having a preamble portion and a payload portion, and a cyclic prefix removal block configured to remove cyclic prefixes from received MSUs. The system also includes a pilot word identification block configured to identify, in accordance with relative position within the frame structure, J concatenated copies of a first received pilot MSU, RP 0 , followed by P concatenated copies of a second received pilot MSU, RP 1 , that were transmitted based upon a first expected pilot signal-unit EP 0  and a second expected pilot signal-unit EP 1 , and a channel estimation block configured to combine a representation of RP 0  and a representation of RP 1  with complex conjugated forms of EP 0  and EP 1  to create a first channel estimate HE 1 , and to combine the representations of RP 0  and RP 1  with forms of EP 0  and EP 1  that are not complex conjugated to create a second channel estimate HE 2 .  
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0017] Embodiments of the present invention will be more readily understood by reference to the following figures, in which like reference numbers and designations indicate like elements.  
     [0018]FIG. 1 illustrates temporal organization of a block pair.  
     [0019]FIG. 2 illustrates concatenation of block pairs for transmission.  
     [0020]FIG. 3 is a matrix showing a dual block pair signal multiplexing relationships.  
     [0021]FIG. 4 is a signal flow diagram of a Decision Feedback Equalizer.  
     [0022]FIG. 5 shows a Unique Word variation of the multiplexing of FIG. 3.  
     [0023]FIG. 6 illustrates a burst transmission using a Unique Word preamble.  
     [0024]FIG. 7 shows Pilot Words disposed in a general payload transmission.  
     [0025]FIG. 8 illustrates a use of cyclic prefixes with the multiplexing of FIG. 3.  
     [0026]FIG. 9 illustrates using Unique Words for cyclic prefixes in block pairs.  
     [0027]FIG. 10 shows a dual block pair multiplexing transmission format.  
     [0028]FIG. 11 illustrates communication system features including plural receivers.  
     [0029]FIG. 12 is a block diagram of transmit diversity processing for single-carrier applications using time domain multiplexing.  
     [0030]FIG. 13 illustrates dual block pair signal multiplexing relationships for OFDM.  
     [0031]FIG. 14 is a block diagram of transmit diversity processing for OFDM applications using frequency domain multiplexing.  
     [0032]FIG. 15 shows a modification of the processing of FIG. 14 to use time domain multiplexing and avoid some FFTs.  
     [0033]FIG. 16 is a block diagram showing OFDM transmit diversity receive processing.  
     [0034]FIG. 17 illustrates an example of preamble framing for OFDM transmit diversity.  
    
    
     DETAILED DESCRIPTION  
     [0035] Multiplexed data may be transmitted over two or more antennas, as described more fully below, to enhance the reliability of communication with a receiver (or receivers). The techniques described are particularly effective when the communication is conducted over multipath delay spread channels. Two-antenna diversity can double the effective diversity level of a system operating over such channels. Of course, multipath, in itself, is a form of diversity. Thus, for example, with a system operating over a single channel with three multipaths and having (therefore) a diversity level of three; use of two transmit antennas (with one receiver) as described below could increase the diversity level to 6 (or more). Embodiments that further employ two or more receivers may increase the diversity gains even further.  
     Single Carrier Transmnit Diversity  
     [0036] This description assumes a communication system that is configured to transfer selected signals from a transmission system having a plurality of transmit antennas to a receiving system having one or more antennas. The desired transmission signals are assumed to at least partly take the form of symbols defined in the time domain. FIG. 1 illustrates that a selected number B of symbols may be organized as a symbol block, such as a “Block 0”  102  or a “Block 1”  104 . Ideally, a delay spread guard period  106  is provided before each block (e.g.,  102  and  104 ). For convenience, delay spread guard periods will typically have the same length, D, which may be measured in symbol lengths or time. The length, D, of these delay spread guard regions would typically be longer than the delay spread span of the channel. In one embodiment, these delay spread guard regions would have a ‘cyclic prefix’ format; i.e., they would be composed of the last D symbols of the block that follows them. A combination of sequential blocks, such as the illustrated Block  0  and Block  1 , each preceded by a delay spread guard having a known length that may range down to zero, fonrs a block pair  100 . Note that the two blocks within a block pair are logically paired together, but physically separated from themselves (or other data) by delay spread guard regions  106 . In general, any particular block, such as the “Block 0”  102 , may be the same or different from the other block (e.g., “Block 1”  104 ) of its block pair  100 . It will generally be useful, for minimizing bit error rate (BER) characteristics, if the channels from each antenna to the receiving. system do not change significantly between the beginning and end of transmission of a block pair. Note that the symbols within a block should be adjacent, but that blocks composing a block pair do not have to be adjacent, although they are pictured that way in FIGS. 1 and 2.  
     [0037]FIG. 2 illustrates a sequence of block pairs, including block pairs (m−1)  202 , (m)  204 , (m+1)  206  and (m+2)  208 , which have been concatenated for transmission as an extended payload from a particular antenna. In general, any block pair transmitted from a particular antenna may be different from or identical to any other block pair transmitted from the same antenna at another time.  
     [0038] Block Pair Transmit Multiplexing  
     [0039]FIG. 3 indicates a block multiplexing structure that a two-antenna transmitter may use to transmit the information of each of two sequences in two related forms over block pairs  302  and  304  that resemble the block pair  100  (see FIG. 1). {s 0 [n]} is a signal set describing a first block  306  of the block pair  302  transmitted by Transmit Antenna  0 , while {s 1 [n]} is a signal set that describes a second block  308  of the block pair  302 . {s 0 [n]} and {s 1 [n]} each describe a sequence of length B symbols, 0≦n&lt;B−1, that represents information that is to be delivered to a receiver via the two transmit antennas.  
     [0040] A block  310  is the first block of the block pair  304  transmitted by Transmit Antenna  1 , while block  312  is the second block of the block pair  304  transmitted by Transmit Antenna  1 . The first block  306  of the block pair  302  conveys the same information as the second block  312  of the block pair  304 , but in a different form. As compared to the block  306 , the block  312  is a time-inverted sequence of the complex conjugate of the symbols that form the symbol sequence {s 0 [n]}. Similarly, the first block  310  of the block pair  304  is a time-inverted sequence of the negative complex conjugate of the symbols of the sequence {s 1 [n]}.  
     [0041] Thus, Transmit Antenna  1  transmits blocks having the same information as is transmitted by related blocks of Transmit Antenna  0 , but in reverse time order, and the blocks of Transmit Antenna  1  have a sequence of symbols that are the (positive or negative) complex conjugate of the symbols of the related blocks of Transmit Antenna  0  in a sequence that is also time-reversed cyclically about zero, modulo-B.  
     [0042] It should be understood that the signal sets {s 0 [n]} and {s 1 [n]} are only nominally in an “unmodified” form. Either or both {s 0 [n]} and {s 1 [n]} may, of course, be related to other symbol sequences that are the actual symbols which are being sent. Thus, either of these signals may in fact be, for example, a time-inverted, negated and/or complex-conjugated version of the actual desired symbols. This merely reflects the generality of the signal sets {s 0 [n]} and {s 1 [n]}, and does not affect the relationship between blocks that are diagonally positioned within the space-time matrix of blocks shown in FIG. 3.  
     [0043] Transmit and Receive Signal Relationships  
     [0044] Define S 0 (e jω ), S 1 (e jω ), N 0 (e jω ), N 1 (e jω ), H 0 (e jω ), and H 1 (e jω ) as the Discrete-time Fourier transforms (DTFTs), respectively, of the symbol sequences {s 0 [n]} and {s 1 [n]} (each normalized, without loss of generality, so that their average symbol energy is 1); additive white, zero-mean, σ 2 -variance noise sequences {n 0 [n]} and {n 0 [n]}; and the channel impulse responses {h 0 [n]} and {h 1 [n]} that are associated with each transmit antenna Due to the multiplexed transmit signals, each received block of payload symbols (which is typically separated from other blocks by delay spread guard intervals) includes information from both blocks of a received block pair. Accordingly, the information from individual blocks can only be extracted by combining information from the two blocks of a block pair. The received signals associated with each individual block of a block pair, interpreted in the frequency domain, are:  
                         R   0          (          j                 ω       )       =           H   0          (          j                 ω       )              S   0          (          j                 ω       )         -         H   1          (          j                 ω       )              S   1   *          (          j                 ω       )         +       N   0          (          j                 ω       )                         R   1          (          j                 ω       )       =           H   0          (          j                 ω       )              S   1          (          j                 ω       )         +         H   1          (          j                 ω       )              S   0   *          (          j                 ω       )         +       N   1          (          j                 ω       )                 .           Eqn   .              1                       
 
