A Temporary Model for EFM/MIMO Cable Characterization

The multiple-input multiple-output (MIMO) characterization of a cable of twisted pairs merits attention and measurement for studies in ethernet in first mile (EFM) efforts. Quads or other groups of twisted pair within a cable may be combined for better transmission/duplexing: The interaction between lines within a subgroup or the entire cable can be exploited to improve performance and reduce transceiver complexity, motivating a model. This note suggests a temporary model for MIMO FEXT that can be used to evaluate/test EFM. Figure 1 – Matrix Channel The MIMO FEXT Channel: Figure 1 illustrates the matrix or MIMO FEXT twisted-pair channel. Each of the M inputs to this matrix channel may produce a component of the signal at each of the K outputs. Usually, M=K. For instance, a quad (4 twisted pairs tightly packed together) has M=4 inputs and M=4 outputs and a total of K M ⋅ = 16 transfer functions of interest. These K M ⋅ transfer functions can be summarized in a M K × matrix H . The 1 × K vector of channel outputs Y is then related to the 1 × M vector of channel inputs X by HX Y = . (1) Ultimately, the designer would desire the exact H for each binder of wires: Any FEXT information is contained within this matrix. Approximate models are of interest in evaluating the various EFM opportunities in terms of range, rates, and service applications/market. In recognition that such transfer matrices either are not well known, this note suggests an H model for temporary use in EFM studies in the near-term. NEXT matrix models are of less MIMO interest since NEXT is either avoided by duplexing choice or by echo/NEXT cancellation between lines. The th km element of [ ] M m K k km f H ,..., 1 1 ) ( = = = H is the transfer function from input m to output k. When m=k, then ( ) f H is simply the transfer function of the th k line, ( ) f Hkk , and can be determined from basic transmission line theory, given the length and RLCG parameters of the line [1]. Reference [1] also models FEXT power transfer of the off-diagonal terms as proportional to the line transfer function ( ) f Hkk , the square of frequency 2 f , and the length of the line (in meters), d , which is explained on page 90 of [2]. This corresponds to a crosstalk-insertion loss transfer path of ( ) ( ) ( ) d jf f H h f H kk fext km ⋅ ⋅ ⋅ = (2) with a worst-case value of ( ) 11 21 10 8 . 4 / 3048 . 10 74 . 7 − − × = ⋅ × = ft m h fext for two adjacent category 3 telco-plant crosstalking lines. Equation (2) is for one crosstalking line – thus an extra multiplicative factor of