Home Networking Basis: Transmission Environments and Wired/Wireless Protocols

2.3.1 Noise Power and Power Spectrum Density

The severity of a particular noise can be measured from its power level or its power density level. The magnitude of a noise can be as high as a few tens of microvolts. The noise power is usually expressed in decibels (dbm), which is defined as

Equation 2.48

where v is the average voltage of the noise, R = 100 is the receiver input impedance, and P_m = 0.001 is the reference of 1 milliwatt (mW). The noise power spectrum density (PSD) is usually expressed in decibels per hertz (dBm/Hz), which is defined as

Equation 2.49

where B is the bandwidth of noise of particular interest measured in Hertz. For an example, the background noise power density is about 140 dBm/Hz while receiver front end electronics thermal noise power density could be made to be lower than 150 dBm/Hz.

2.3.2 Crosstalk Noise

There are usually at least two pairs within a twisted pair cable or an in-house telephone wiring. Because of capacitive and inductive in-balance coupling, there is crosstalk between each pair even though pairs are well insulated at DC. For broadband systems, where the signal bandwidth is well beyond the voice frequency, the crosstalk could become a limiting factor to the achievable transmission throughput. Crosstalk noise can be further divided into Near End Crosstalk (NEXT) and Far End Crosstalk (FEXT) noises. The severity of crosstalk could also be related to the system installation scale (i.e., the total number of pairs used in the same twisted pair cable). Crosstalk coupling loss models have been developed for NEXT and FEXT by considering the different numbers of disturbers.

NEXT is defined as the crosstalk effect between a pair of transceivers that transmit and receive signals at the same end of a twisted pair cable or an in-house wiring that shares the same frequency band. In other words, the NEXT noise at a particular transceiver is caused by signals transmitted by other transceivers at the same end of the twisted cable. Specifically, as indicated by Figure 2.15, a Near End Transceiver i would experience NEXT noise from the Near End Transceiver j if they share the same frequency spectrum simultaneously. Here, twisted pair j is the disturbing pair carrying disturbing signal and twisted pair i is the disturbed pair.

FEXT is defined as the crosstalk effect between a pair of transceivers located at opposite ends of two separate pairs within the same twisted pair cable or in-house wiring. In other words, the FEXT noise at a particular transceiver is caused by signals transmitted by transceivers of other pairs at the opposite end of the twisted cable. Specifically, as indicated by Figure 2.16, a Near End Transceiver i would experience FEXT noise from the Far End Transceiver j if they share the same frequency spectrum within the same twisted pair cable.

NEXT is usually stronger than FEXT. Exceptional examples, where FEXT becomes more effective, are Frequency Division Multiplexing (FDM) and Time Division Multiplexing (TDM) between opposite transmission directions. In an FDM transmission system, all transmissions on different pairs from point A to point B use a frequency band of F₁, and all transmissions from point B to point A use a frequency band of F₂ where F₁ and F₂ are non-overlapping. In a TDM transmission system, all transmissions on different pairs from point A to point B use a time slot of T₁, and all transmissions from point B to point A use a time slot of T₂, where T₁ and T₂ are alternating in sequence.

2.3.3 NEXT and FEXT Models

The simplified 49 disturber NEXT model developed for DSL simulation studies has 57 dB of loss at 80 kHz and a linear (log-log scale) slope of 15 dB/decade. Specifically, the NEXT model can be expressed as

Equation 2.50

where f is in hertz, k_NEXT = 8.82 x 10^-14, and NEXT₄₉ is a ratio that can be expressed in decibels by taking base 10 log of NEXT₄₉ and then multipling 10. This simplified NEXT model can also be generalized for N disturbers as

Equation 2.51

Notice that the loss difference between 1 disturber and 49 disturbers is about 10 dB.

The simplified 49-disturber FEXT model, which was also developed for DSL studies, is proportional to the square of frequency and the insertion loss of the twisted pair cable. The model can be expressed as

Equation 2.52

where k_FEXT = 8 x 10 ²⁰ is empirically derived based on the FEXT measurements, d is the twisted cable length in feet, f is frequency in hertz, and |H(f)|² is the insertion loss of the twisted pair cable.

Because NEXT distribution is similar to FEXT distribution, the same power sum scale for NEXT can also be applied to FEXT, in which case we have

Equation 2.53

NEXT models are more applicable for many Local Area Network (LAN) and home network transmission simulation studies. Besides the simplified NEXT model developed for DSL simulation studies, we can also derive NEXT models for Category 3, Category 4, and Category 5 twisted pair cables as well as other in-house telephone wirings based on some valid measurements. It was found that the one disturber Category 3 twisted pair of 50-ft NEXT model is about the same as that of 49 disturbers developed for DSL simulation studies. NEXT models for Category 4 and 5 twisted cables have more losses. On the other hand, some in-house wirings show much poorer NEXT characteristics. Estimated values of NEXT₄₉ of these twisted pair cables and a relatively poor in-house wiring are listed in Table 2.4 [5].

Figure 2.17 shows NEXT models based on these estimated parameters. The poor NEXT characteristics of some in-house wiring are a result of the fact that each pair is not individually twisted or that there is no twist at all.