     [0045] Note that DTFTs are used for frequency domain descriptions for generality, but this is in no way limiting: a B-point (or, more generally, an implementation using a K-point) Discrete Fourier Transform (DFT) would uniformly sample the DTFT response over the interval ωε[0,2π), yielding B (or K) samples.  
     [0046] The received signal is a merger of the concurrently transmitted blocks, so processing facilities should identify received block pairs (through their time relationship with a preamble, for example), and combine forms of the received block pairs with forms of the channel response estimates. Assuming that the frequency domain channel responses H 0 (e jω ) and H 1 (e jω ) are known (or estimated), a received block pair R 0  and R 1  may be filtered and combined according to the frequency domain combining scheme  
                         C   0          (          j                 ω       )       =           H   0   *          (          j                 ω       )              R   0          (          j                 ω       )         +         H   1          (          j                 ω       )              R   1   *          (          j                 ω       )                           C   1          (          j                 ω       )       =         -       H   1          (          j                 ω       )                R   0   *          (          j                 ω       )         +         H   0   *          (          j                 ω       )              R   1          (          j                 ω       )                   .           Eqn   .              2                       
 
     [0047] Processing the block pair, R 0  and R 1 , thus includes filtering various forms of the received blocks with a form of a channel estimate, and in the frequency domain the filtering may consist of multiplying a form of a channel estimate by a form of a received block. The appropriate filtered results are then combined (in the frequency domain case, added) to produce a pair of combiner outputs C 0  and C 1 . Using the expanded representation of the received blocks provided by Eqn. 1, the combiner outputs are seen to be  
                               C   0          (          j                 ω       )       =                (                H   0          (          j                 ω       )            2     +              H   1          (          j                 ω       )            2       )            S   0          (          j                 ω       )         +                                H   0   *          (          j                 ω       )              N   0          (          j                 ω       )         +         H   1          (          j                 ω       )              N   1   *          (          j                 ω       )                                       C   1          (          j                 ω       )       =                (                H   0          (          j                 ω       )            2     +              H   1          (          j                 ω       )            2       )            S   1          (          j                 ω       )         -                                H   1          (          j                 ω       )              N   0   *          (          j                 ω       )         +         H   0   *          (          j                 ω       )              N   1          (          j                 ω       )                         .           Eqn   .              3                       
 
     [0048] Applying the following definitions:  
               D        (          j                 ω       )       ≡     (                H   0          (          j                 ω       )            2     +              H   1          (          j                 ω       )            2       )             Eqn   .              4             and                                     N     C   0            (          j                 ω       )       =           H   0   *          (          j                 ω       )              N   0          (          j                 ω       )         +         H   1          (          j                 ω       )              N   1   *          (          j                 ω       )                           N     C   1            (          j                 ω       )       =         -       H   1          (          j                 ω       )                N   0   *          (          j                 ω       )         +         H   0   *          (          j                 ω       )              N   1          (          j                 ω       )                   ,           Eqn   .              5                       
 
     [0049] the expressions for the fiequency domain representation of the combiner outputs C 0 (e jω ) and C 1 (e jω ) become  
                       C   0          (          j                 ω       )       =         D        (          j                 ω       )              S   0          (          j                 ω       )         +       N     C   0            (          j                 ω       )                         C   1          (          j                 ω       )       =         D        (          j                 ω       )              S   1          (          j                 ω       )         +       N     C   1            (          j                 ω       )                       Eqn   .              6                       
 
     [0050] In view of Eqn. 6, estimates of S 0 (e jω ) and S 1 (e jω ) may be obtained using any equalization technique that will substantially remove the influence of D(e jω ).  
     [0051] Equalization  
     [0052] Many equalization techniques exist. A linear equalizer may be used in an effort to eliminate D(e jω ) through pre-multiplication by an appropriate equalizer characteristic that is generally inverse to D(e jω ):  
                             S   ^     0          (          j                 ω       )       linear     =         E        (          j                 ω       )       linear            C   0          (          j                 ω       )                             S   ^     1          (          j                 ω       )       linear     =         E        (          j                 ω       )       linear            C   1          (          j                 ω       )                 .           Eqn   .              7                       
 
     [0053] Linear equalizer functions may take various forms. As examples, the linear equalizer solution obtained using a zero forcing (ZF) optimization criterion would be  
                   E        (          j                 ω       )       linear   ZF     =     1     D        (          j                 ω       )           ,           Eqn   .              8                       
 
     [0054] whereas a linear equalizer solution obtained using a Minimum Mean Squared Error (MMSE) optimization criterion would be  
                 E        (          j                 ω       )       linear   MMSE     =       1       D        (          j                 ω       )       +     σ   2         .             Eqn   .              9                       
 
     [0055] Because D is defined in Eqn. 4, frequency domain processing facilities may therefore equalize the combiner outputs by dividing each output by a quantity that reflects a sum of the individual channel response magnitudes. In the case of MMSE, the divisor sum further includes a term σ 2  that reflects a normalized reciprocal of the signal to noise ratio (SNR) measured for the received signal. The aforesaid equalization results may be directly interpreted as estimates Ŝ 0 (e jω ) and Ŝ 1 (e jω ), whereupon (soft) equalized estimates of the symbol sequences {s 0 [n]} and {s 1 [n]} may be obtained directly by computing inverse DTFTs (I-DTFTs) of the estimates.  
     [0056] Instead of performing frequency domain processing, the facilities may perform combining and equalization in the time domain using block length-B circular convolutions (denoted by the operator ‘{circle over (x)}’), where  
                             s   ^     0          [   n   ]       linear     =         e   linear          [   n   ]       ⊗       c   0          [   n   ]                             s   ^     1          [   n   ]       linear     =         e   linear          [   n   ]       ⊗       c   1          [   n   ]                 ,           Eqn   .              10                                 c   0          [   n   ]       =                  h   0   *          [       (     B   -   n     )                   mod                   (   B   )       ]       ⊗       r   0          [   n   ]         +                              h   1          [   n   ]       ⊗       r   1   *          [       (     B   -   n     )                   mod                   (   B   )       ]                                     c   1          [   n   ]       =                -       h   1          [   n   ]         ⊗       r   0   *          [       (     B   -   n     )                   mod                   (   B   )       ]         +                              h   0   *          [       (     B   -   n     )                   mod                   (   B   )       ]       ⊗       r   1          [   n   ]                       ,           Eqn   .              11                       
 
     [0057] and the lower-case variables are time domain representations of upper-case frequency domain variables. Thus, in the tine domain the combiner outputs may be based on forms of received blocks filtered by forms of channel estimates, just as in the frequency domain. In the time domain case, the various forms of the received blocks, and of the channel estimates, may differ by not only complex conjugation (positive or negative), but also by time-reordering of the symbol sequences, and in particular by cyclic time reversal of the time sequence of the corresponding block symbols. The equalization filtering may be performed by circular convolution between block-length sequences. The equalizer e linear [n] may be derived from an I-DTFT of E(e jω ) linear  if frequency domain information on the channel impulse responses is immediately available. If not, the time domain responses may be frequency transformed to generate H 0 (e jω ) and H 1 (e jω ), and then E(e jω ) linear  May be derived, for example, by further processing according to Eqn. 8 or Eqn. 9.  
     [0058]FIG. 4 Illustrates equalizer elements In an equalizer subsystem that may be less prone, than a linear equalizer, to emphasize noise in frequency bands where notches occur. FIG. 4 shows a signal to be equalized  402  progressing through a typical Decision Feedback Equalizer (DFE) having two equalizer processing elements: a feedforward (linear) filter  404 , and a decision feedback filter  406  that subtracts symbol decisions made in the time domain. The linear feedforward filter element  404  generates intermediate equalized results  
                         Z   0          (          j                 ω       )       =         E        (          j                 ω       )       FF            C   0          (          j                 ω       )                         Z   1          (          j                 ω       )       =         E        (          j                 ω       )       FF            C   1          (          j                 ω       )                 ,           Eqn   .              12                       
 
     [0059] and an I-DTFT may be applied to the equalized results to yield time domain sequences z 0 [n] and z 1 [n]. Each of these sequences may then be separately operated upon in the time domain by the decision feedback filter  406 , and may use identical feedback coefficients f[n] to provide an equalized signal  408  in the form of estimates {ŝ 0 [n]} and {ŝ 1 [n]}.  
     [0060] A MMSE criterion-optimizing DFE may use the feedforward filter  
                   E        (          j                 ω       )       FF   MMSE     =       F        (          j                 ω       )           D        (          j                 ω       )       +     σ   2           ,           Eqn   .              13                       
 
     [0061] where F(e jω ) is the DTFT of f[n]. A zero-forcing solution would be identical to the MMSE solution, except that it would not possess the σ 2  found in Eqn. 13, which reflects the normalized reciprocal of the receiver SNR.  
     [0062] The frequency domain filtering described in Eqn. 12 may, in the alternative, be implemented in the time domain. The signal processing may filter the combiner outputs by circularly convolving them with an equalization sequence e FF [n]:  
                           z   0          [   n   ]       linear     =         e   FF          [   n   ]       ⊗       c   0          [   n   ]                           z   1          [   n   ]       linear     =         e   FF          [   n   ]       ⊗       c   1          [   n   ]                 ,           Eqn   .              14                       
 
     [0063] where e FF [n] is the I-DTFT of E(e jω ) FF (in either its MMSE or zero-forcing forms).  
     Channel Estimation  
     [0064] It is, of course, very helpful to obtain good channel estimates, since the estimates of the transmitted sequences may depend upon the channel estimates at a number of stages. Manipulation of Eqn. 1 reveals that the frequency domain channel characteristics can be expressed as  
                             H   0          (          j                 ω       )       =                      S   0   *          (          j                 ω       )              R   0          (          j                 ω       )         +         S   1          (          j                 ω       )              R   1   *          (          j                 ω       )                        S   0          (          j                 ω       )            2     +              S   1          (          j                 ω       )            2         -                                  S   0   *          (          j                 ω       )              N   0          (          j                 ω       )         +         S   1          (          j                 ω       )              N   1   *          (          j                 ω       )                        S   0          (          j                 ω       )            2     +              S   1          (          j                 ω       )            2                                     H   1          (          j                 ω       )       =                      S   0          (          j                 ω       )              R   1          (          j                 ω       )         -         S   1          (          j                 ω       )              R   0          (          j                 ω       )                        S   0          (          j                 ω       )            2     +              S   1          (          j                 ω       )            2         -                                    S   0          (          j                 ω       )              N   1          (          j                 ω       )         -         S   1          (          j                 ω       )              N   0          (          j                 ω       )                        S   0          (          j                 ω       )            2     +              S   1          (          j                 ω       )            2         .                         Eqn   .              15                       
 
     [0065] This leads to calculations that may be performed by the receiver signal processing facilities to obtain channel estimates, including the frequency domain MMSE estimates  
                           H   ^     0          (          j                 ω       )       MMSE     =             S   0   *          (          j                 ω       )              R   0          (          j                 ω       )         +         S   1   *          (          j                 ω       )              R   1          (          j                 ω       )                        S   0          (          j                 ω       )            2     +              S   1          (          j                 ω       )            2     +     σ   2                             H   ^     1          (          j                 ω       )       MMSE     =             S   0          (          j                 ω       )              R   1          (          j                 ω       )         -         S   1          (          j                 ω       )              R   0          (          j                 ω       )                        S   0          (          j                 ω       )            2     +              S   1          (          j                 ω       )            2     +     σ   2                       Eqn   .              16                       
 
     [0066] and zero-forcing estimates  
                             H   ^     0          (          j                 ω       )       ZF     =             S   0   *          (          j                 ω       )              R   0          (          j                 ω       )         +         S   1   *          (          j                 ω       )              R   1          (          j                 ω       )                        S   0          (          j                 ω       )            2     +              S   1          (          j                 ω       )            2                             H   ^     1          (          j                 ω       )       ZF     =             S   0          (          j                 ω       )              R   1          (          j                 ω       )         -         S   1          (          j                 ω       )              R   0          (          j                 ω       )                        S   0          (          j                 ω       )            2     +              S   1          (          j                 ω       )            2                 .           Eqn   .              17                       
 
     [0067] The channel estimates of Eqns. 16 and 17 are based upon arbitrary symbol data sequences {s 0 [n]} and {s 1 [n]}. Unfortunately, the arbitrary symbol data sequences must generally be estimated themselves, thus compounding any inaccuracies. It may be useful to avoid relying exclusively on such estimates for further deriving estimates of the channel response.  
     [0068] Preambles and Pilot Words  
     [0069] The channel estimation process will be less reliant on received symbol estimates when known sequences of symbols are transmitted at identifiable times. These known sequences may be referred to generally as “pilot symbols,” although it should be understood that such sequences might also appear in preambles, or in other forms. In many cases, an identical sequence will be consistently transmitted as pilot symbols, and this fact may be exploited to reduce the complexity of channel estimates computation according to algorithms Such as those listed in Eqns. 16 and 17.  
     [0070] Pilot sequences with constant magnitude spectrum, i.e.,  
                    S   pilot          (          j                 ω       )            2     =   K     ,                 
 
     [0071] are desirable, because this condition reduces noise emphasis (within certain frequency bands) in the estimation process. Examples of sequences having constant magnitude spectrum properties (or, equivalently, ‘perfect’ circular autocorrelation properties) may be found, for example, within a trio of references including: “Phase Shift Codes with Good Periodic Correlation Properties” by R. L Frank and S. A. Zadoff, IRE Trans. Information Theory, October, 1962, pp. 381-382; “Polyphase Codes with Good Periodic Correlation Properties” by D. C. Chu, IEEE Trans. Information Theory, July, 1972, pp. 531-532; and “Periodic Sequences With Optimal Properties for Channel Estimation and Fast Start-up Equalization” by A. Milewski, IBM J. Res. And Development, September 1983, pp. 426-431. Each of these references is hereby incorporated herein in its entirety.  
     [0072] For embodiments that use such constant magnitude pilot sequences, the MMSE channel estimation step in Eqn. 16 may be reduced to  
                             H   ^     0          (          j                 ω       )       MMSE     =       1       2      K     +     σ   2                S   pilot   *          (          j                 ω       )            (         R   0          (          j                 ω       )       +       R   1          (          j                 ω       )         )                           H   ^     1          (          j                 ω       )       MMSE     =       1       2      K     +     σ   2                S   pilot          (          j                 ω       )            (         R   1          (          j                 ω       )       -       R   0          (          j                 ω       )         )               ,           Eqn   .              18                       
 
     [0073] which does not rely on estimates of the transmitted signals, but instead relies upon the known pilot sequence, the frequency domain representations of the received blocks of the block pair, and a (normalized reciprocal) SNR measured for the receiver.  
     [0074] Note that these channel estimations may, instead, be performed in the time domain, using circular convolution of time domain versions of the received blocks, and two versions of the pilot signal (one the complex conjugate and cyclic time reversal of the other), which are known. Thus, if the pilot sequences are identical and have constant magnitude frequency response, then the receiver signal processing may perform the following functions to produce time domain channel estimates, which may then be used to combine the block pairs in the time domain, as described for example by Eqn. 11:  
                             h   ^     0          [   n   ]       MMSE     =       1       2      K     +     σ   2                  s   pilot   *     [       (     B   -   n     )                     mod   (   B   )       ]     ⊗     (         r   0          [   n   ]       +       r   1          [   n   ]         )                               h   ^     1          [   n   ]       MMSE     =       1       2      K     +     σ   2                  s   pilot          [   n   ]       ⊗     (         r   1          [   n   ]       -       r   0          [   n   ]         )                              .           Eqn   .              19                       
 
     [0075] If arbitrary (but known) reference sequences are used that do not necessarily have constant magnitude response, then the receiver signal processing may derive channel estimates (in the time domain) by performing the steps of Eqn. 20:  
                             h   ^     0          [   n   ]       MMSE     =       g        [   n   ]       ⊗     (           s     pilot   0     *     [       (     B   -   n     )                     mod   (   B   )       ]     ⊗       r   0          [   n   ]         +           s     pilot   1     *     [       (     B   -   n     )                     mod   (   B   )       ]     ⊗   r                     1        [   n   ]           )                             h   ^     1          [   n   ]       MMSE     =       g        [   n   ]       ⊗     (           s     pilot   0            [   n   ]       ⊗       r   1          [   n   ]         -         s     pilot   1            [   n   ]       ⊗       r   1          [   n   ]           )                                 
          where                   g        [   n   ]                     is                 the                 I        -        DTFT                 of             Eqn   .              20                 G        (          j                 ω       )       =       1                S   0          (          j                 ω       )            2     +              S   1          (          j                 ω       )            2     +     σ   2         .             Eqn   .              21                       
 
     [0076] Efficient use of pilot symbols is always a system design goal, since pilot symbols improve receiver performance but also add to system overhead. Certain pilot symbol structures, such as constant magnitude pilot sequence, are preferred because they permit efficiencies such as described above.  
     [0077]FIG. 5 illustrates a grouping of pilot symbols composed of identical sequence units that may be called ‘Unique Words’ (UWs). These UWs may be chosen to have good autocorrelation properties, such as those described in the trio of three references identified above. Each of the UWs is of length U symbols, and, for best effect, is preferably at least as long as the delay spread that is observed on the operating channel. Furthermore, as compared to ‘dual-blocks’ for payload data (see FIGS. 1 and 2), UWs are likely to be shotrter, repeated in groups, and averaged before processing.  
     [0078] As shown in FIG. 5, an identical UW block  502  is repeated J times using the format shown for the block  306  in FIG. 3 to form a first repetition block  504  for transmit antenna  0 , and is also repeated P times using format shown in block  308  of FIG. 3 to form a second repetition block  506  for the transmit antenna  0 . Similarly, UWs  510  (related to the UWs  502 ) are repeated J times using the format of the block  310  of FIG. 3 to form a repetition block  504  for transmit antenna  2 , and UWs  512  (differently related to the UWs  502 ) are repeated P times using the format of the block  312  of FIG. 3 to form a second repetition block  506  for the transmit antenna  2 . This grouping reduces overhead, since the first UW in each repeated block also serves as a cyclic prefix guard interval to guard the signals that follow from the corrupting delay spread of previously transmitted signals. Because it serves as a guard interval, the first UW in a repetition block might be corrupted and thus not useful for channel estimation purposes. However, the successive (J−1) or (P−1) blocks are typically usable. J and P will commonly be identical values.  
     [0079] To perform channel estimation, each of the useable UWs within a repetition block  504  may be paired with a corresponding UW within the corresponding repetition block  506 . The receiver signal processing may then estimate the channels in the frequency domain by performing the steps described by Eqn. 18 (following a Fourier transform, such as a fast Fourier Transform FFT or DTFT), or in the time domain by performing the steps described by Eqn. 19. If J=P, and if the first UW is used exclusively as a cyclic prefix, then (J−1) channel estimates may be made, one from each pair of UWs, and the resulting (J−1) channel estimates may then be averaged. (Up to (J−1)*(P−1) different estimates could be made and then averaged to small advantage over the (J−1) different estimates described.) A more computationally efficient (but mathematically substantially identical) approach is to average together the (J−1) blocks within the repetition block  504 , average together the (P−1) uncorrupted blocks within the repetition block  506 , and then apply estimation techniques such as Eqn. 18 or Eqn. 19 on these averaged results. This technique is convenient even when J≠P.  
     [0080] Burst transmissions often require channel estimation before processing of the payload data can commence. FIG. 6 illustrates a burst communication timing structure  600  that uses a burst preamble  602  to assist in initial channel estimation. Referring also to FIG. 5, the preamble  602  is one location where the pilot symbol structure of FIG. 5 may be applied, using repetition blocks  504  and  506  of UWs (which may take the form of UWs  502 ,  510  or  512 ). Payload data  604  may itself consist of one or more dual blocks (e.g.,  100  in FIG. 1). A ramp-up region  606 , where the transmitter ramps up its output power, may also be constructed as a (partial) cyclic prefix, in which event it could include several of the last symbols within a first UW  610  in the burst preamble  602 . Use of such a ramp-up  606  can reduce timing accuracy requirements for the reception of a burst, and enable more efficient utilization of the symbols within the preamble  602 . A ramp-down region  612  typically also exists, and may reduce spurious emissions that would otherwise result from a sharp step in transmit power.  
     [0081] Most communication channels change with time. If a burst is short enough, and the channel change is slow enough, no update of a channel estimate may be necessary. However, for continuous communication channels, or longer bursts, updated channel estimates are generally necessary. Such estimates may be derived from the arbitrary payload data (e.g.,  604 ). The transmitter may also insert a known sequence, referred to as a pilot word, from which the channel can be estimated.  
     [0082]FIG. 7 illustrates the insertion of pilot words  702  within a representative payload  704 . In one structure, pilot words are arranged in a form as illustrated in FIG. 5, with a repetition block  504  of UWs followed by a repetition block  506  of UWs. Pilot words may be inserted after one or more block pairs, for example after multiple block pairs  706  or  708 , and may have a periodic spacing interval if multiple block pairs  706  and  708  have the same length. Pilot words may have a basic format similar to a preamble, although the number of sub-blocks (e.g., UWs) in a preamble repetition block is likely to differ from the number of sub-blocks in a pilot word repetition block.  
     [0083] Dual Block Structure Refinements  
     [0084]FIG. 8 illustrates use of cyclic prefixes by transmitter processing facilities with block pair structures  802  (for the first transmit antenna) and  804  (for the second transmit antenna). Aside from the explicit cyclic prefixes, the block pairs  802  and  804  are similar to the general block pair  100  of FIG. 1 with the multiplexing features shown in FIG. 3. As can be seen, a cyclic prefix  806  is composed of the last U symbols  808  that typically form part of a “Block 0”  810 . Similarly, a cyclic prefix  814  is formed of the last U symbols (not separately identified) of a “Block 1”  814 . The blocks  810 ,  814 ,  816  and  818  are shown to have the multiplexing structure of the respective blocks  306 ,  308 ,  310  and  312  of FIG. 3. The cyclic prefixes  806 ,  812 ,  820  and  822  each perform the function of the general delay spread guard interval  106  illustrated in FIG. 1.  
     [0085]FIG. 9 illustrates a specific case of dual block structure in which a Unique Word (UW)  902  is used to implement the cyclic prefix used as a guard interval for blocks  904  and  906 . As in FIG. 8, the block  904  includes (B+U) symbols. However, since the U symbols of the UW  902  generally do not carry new information (such as data to be conveyed across the wireless link), and since the last U symbols of the payload of the block  904  are identical to the UW  902 , the effective payload  908  of the block  904  is (B−U) symbols.  
     [0086]FIG. 10 illustrates the portions  1002  of blocks  904 ,  906 ,  1004  and  1006  that the receiver signal processing may be restricted to considering for most sequence calculations, since the portions  1002  follow the UW cyclic prefix that functions as a delay spread guard interval. One or more UWs may thus incorporated into the equalizer portions  1002 . While not generally constituting new data, these UWs may be used to initialize the memory of the feedback filter used in a Decision Feedback Equalizer as described with respect to FIG. 4. FIG. 10 also illustrates the UW cyclic prefix structure of FIG. 9, in the context of a block pair  1012  for transmit antenna  0  and a block pair  1014  for transmit antenna  1 , that follows the general dual block pair multiplexing structure illustrated in FIG. 3. The generality of the symbol sequences of such dual block pairs should be borne in mind, since if {b 0 [n]} 32  {c 0 *[(N−n) mod(N)]} and the latter is substituted for the former, then an apparently different signal multiplexing format is described by the block pair structure of FIG. 10. However, such difference is apparent only, and involves only a substitution of form that is encompassed by the generality of block symbol sequences.  
     [0087]FIG. 11 illustrates a wireless link system including a link medium  1100 , a transmission system  1102  (shown as above the medium  1100 ), and a receiver system  1104  (shown as below the medium  1100 ). The transmission system  1102  includes a transmit signal generator block  1106  that may be configured to prepare at least two signals using any combination of the block pair transmission techniques discussed above. The transmit signal generator block  1106  delivers multiplexed signals (e.g., a first block pair) to a first transmit antenna Tx 0   1108 , and related multiplexed signals (e.g., a second block pair) to a second transmit antenna Tx 1   1110 . The receiver system  1104  is shown with two cooperating receivers  1112  and  1114 .  
     [0088] The first receiver system  1112  may be viewed as a stand-alone receiver, operating according to the teaching above, by ignoring the second receiver  1114  for a moment. The first receiver system  1112  includes a first receive antenna Rx 0   1116 , which provides the signals received from Tx 0   1108  and Tx 1   1110  via two wireless channels, which are represented as h 0,0  and h 1,0 . A combining and linear equalization block  1118  may, in general, process the received block pairs in any combination of time domain and/or frequency domain, as described above, to provide outputs  1120  and  1122 . If the outputs  1120  and  1122  are in the time domain (either because they were processed in the time domain, or by inverse Fourier transform from a frequency domain representation), they may be interpreted directly as the receiver&#39;s estimates of the transmitted sequences S 0  and S 1 , essentially bypassing further processing and becoming estimate outputs (this technique is not shown).  
     [0089] However, the outputs may be frequency domain representations z 0,0  and z 1,0 , as shown. In this event, blocks  1124  and  1126  may weight the respective outputs by the SNR measured for Rx 0  to effect maximal ratio combining. Since the second receiver  1114  is being ignored, the SNR weighted resultants gain nothing from the summing blocks  1128  and  1130 , and go to blocks  1132  and  1134 , respectively. If the resultants are already in the time domain, the sums may be interpreted directly as transmitted symbol sequence estimates, or may be passed on directly for decision feedback filtering. If the resultants are in the frequency domain, then blocks  1132  and  1134  may simply transform by inverse Fourier to the time domain and interpret the results as transmitted sequence estimates.  
     [0090] The blocks  1132  and  1134  may also perform decision feedback filtering as described above to produce outputs  1136  and  1138  as decision feedback equalized estimates of the transmitted sequences {ŝ 0 [n]} and {ŝ 1 [n]} (indicated as s 0  and s 1 ), respectively. Each of the blocks shown within the first receiver  1112  thus represents a possible system block for a receiver using some combination of the time and/or frequency domain combining and equalization techniques described herein.  
     [0091]FIG. 11 also illustrates an extension of the techniques described herein for using a plurality of cooperating receivers. The second receiver  1114  is now taken into consideration, beginning with a second antenna  1140 , which receives the multiplexed signals from Tx 0   1108  and Tx 1   1110  via two corresponding channels represented as h 0,1  and h 1,1 . The two receivers each perform transmit diversity combining and linear (feedforward) equalization independently, as shown, in their respective combining and linear equalization blocks  1118  and  1142 .  
     [0092] For cooperating receivers, the combining and linear equalization block  1142  will generally be configured identically to the block  1118 . The signals may be transformed to the frequency domain within the combining and linear equalization processes, as described above and preferably by the same processing used in the combining block  1118 , to provide frequency domain outputs  1144  and  1146 , indicated as z 0,1  and z 1,1 . Weighting by the SNR determined for Rx 1  to effect maximal ratio combining may be performed in the blocks  1148  and  1150 .  
     [0093] At this point in cooperating receiver processing, the weighted resultants from the second receiver  1114  are added, at the summing blocks  1128  and  1130 , respectively, to the weighted resultants developed within the first receiver  1112 . The sums from these blocks may then be converted to the time domain by inverse Fourier transformation. As shown, decision feedback filtering may be performed on the summed resultants in the blocks  1132  and  1134 , respectively, and the outputs  1136  and  1138  may be interpreted as estimates of the transmitted sequences {ŝ 0 [n]} and {ŝ 1 [n]} (indicated as s 0  and s 1 ), respectively. The channel equalization is expected to correct for carrier phase and timing offsets, so that the SNR-weightilg procedure does not require phase-alignment of the two inputs that feed the summing blocks  1128  and  1130 . If the equalization does not completely compensate for carrier phase offsets, phase alignment may be necessary.  
     [0094] Additional receivers may also be used, performing the functions shown for the second receiver  1114 , and similarly summing their combined and weighted outputs into the summing blocks  1128  and  1130 , for (typically) further processing through decision feedback filters to produce estimates of the transmitted sequences.  
     [0095] When pilot symbols are used, typically each receiver independently performs channel estimation. When arbitrary data is used as a reference for channel estimation, each receiver may still independently perform channel estimation, but the sequence estimates at the output of the decision feedback filters may need to be fed back to the corresponding receiver to improve the reliability of the symbol estimates used by the channel estimation procedure.  
     [0096] Single Carrier Diverse Antenna Processing for Delay-Spread Channels  
     [0097]FIG. 12 is a block diagram of processing blocks for some embodiments of single carrier diverse antenna transmission processing. Source bits, indicated at a block  1204 , may be modulated into a sequence of samples at a processing block  1204 . Note the slight change in terminology from “symbols” to “samples,” which will facilitate comparison between FIG. 12 and subsequent figures. Modulation may be performed by any appropriate technique, such as Quadrature Amplitude Modulation (QAM), in which case the samples of the resulting sequence will each have two orthogonal components (a real component and an imaginary component). A processing block  1206  represents selecting or identifying blocks of an appropriate length (B samples, for consistency). These B-point blocks are conveyed (as indicated by a processing arrow  1208 ) to a processing block  1210 , where they are multiplexed for transmission from diverse antennas according to time domain techniques as described hereinabove in great detail. The block  1210  multiplexing results in “dual block pairs” as described with respect to FIG. 3. Referencing FIG. 3 as well as FIG. 12, B-point blocks  306  and  308  constitute a first block pair  302 , while B-point blocks  310  and  312  constitute a second block pair  304 . The B-point blocks  306  and  308  are conveyed as indicated by processing arrow  1212  to a processing block  1214 , where the last U samples of each block are copied and prepended to the block as a cyclic prefix. Cyclic prefixes are similarly prepended to the B-point blocks  310  and  312 , after they are conveyed as shown by processing arrow  1216 , in a processing block  1218 . Prepending the last U samples of each B-point block establishes (B+U)-point blocks, which are conveyed for further processing as indicated by processing arrows  1220  or  1222 . Such further processing may include serializing the samples at a block  1224  or  1226 , digitally filtering the samples at a block  1228  or  1230 , converting the samples from digital to analog at block  1232  or  1234 , amplifying the resulting radio frequency signal at block  1236  or  1238 . This processing is exemplary, and any appropriate process may be used for converting the (B+U)-sample block pairs into signals for transmission. However processed, the resulting signals will be radiated by a first antenna  1240 , or by a second antenna  1242 , respectively.  
     Transmit Diversity Applied to OFDM for Delay Spread Channels  
     [0098] Orthogonal Frequency Division Multiplexing (OFDM) communications can benefit from techniques described herein, and many of the signal relationship equations that are specified above are applicable to OFDM communication signals. FIG. 13 illustrates relationships that may be used with OFDM processing to multiplex a single stream of information into dual streams of OFDM symbol pairs for transmission by dual antennas.  
     [0099] Terminology differences between OFDM and single-carrier signals warrant consideration. The term “OFDM symbol” is generally used herein for distinction from single carrier “blocks.” However, both OFDM symbols and single carrier blocks are examples of “signal units.” Signal units may have an associated length of an integer number of “points.” Thus, for example, an N-point OFDM symbol on the one hand, and a block of N samples of a single carrier signal on the other hand, may both be referred to as N-point signal units.  
     [0100] OFDM Block Pair Multiplexing  
     [0101]FIG. 13 shows a first pair of OFDM symbols  1302  associated with a first antenna (Transmit Antenna  0 ), and a second OFDM symbol pair  1304  associated with a second antenna (Transmit Antenna  1 ). In accordance with standard OFDM processing, each OFDM symbol is derived from N sample points, and thus will be referred to as an N-point OFDM symbol. The first OFDM symbol pair  1302  includes a first N-sample OFDM symbol  1306  having the form S 0 (e j2πn/N ), n={0,1, . . . , N−1} and a second N-sample OFDM symbol  1308  having the form S 1 (e j2πn/N ), n={0,1, . . . N−1}. The second OFDM symbol pair  1304  includes a third N-sample OFDM symbol  1310  and a fourth N-sample OFDM symbol  1312 . The third OFDM symbol  1310  has the form −S 1 *(e j2πn/N ), n={0,1, . . . , N−1}, and is thus related to the second OFDM symbol  1308  as its negative complex conjugate. The fourth OFDM symbol  1312  is related as the positive complex conjugate of the first OFDM symbol  1306 , and accordingly takes the general form S 0 *(e j2πn/N ), n={0,1, . . . , N−1}.  
     [0102] OFDM Transmit Diversity Processing  
     [0103] Cyclic prefixes may improve reception accuracy for OFDM symbols, particularly in delay-spread channels. FIG. 14 illustrates OFDM transmit diversity processing that includes prepending cyclic prefixes to transmission blocks in a manner that is analogous in many regards to the single-carrier processing illustrated in FIG. 12. An important distinction, however, is the frequency domain processing of a block  1400  by which pairs of incoming N-sample OFDM symbols are multiplexed into dual N-sample OFDM symbol pairs in accordance with the forms shown in FIG. 13.  
     [0104] In FIG. 14, a first block  1404  represents appropriate steps to modulate incoming source bits into samples. Any modulation technique may be used for this step that is compatible with the other processing, with QAM being typical. At a block  1406 , sets of N resulting samples are formed into N-sample OFDM symbols. The N point symbols are conveyed, as indicated by the arrow  1408 , to the processing block  1400  for multiplexing as described above, such that pairs of N-sample OFDM symbols are multiplexed into dual OFDM symbol pairs related as shown in FIG. 13.  
     [0105] A processing arrow  1450  indicates that N-point OFDM symbols (for example, sets of N-sample OFDM symbols  1306  and  1308  in FIG. 13) are conveyed to a block  1452 , where an inverse FFT is perfonied to generate blocks of N time domain samples. Similarly, a processing arrow  1454  represents conveying N-point OFDM symbols (for example, sets of N-sample OFDM symbols  1310  and  1312  in FIG. 13) to a block  1456  for inverse FFT processing to generate N-sample blocks in the time domain. From this point forward, the steps may be very similar to those shown in FIG. 12, and thus the reference numbers are similar. As indicated by an arrow  1412  (or  1416 ), the N-point time domain samples may be conveyed to a block  1414  (or  1418 ) where the last K samples of the block are prepended to form a cyclic prefix. This creates blocks of (N+K) samples, which are conveyed as indicate by an arrow  1420  (or  1426 ) to a filter  1428  (or  1430 ), a digital to analog converter  1432  (or  1434 ), and an RF output state  1436  (or  1438 ).  
     [0106] Improved Processing for OFDM Dual Symbol Pair Transmission  
     [0107] The result achieved by processing according to FIG. 14 may also be achieved as shown in FIG. 15. In particular, an inverse FFT may be performed at a processing block  1500  on N-point OFDM symbols that are received, as indicated by arrow  1408 , after modulation of source bits in block  1404  and packing into N-sample OFDM symbols in block  1406 , in the same manner as indicated in FIG. 14. However, the processing block  1500  may perform an inverse FFT on each of the received N-point OFDM symbols, yielding N-point blocks of time domain samples that are passed on for further processing as indicated by an arrow  1508 . Multiplexing of the N-sample blocks for transmission from diverse antennas may then be done in the time domain in a processing block  1510 .  
     [0108] Such time domain multiplexing is described above in detail, and may yield dual pairs of blocks of symbols that are related as shown and described with respect to FIG. 3, or in an equivalent form. As described more fully above, such time domain multiplexing creates N-point blocks that are related not only by complex conjugation (with or without real inversion), but also by time reversal of the samples of the block, modulo N. Once these time-domain dual block pairs are generated in the processing block  1510 , they may be transferred (arrow  1412  or  1416 ) for addition of the cyclic prefix (processing block  1414  or  1418 ), and the resulting (N+K)-sample blocks may be conveyed (arrow  1420  or  1422 ) for further processing in the same manner as shown in FIG. 14.  
     [0109] Only half as many inverse FFTs need be performed according to the processing shown in FIG. 15, as compared with the processing shown in FIG. 14, if other factors are the same (such as data rate, modulation technique, number of points in OFDM symbols, and so on). That is because block  1500  performs inverse FFTs on only the “original” N-point OFDM symbols received as shown by arrow  1408 , whereas in FIG. 14 inverse FFTs are performed (at blocks  1452  and  1456 ) on the different forms ( 1450 ,  1454 ) that are derived from each of the “original” OFDM symbols (from  1408 ) by multiplexing in the block  1400 . The difficulty of multiplexing time-domain N-point blocks into dual block pairs (block  1510 ) may be comparable to the difficulty of multiplexing frequency-domain N-sample OFDM symbols into dual OFDM symbol pairs (block  1400 ), and, therefore, processing in accordance with FIG. 15 may require significantly less effort than processing in accordance with FIG. 14, other conditions being equal.  
     [0110] OFDM Transmit Diversity Receiver Processing  
     [0111]FIG. 16 illustrates exemplary receive processing for OFDM diverse antenna transmissions. Signals received at an antenna  1602  may be amplified with a RF amplifier as shown at block  1604  before the signal is digitized in an A/D converter at block  1606 . Digital filtering may then be performed in a block  1608  (filtering may also be performed elsewhere) before (N+K)-sample blocks, including cyclic prefixes, are identified at a block  1610 . The cyclic prefix may be removed from the N+K samples at a block  1614  to yield N-sample blocks. The N-sample blocks may be converted to a frequency-domain representation by means of a FFT at a block  1618  to yield N-point OFDM symbols.  
     [0112] The received N-point OFDM symbols should be identified as pairs R 0 , R 1  (typically by expected position with respect to a preamble or pilot word), and then combined and equalized in a block  1622  to extract an estimate of the transmitted OFDM symbols. Combining may be done in any appropriate manner, such as in accordance with Eqn. 2 above, to yield C 0  and C 1 . These intermediate results may be equalized, for example in accordance with Eqn. 7 (linear equalization), with E determined by ZF optimization (Eqn. 8) or MMSE (Eqn. 9). A resulting estimate of the transmitted OFDM symbols may then be demodulated, typically into blocks of parallel data that may need to be re-serialized in a block  1626 . The OFDM symbol estimate may then be decoded in a block  1628  to yield a reconstruction of the original source bits that informed the OFDM transmission.  
     [0113] Channel Estimation with OFDM  
     [0114] Combining and equalization for received pairs of N-point OFDM symbols depends upon estimating channel responses for the two channels. For channel estimation purposes, it is often useful to transmit OFDM symbols that are expected by the receiver, thus eliminating uncertainty due to estimation of the signal. Such expected symbols may be called “pilot symbols” (“PSs”) in regard to OFDM, which is an example of a “pilot signal unit.” The known symbols may be sent, for example, as part of pilot words that are interspersed within payload transmissions in the manner shown in FIG. 7, or as part of a burst preamble, in the general manner shown in FIG. 6. Given known symbols S 0 , S 1  (and the related symbols derived therefrom), channel estimates may be determined using MMSE techniques in accordance with Eqn. 16, or by zero forcing techniques as indicated in Eqn. 17. Channel estimates may be developed using special pilot words, as described below  
     [0115] Preambles and Pilot Words with OFDM  
     [0116]FIG. 17 illustrates a burst frame structure  1700  for an OFDM communication. Transmitted OFDM symbols are simply represented as S x . A ramp-up period  1702  may be used with any signal, related to the preamble or not, to bring the transmit power up to the desired level. The ramp-up may be omitted, or may partially overlap the burst preamble, though this could impair accuracy if the cyclic prefix is not sufficiently long compared to the range (or spread) of delays experienced by the channel. A burst preamble may be transmitted next, followed by a payload  1706 . At the end of the burst, a ramp down period may be provided. The payload  1706  may optionally be interspersed with pilot words, generally in the manner shown in FIG. 7. Details of a range of embodiments for the burst preamble  1704  are shown in FIG. 17 and described below, and pilot words within a payload may also utilize the same range of structures that is described for preambles. The broken lines extending from the burst preamble  1704  identify structural details that may be included within a burst preamble (or within a pilot word).  
     [0117] Repetitive Pilot Symbols  
     [0118] Within the details of the burst preamble, a first pilot symbol (PS)  1710  is identified as an OFDM symbol S 0 . The first PS  1710  may be followed by one or more additional PSs, represented as a PS  1712  to a PS  1714 , for a total of J such PSs. A cyclic prefix  1716  will typically be useful, particularly in significantly delay-spread channels. It will generally constitute the last K samples of the L samples in the first PS  1710 . There is no general requirement that the first PS  1710  be the same symbol as any other PS in the preamble. However, repeated symbols obviate a need for cyclic prefixes between such repeated symbols, resulting in some increase in efficiency. Accordingly, each of the PSs  1710  to  1714  are shown, in FIG. 17, as equal to S 0 .  
     [0119] In order to utilize the dual-symbol pair antenna diversity multiplexing described above, a second set of one or more PSs  1720  to  1724  (for a total of P PSs, where typically P=J) may follow the J PSs  17   10  to  1714 . These are identified as each being S 1 , which may be the same or different than S 0 . As before, a cyclic prefix  1726  may be used, and only one such cyclic prefix is needed for all J PS if the PSs  1720  to  1726  are identical. The structure illustrated by the first cyclic prefix  1716  to the optional last PS  1724  represents the transmission from a first antenna.  
     [0120] In accordance with dual symbol-pair diverse transmit antenna multiplexing techniques, a second antenna may transmit PSs (pilot symbols) that are related to those sent on the first antenna. These are represented in FIG. 17 as PSs  1730  to  1744 , with vertical alignment of the various PSs indicating temporal transmission time alignment. Thus, PSs  1730  and optional additional PSs  1732  and  1734  (generally a total of J PSs) will be transmitted from the second antenna approximately concurrently with the J PSs  1710  to  1714  that are transmitted from the first antenna. There may be a first cyclic prefix based upon the last K samples of the PS  1730 . PSs  1730  to  1734  are shown as being identical to each other, and more cyclic prefixes may be needed if this is not the case. A further set of P PSs may follow the PSs  1730  to  1734 , including a first PS  1740  and optional additional PSs  1742  to  1744 . A cyclic prefix prepended to the PS  1740  may be derived from the last K samples of the PS  1740 .  
     [0121] Varying Pilot Symbol Size and Repetition Number  
     [0122] PSs need not reflect the same number of samples (or points) as symbols that are used for other purposes, such as payload transmission. For example, an OFDM transmitter may typically employ 256-point symbols for payload transmission, and yet employ 64-point PSs (pilot symbols). Note that if the PS  1710  is approximately the length desired for the cyclic prefix  1716 , then the cyclic prefixes ( 1716 ,  1726 ,  1736 ,  1746 ) may be made identical to their respective PSs  1710 ,  1720 ,  1730 ,  1740 —S 0 , S 1 , −S 1 * and S 0 *, respectively.  
     [0123] Depending upon the current channel conditions and signal to noise ratio, burst preambles may utilize varying numbers J and/or P of PSs. Thus, if a somewhat better channel estimate is needed, J may be changed from 4 to 5, a 25% step, which requires a much smaller additional time (and thus effective communication bandwidth) “penalty” than would be incurred if PSs were limited to the payload length (e.g., 256), and J had to be increased from 1 to 2. Moreover, employing repetitive PSs provides up to J*P channel estimates. This product may be increased without incurring a transmission time penalty by decreasing the size of PSs.  
     [0124] As a further benefit, if each pilot word is shorter, pilot words may be interspersed more frequently within payloads without incurring a time penalty. More frequent pilot words may be particularly useful in conjunction with rapidly varying channels, such as may be caused by a fast-moving receiver. Additionally or alternatively, the length of pilot words within a payload may be adjusted by finer incremenits if the pilot words are composed of shorter PSs. Changes in the pilot words (and preambles), such as PS length, repetition number J and/or P, and time between pilot words, may be varied dynamically depending upon conditions of the channel. Thus, using PSs with different, typically shorter, lengths, and in repetition groups having varying numbers for J and P, may provide useful flexibility for preambles and pilot words in some systems.  
     [0125] Processing shorter PSs may require configuring the FFT and IFFT processors to handle such shorter symbols. The frequency domain channel response estimate representations will typically be wanted with the same number of points as the payload symbols. If the PSs have less points than payload symbols, the PS length can be extended by interpolation, using an interpolation filter such as sin(x)/x, to match the payload symbol length, and the extended “PSs” can then be processed using payload symbol-length processing. It is also possible to perform the interpolation later, after some portion of the processing has been performed with reduced-length PSs. The interpolation may even be performed after reduced frequency-sample channel estimates have been derived from reduced-point PSs.  
     [0126] Receive Processing of OFDM PS Pairs  
     [0127] At the receiver, dual PS pairs can be identified and combined together in accordance with the transmit diversity demultiplexing techniques described above. The dual PS pairs were presumably transmitted as two forms of two PS symbols, as indicated in FIG. 13. For example, the PS  1730  is related as the negative complex conjugate of the PS  1720 , while the PS  1740  is related as the (positive) complex conjugate of the PS  1710 . Furthermore, the PS  1710  is transmitted from the first antenna approximately concurrently as the PS  1730  from the second antenna, and PSs  1720  and  1740  are similarly concurrent. These four PSs thus form a dual PS pair for transmission, which appears at a receive antenna as a single pair of PSs. The received pairs of multiplexed (or merged) PSs will be referred to as RP 0  (from merged concurrent PSs  1710  and  1730 ) and RP 1  (from merged concurrent PSs  1720  and  1742 ). RP 0  and RP 1  may be combined (or demultiplexed) to extract estimates of the original symbols PS 0  and PS 1 , or may be used for channel estimation.  
     [0128] Noise effects on any estimation processes may be reduced by averaging in several ways. Because all significant noise is additive, the simple expedient of averaging together each set of J (or P) PSs, then processing the resulting averages as a dual PS pair, will reduce noise effects on channel estimates approximately equivalently to more complex techniques that may be employed. Assuming that the transmission was as shown in FIG. 17, the receiver may receive J versions of RP 0 , and P versions of RP 1 . The J versions of RP 0  may be averaged together to form A J RP 0 , the P versions of RP 1  may be averaged together to form A P RP 1 . Two such resultant averages (generally, A N RP X ) may be used to estimate the channel responses H 0  and H 1 , according to Equations 16 or 17, by substituting A N RP X  for R X , and the known values PS X  for S X .  
     [0129] Alternatively, any of the J versions of RP 0  may be substituted for R 0 , and any of the P versions of RP 1  may be substituted for R 1  in Equations 16 or 17 (along with PS X  for S X ) to obtain up to J*P different estimates for H 0  and H 1 . In order to realize most of the noise averaging effects by this technique, each of the J versions of RP 0 , and each of the P versions of RP 1 , should be used in at least one estimate of H 0  and H 1 . The different estimates of H 0  and H 1  thus derived may then be averaged together. Thus, for example, if P=J=2, a first pair of estimates H 0  and H 1  may be derived from combination of the first RP 0  with the first RP 1 , a second pair of estimates H 0  and H 1  may be derived from combination of the second RP 0  with the second RP 1 , and these two pair of estimates may be averaged to form an improved estimate of H 0  and H 1 . Up to P*J different estimates of channel may be derived, but for most practical systems the extra estimates add little information to improve the ultimate averaged channel estimates.  
     [0130] Referring again to FIG. 17, the first transmitted PS pair ( 1710  and  1730 ) may be temporally separated from the second transmitted PS pair ( 1730  and  1740 ). As long as the PSs are repetitive, as shown in FIG. 17, further dual PS pairs may be identified as: the pair  1710 / 1730  with the pair  1722 / 1742 , or with the pair  1724 / 1744 ; and the pair  1712 / 1732  with the pair  1720 / 1740 , or with the pair  1722 / 1742 , or with the pair  1724 / 1744 , and so on. Each of the identified dual PS pair combinations may be processed to obtain a different estimate for the channel responses, H 0  and H 1 . (Note the shorthand representation of simple uppercase letters for frequency domain values.) These various different estimates (up to J*P, preferably at least [J+P]/2 using each RP 0  and each RP 1  once) may then be averaged together to obtain an improved estimate.  
     [0131] The embodiments of transmitter symbol multiplexing and receiver equalization and symbol recovery that are described above are intended to assist with understanding of the invention that is claimed in each claim that follows this description. The description illustrates and explains exemplary implementation of aspects of such claimed invention, but should not be construed as limiting the scope of such invention, which instead is precisely defined by the express language of a claim.  
     [0132] While the above description has pointed out novel features of the invention as applied to various embodiments, the skilled person will understand that various omissions, substitutions, and changes in the form and details of the methods and systems illustrated may be made without departing from the scope of the invention. For example, extra translations of symbol blocks may create alternative multiplexing forms that are, however, entirely equivalent to those described above. The skilled person will be able to adapt the details described herein to communications systems having a wide range of modulation techniques, transmitter and receiver architectures, and generally any number of different formats. In particular, each functional combination of multiplexing, combining, equalization and framing techniques and/or system elements described herein, with other wireless communication techniques and/or system elements that are presently known or later developed, is contemplated as an alternative or equivalent embodiment of an aspect of the invention.  
     [0133] The various techniques set forth above may be performed within, or by, any appropriate signal processing facilities. Different facilities may divide tasks up in different ways than those illustrated. For example, transmitter signal processing may be performed in any number of processing modules or subsections, whether or not they track the logical structure illustrated, as long as the same or equivalent functions are ultimately performed somewhere. Receiver signal processing may similarly be performed in different orders and combinations, providing that equivalent functions are performed somewhere. Any appropriate techniques for multiplexing at the transmitter, and for combining (demultiplexing) at the receiver, may be used in conjunction with the framing, preamble and pilot word forms described above.  
     [0134] Each practical and novel combination of the elements described hereinabove, and each practical combination of equivalents to such elements, is contemplated as an embodiment of the invention. Because many more element combinations are contemplated as embodiments of the invention than can reasonably be explicitly enumerated herein, the scope of the invention is properly defined by the appended claims rather than by the foregoing description. All variations coming within the meaning and range of equivalency of the various claim elements are embraced within the scope of the corresponding claim. Specific combinations of elements are set forth as claims, appended below, to define the invention in various aspects. It should be understood that due to the imperfection of humans and language, a particular claim may not perfectly define such invention. For example, no claim is intended to encompass the prior art, and each claim should be reasonably interpreted, if possible, to avoid such unintended coverage. Conversely, each claim is intended to encompass any system or method that differs only insubstantially from the literal language of such claim, so long as such system or method is not, in fact, an embodiment of the prior art. To this end, each described element in each claim should be construed as broadly as possible, and moreover should be understood to encompass any equivalent to such element insofar as possible without also encompassing the prior art.